(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 431480, 9461] NotebookOptionsPosition[ 412511, 8910] NotebookOutlinePosition[ 415292, 8994] CellTagsIndexPosition[ 415212, 8989] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["\<\ Mathematical Modelling and Scientific Computing in the Biosciences\ \>", "Title", CellChangeTimes->{{3.413552660922897*^9, 3.413552675466538*^9}}], Cell[TextData[{ StyleBox["\n", FontVariations->{"Underline"->True}], "Lecture 2: 11 March 2007" }], "Subtitle", CellChangeTimes->{ 3.413608468684486*^9, {3.414157000366563*^9, 3.414157012228213*^9}}], Cell[CellGroupData[{ Cell["Computer Sessions: HF 107", "Section", CellChangeTimes->{{3.41422576999704*^9, 3.414225782987179*^9}, { 3.414225927071576*^9, 3.414225936159344*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Session 1", FontVariations->{"Underline"->True}], ": Monday 11-12" }], "Subsection", CellChangeTimes->{{3.414225794369997*^9, 3.414225811604581*^9}}], Cell["\<\ T. Unterthiner, M. Wischenbart, S. Brunner, M. Kolmbauer, A. Salfinger, W. \ Lichtberger ,A. Pomarolli\ \>", "Item", CellChangeTimes->{{3.414225837983144*^9, 3.414225862701574*^9}, { 3.414228202823499*^9, 3.414228216550741*^9}, {3.414228360125737*^9, 3.414228366914196*^9}, {3.414228449482244*^9, 3.414228463350309*^9}, { 3.414232843071497*^9, 3.41423285619409*^9}, {3.414232886839202*^9, 3.414232887140567*^9}, 3.414234900132188*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Session 2", FontVariations->{"Underline"->True}], ": Monday 12-1" }], "Subsection", CellChangeTimes->{{3.414225794369997*^9, 3.414225811604581*^9}, { 3.414225870619541*^9, 3.414225874620138*^9}}], Cell["A. Kothmeier, P. Leimlehner, N. Stein, A. Michelic, C. Frech", "Item", CellChangeTimes->{{3.414225837983144*^9, 3.414225908251138*^9}}], Cell[TextData[{ "First session: ", StyleBox["31 March", FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.414225954704757*^9, 3.414225985528813*^9}, { 3.41422824622184*^9, 3.414228246874243*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Overview: ", "Section", CellChangeTimes->{{3.413552837957709*^9, 3.413552850020701*^9}, { 3.414157020103515*^9, 3.414157027480763*^9}, {3.414225980010449*^9, 3.414225981575778*^9}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematical Biology I: an Introduction", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0.6, 0.4, 0.2]], ", J. D. Murray, Springer 2001. " }], "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.413553118021138*^9, 3.413553172072806*^9}, 3.413600548023816*^9, 3.413609408692294*^9}], Cell[" singular perturbation", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.413553417542369*^9, 3.413553420648648*^9}, { 3.413553574478385*^9, 3.413553588686996*^9}, {3.413553693389803*^9, 3.413553702007969*^9}, 3.413600548024077*^9, 3.41422211130777*^9}], Cell[" derivation of Michaelis-Menten rate rule", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.413553417542369*^9, 3.413553420648648*^9}, { 3.413553574478385*^9, 3.413553588686996*^9}, {3.413553693389803*^9, 3.413553702007969*^9}, 3.413600548024077*^9, {3.41422211130777*^9, 3.414222136041621*^9}}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{ "SetDirectory", "[", "\"\<~/Teaching/MathModelBioSciences_Summer08/Lecture2/\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{"Plot", ",", RowBox[{"PlotStyle", "\[Rule]", " ", "Thick"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"400", ",", "300"}], "}"}]}]}], " ", "]"}], ";"}]}], "Input", CellOpen->False, InitializationCell->True, CellChangeTimes->{{3.4136094377778*^9, 3.413609457025486*^9}, { 3.414157051171629*^9, 3.414157121648534*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Enzyme Kinetics: ODE System", "Section", CellChangeTimes->{{3.414196962235391*^9, 3.414196977538243*^9}}], Cell[CellGroupData[{ Cell["Interpreting Reactions and Non-Dimensionalization", "Subsection", CellChangeTimes->{{3.414222270866354*^9, 3.414222289171237*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"<<", "xlr8r.m"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"EnzymeODE", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"interpret", "[", RowBox[{"{", RowBox[{"{", RowBox[{ OverscriptBox[ RowBox[{"s", "\[RightArrowLeftArrow]", "p"}], "e"], ",", RowBox[{"k", "[", "1", "]"}], ",", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], ",", RowBox[{"k", "[", "2", "]"}], ",", "0"}], "}"}], "}"}], "]"}], "//", "First"}], ")"}], "/.", RowBox[{ RowBox[{"Bind", "[", RowBox[{"e", ",", "s"}], "]"}], "\[Rule]", " ", "c"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"eTot", "[", "t", "]"}], "=", RowBox[{ RowBox[{"e", "[", "t", "]"}], "+", RowBox[{"c", "[", "t", "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["eTotReplaceRule", FontColor->RGBColor[1, 0, 0]], "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"eTot", "[", "t", "]"}], "==", "e0"}], ",", " ", RowBox[{"e", "[", "t", "]"}]}], "]"}], "//", "Flatten"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["SelectedVar", FontColor->RGBColor[1, 0, 1]], "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"c", "'"}], "[", "t", "]"}], ",", " ", RowBox[{ RowBox[{"s", "'"}], "[", "t", "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TwoDEnzymeODE", "=", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Pick", "[", RowBox[{"EnzymeODE", ",", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ StyleBox["SelectedVar", FontColor->RGBColor[1, 0, 1]], ",", " ", "#"}], "]"}], "&"}], " ", ",", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], "&"}], ",", " ", "EnzymeODE"}], "]"}]}], "]"}]}], "]"}], "\\\[IndentingNewLine]"}], "//.", StyleBox["eTotReplaceRule", FontColor->RGBColor[1, 0, 0]]}], "/.", RowBox[{"{", RowBox[{"Rule", "\[Rule]", " ", "Equal"}], "}"}]}], " ", ")"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"DepVarNonDimensionalRule", "=", RowBox[{"{", " ", RowBox[{ RowBox[{ RowBox[{"u", "[", "t", "]"}], "==", FractionBox[ RowBox[{"s", "[", "t", "]"}], "s0"]}], ",", " ", RowBox[{ RowBox[{"v", "[", "t", "]"}], "==", FractionBox[ RowBox[{"c", "[", "t", "]"}], "e0"]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ReplaceDepVar", "=", RowBox[{ RowBox[{"Solve", "[", RowBox[{"DepVarNonDimensionalRule", ",", " ", RowBox[{"{", RowBox[{ RowBox[{"s", "[", "t", "]"}], ",", " ", RowBox[{"c", "[", "t", "]"}]}], "}"}]}], "]"}], "//", "Flatten"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ReplaceDepVar", "=", RowBox[{ RowBox[{"Join", "[", RowBox[{"%", ",", " ", RowBox[{"(", RowBox[{"ReplaceDepVar", "/.", RowBox[{ RowBox[{"f_", "[", "t_", "]"}], "\[Rule]", " ", RowBox[{ RowBox[{"f", "'"}], "[", "t", "]"}]}]}], " ", ")"}]}], "]"}], "//", "Flatten"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NewTwoDEnzymeODE", "=", RowBox[{ RowBox[{"TwoDEnzymeODE", "/.", "%"}], "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"f_", "'"}], "[", "t", "]"}], "\[Rule]", " ", RowBox[{ RowBox[{ RowBox[{"f", "'"}], "[", "\[Eta]", "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"k", "[", "1", "]"}], " ", "e0"}], ")"}]}]}], ",", RowBox[{"t", "\[Rule]", "\[Eta]"}]}], " ", "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "TableForm"}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.414126482541607*^9, 3.414126695668775*^9}, { 3.414126785942751*^9, 3.414126798453333*^9}, 3.414132612675897*^9, { 3.414156625905953*^9, 3.414156626437158*^9}, {3.414156677221368*^9, 3.414156685847692*^9}, {3.414156836410715*^9, 3.414156853343735*^9}, { 3.41415688731652*^9, 3.414156897756517*^9}, {3.414156960389798*^9, 3.414156985183196*^9}, {3.414170365713225*^9, 3.414170387748838*^9}, { 3.414170443052018*^9, 3.414170464607399*^9}, {3.414170753252542*^9, 3.414170753409731*^9}, {3.414170812985602*^9, 3.414170836305018*^9}, { 3.414170917775846*^9, 3.414170952371218*^9}, {3.414172839661582*^9, 3.414172872340422*^9}, {3.414173013452875*^9, 3.41417303336515*^9}, 3.414173118526437*^9, {3.414175335863502*^9, 3.414175358972508*^9}, { 3.41417539052377*^9, 3.414175394283964*^9}, {3.4141754253345*^9, 3.414175618533183*^9}, {3.414222177585112*^9, 3.414222180959002*^9}}], Cell[BoxData["\<\"xlr8r 0.63 loaded 11-March-2008 13:49:50.495418 using \ Mathematica 6.0 for Linux x86 (32-bit) (April 20, 2007)\"\>"], "Print", CellChangeTimes->{{3.414228589847217*^9, 3.414228590500091*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"e0", " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"(", RowBox[{"e0", "-", RowBox[{"e0", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], ")"}]}]}]}]}, { RowBox[{ RowBox[{ SuperscriptBox["e0", "2"], " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{ RowBox[{"-", "e0"}], " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"e0", " ", RowBox[{"k", "[", "2", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"(", RowBox[{"e0", "-", RowBox[{"e0", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], ")"}]}]}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.414228590073039*^9, 3.414228590547373*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Further Manipulations to Desired Form", "Subsection", CellChangeTimes->{{3.414197013002778*^9, 3.414197025203294*^9}, { 3.414222310755191*^9, 3.414222318499215*^9}}], Cell[CellGroupData[{ Cell["MoveFactor Function", "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414222390123858*^9, 3.414222396178524*^9}, { 3.414223955568349*^9, 3.414223959802621*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"MoveFactor", "[", RowBox[{ RowBox[{"eqnList_", "?", "ListQ"}], ",", RowBox[{"whichSide_", "?", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"#", "==", "\"\\""}], "||", RowBox[{"#", "==", "\"\\""}]}], "&"}], ")"}]}]}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"togetheredEqnList", "=", RowBox[{"Together", "[", "eqnList", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"whichSide", "\[Equal]", "\"\\""}], ",", RowBox[{ RowBox[{"pickWhich", "[", "x_", "]"}], ":=", RowBox[{"First", "[", "x", "]"}]}], ",", RowBox[{ RowBox[{"pickWhich", "[", "x_", "]"}], ":=", " ", RowBox[{"Last", "[", "x", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"transFormTimes", "[", "f_", "]"}], ":=", RowBox[{"If", "[", RowBox[{ RowBox[{"f", "===", " ", "Times"}], ",", "myTimes", ",", "myOne"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"myOne", "[", "factors__", "]"}], ":=", " ", "1"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"myTimes", "[", "factors__", "]"}], ":=", " ", RowBox[{"Select", "[", RowBox[{ RowBox[{"List", "[", "factors", "]"}], ",", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"AtomQ", "[", "#", "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#", ",", " ", RowBox[{"Power", "[", RowBox[{"_Symbol", ",", "_Integer"}], "]"}]}], "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#", ",", " ", RowBox[{"Power", "[", RowBox[{ RowBox[{"_Symbol", "[", "_Integer", "]"}], ",", "_Integer"}], "]"}]}], "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#", ",", RowBox[{"_Symbol", "[", "_Integer", "]"}]}], "]"}]}], ")"}], "&"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Prefactors", "=", RowBox[{ RowBox[{ RowBox[{"Times", "@@", "#"}], "&"}], "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"MapAt", "[", RowBox[{"transFormTimes", ",", RowBox[{"pickWhich", "[", "#", "]"}], ",", "0"}], "]"}], "&"}], "/@", "togetheredEqnList"}], ")"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Head", "[", "#1", "]"}], "[", RowBox[{ RowBox[{ RowBox[{"First", "[", "#1", "]"}], "/", RowBox[{"Prefactors", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}]}], ",", " ", RowBox[{ RowBox[{"Last", "[", "#1", "]"}], "/", RowBox[{"Prefactors", "[", RowBox[{"[", RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}]}]}], "]"}], "&"}], ",", " ", "togetheredEqnList"}], "]"}], "]"}], ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, InitializationCell->True, CellChangeTimes->{{3.414126884349991*^9, 3.414126946064531*^9}, { 3.414126981662942*^9, 3.414127028265874*^9}, 3.414127075547696*^9, { 3.414127107163731*^9, 3.414127184404916*^9}, {3.414127218260106*^9, 3.41412728077075*^9}, {3.414129347380524*^9, 3.414129419810023*^9}, { 3.414129453411503*^9, 3.414129467295473*^9}, {3.414129517510335*^9, 3.414129555431791*^9}, {3.414129591755608*^9, 3.414129645047962*^9}, { 3.414129947401458*^9, 3.414130155301381*^9}, {3.414130211353771*^9, 3.41413035480401*^9}, {3.414130394180351*^9, 3.414130438830367*^9}, { 3.414130537327494*^9, 3.414130548094061*^9}, {3.414130771470283*^9, 3.414130779257044*^9}, {3.414130818648242*^9, 3.414130860625131*^9}, { 3.414130918783696*^9, 3.414130946512864*^9}, {3.414131365940643*^9, 3.414131382454572*^9}, {3.41413142754429*^9, 3.414131465456416*^9}, { 3.414131503713928*^9, 3.414131506435002*^9}, {3.414131564160377*^9, 3.414131565764611*^9}, {3.41413169718224*^9, 3.414131864476991*^9}, { 3.414131954641577*^9, 3.414131985953066*^9}, {3.41413201932572*^9, 3.414132033256126*^9}, {3.414132072672577*^9, 3.414132535130122*^9}, { 3.414132702064557*^9, 3.414132716072088*^9}, {3.414134064036571*^9, 3.414134120075825*^9}, {3.414134182879203*^9, 3.414134238697132*^9}, { 3.41414591273409*^9, 3.41414593673142*^9}, {3.41414750978124*^9, 3.414147570881529*^9}, {3.414147611931108*^9, 3.414147646665971*^9}, { 3.414147691885518*^9, 3.414147693159505*^9}, {3.41414843565379*^9, 3.414148461754978*^9}, {3.414149720726067*^9, 3.414149722949792*^9}, { 3.414150592030231*^9, 3.414150592171882*^9}, {3.414150627832192*^9, 3.414150633130085*^9}, {3.414173124670848*^9, 3.414173191958022*^9}, { 3.414173234160254*^9, 3.414173240254069*^9}, {3.414173312099451*^9, 3.414173314651194*^9}, {3.414173490902292*^9, 3.414173492593057*^9}, { 3.414173546374049*^9, 3.414173629189647*^9}, {3.414173737754159*^9, 3.414173739997166*^9}, {3.414173792636656*^9, 3.414173794459696*^9}, { 3.414173872900737*^9, 3.414173874124157*^9}, {3.414173904328996*^9, 3.41417390578191*^9}, {3.414173951489481*^9, 3.414173957842625*^9}, { 3.414174246816289*^9, 3.414174256498079*^9}, {3.414174289845635*^9, 3.414174291858324*^9}, {3.414174375814396*^9, 3.414174461912306*^9}, { 3.41417451092461*^9, 3.414174612927021*^9}, {3.414175241252139*^9, 3.414175252212791*^9}, {3.414175282799182*^9, 3.414175304881536*^9}, { 3.414175748381419*^9, 3.414175756201509*^9}, 3.414222396178714*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Applying Manipulations", "Subsubsection", CellChangeTimes->{{3.414223973430697*^9, 3.414223980065096*^9}}], Cell[CellGroupData[{ Cell[BoxData["NewTwoDEnzymeODE"], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"e0", " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"(", RowBox[{"e0", "-", RowBox[{"e0", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], ")"}]}]}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["e0", "2"], " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{ RowBox[{"-", "e0"}], " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"e0", " ", RowBox[{"k", "[", "2", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"(", RowBox[{"e0", "-", RowBox[{"e0", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], ")"}]}]}]}]}], "}"}]], "Output", CellChangeTimes->{3.414230015615098*^9}] }, Open ]], Cell[BoxData[ RowBox[{"MoveFactor", "[", RowBox[{"NewTwoDEnzymeODE", ",", "\"\\""}], "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414222323737737*^9, 3.414222330377181*^9}, { 3.414222406124851*^9, 3.414222430606667*^9}, 3.414222621437177*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "e0"}], " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"e0", " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}]}]]}], ",", RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", FractionBox[ RowBox[{ RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}]}], "-", RowBox[{"e0", " ", RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"e0", " ", RowBox[{"k", "[", "2", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"e0", " ", "s0", " ", RowBox[{"k", "[", "1", "]"}], " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], RowBox[{ SuperscriptBox["e0", "2"], " ", RowBox[{"k", "[", "1", "]"}]}]]}]}], "}"}]], "Output", CellChangeTimes->{3.414230114141119*^9}], Cell[BoxData[ RowBox[{"%", "//", "Expand"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414222438050023*^9, 3.414222441361017*^9}, 3.414222621437476*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", FractionBox[ RowBox[{ RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}]}]], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ FractionBox[ RowBox[{"s0", " ", RowBox[{"u", "[", "\[Eta]", "]"}]}], "e0"], "-", FractionBox[ RowBox[{ RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], RowBox[{"e0", " ", RowBox[{"k", "[", "1", "]"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], RowBox[{"e0", " ", RowBox[{"k", "[", "1", "]"}]}]], "-", FractionBox[ RowBox[{"s0", " ", RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "e0"]}]}]}], "}"}]], "Output", CellChangeTimes->{3.414230137354959*^9}], Cell[BoxData[ RowBox[{"%", "//.", RowBox[{"{", " ", RowBox[{ RowBox[{"e0", "\[Rule]", " ", RowBox[{"\[Epsilon]", " ", "s0"}]}], ",", " ", RowBox[{ FractionBox[ RowBox[{"k", "[", "2", "]"}], RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}]}]], "\[Rule]", " ", "\[Lambda]"}], ",", " ", RowBox[{ FractionBox[ RowBox[{ RowBox[{"k", "[", RowBox[{"-", "1"}], "]"}], " "}], RowBox[{"s0", " ", RowBox[{"k", "[", "1", "]"}], " "}]], "\[Rule]", " ", RowBox[{"(", RowBox[{"K", "-", "\[Lambda]"}], ")"}]}]}], "}"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414222466951746*^9, 3.414222471972573*^9}, 3.414222621437736*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"K", "-", "\[Lambda]"}], ")"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ FractionBox[ RowBox[{"u", "[", "\[Eta]", "]"}], "\[Epsilon]"], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"K", "-", "\[Lambda]"}], ")"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "\[Epsilon]"], "-", FractionBox[ RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "\[Epsilon]"], "-", FractionBox[ RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "\[Epsilon]"]}]}]}], "}"}]], "Output", CellChangeTimes->{3.414230186172416*^9}], Cell[BoxData[ RowBox[{"%", "//", "Together"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414222501653281*^9, 3.414222508249845*^9}, 3.414222621437997*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", FractionBox[ RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}], "\[Epsilon]"]}]}], "}"}]], "Output", CellChangeTimes->{3.414230203448628*^9}], Cell[BoxData[ RowBox[{"NewTwoDEnzymeODE", "=", RowBox[{"MoveFactor", "[", RowBox[{"%", ",", "\"\\""}], "]"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, InitializationCell->True, CellChangeTimes->{{3.414126482541607*^9, 3.414126695668775*^9}, { 3.414126785942751*^9, 3.414126798453333*^9}, 3.414132612675897*^9, { 3.414156625905953*^9, 3.414156626437158*^9}, {3.414156677221368*^9, 3.414156685847692*^9}, {3.414156836410715*^9, 3.414156853343735*^9}, { 3.41415688731652*^9, 3.414156897756517*^9}, {3.414156960389798*^9, 3.414156985183196*^9}, {3.414170365713225*^9, 3.414170387748838*^9}, { 3.414170443052018*^9, 3.414170464607399*^9}, {3.414170753252542*^9, 3.414170753409731*^9}, {3.414170812985602*^9, 3.414170836305018*^9}, { 3.414170917775846*^9, 3.414170952371218*^9}, {3.414172839661582*^9, 3.414172872340422*^9}, {3.414173013452875*^9, 3.41417303336515*^9}, 3.414173118526437*^9, 3.414173436669379*^9, {3.414174640519012*^9, 3.414174746363197*^9}, {3.414175834095128*^9, 3.414175836285585*^9}, { 3.414222459431401*^9, 3.4142224600944*^9}, {3.414222498835149*^9, 3.414222534687271*^9}, 3.414222621438262*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}], ",", RowBox[{ RowBox[{"\[Epsilon]", " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]}], "}"}]], "Output", CellChangeTimes->{3.41422859033577*^9, 3.414230222905423*^9}], Cell[CellGroupData[{ Cell["\<\ Now let's see what equations we get by setting \[Epsilon]=0 (i.e., 0-th order \ perturbation equations).\ \>", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414170186595785*^9, 3.414170240631512*^9}, 3.414222621438522*^9}], Cell[BoxData[ RowBox[{"Order0Eqn", "=", RowBox[{ RowBox[{"MapAll", "[", RowBox[{ RowBox[{ RowBox[{"Limit", "[", RowBox[{"#", ",", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0"}]}], "]"}], "&"}], ",", " ", "NewTwoDEnzymeODE"}], "]"}], "//", "TableForm"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414170242981092*^9, 3.41417026308285*^9}, { 3.414174770704779*^9, 3.414174786083268*^9}, {3.414174883006102*^9, 3.414174905657419*^9}, {3.414175035467797*^9, 3.414175041021133*^9}, 3.414222621438644*^9}] }, Open ]], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"K", "+", RowBox[{"u", "[", "\[Eta]", "]"}]}], ")"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "+", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"K", "+", RowBox[{"u", "[", "\[Eta]", "]"}]}], ")"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{"u", "[", "\[Eta]", "]"}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414230314655232*^9}], Cell[CellGroupData[{ Cell["\<\ But this limiting system of equation is inconsistent with the initial \ conditions, u[0] = 1, v[0] = 0:\ \>", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.41417508567031*^9, 3.414175123375498*^9}, 3.414222621438928*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"ICRule", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Rule]", " ", "1"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Rule]", " ", "0"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Order0Eqn", "/.", RowBox[{"\[Eta]", "\[Rule]", " ", "0"}]}], "/.", "ICRule"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414175018186032*^9, 3.414175074967189*^9}, 3.41422262143905*^9}] }, Open ]], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{"0", "\[Equal]", RowBox[{"1", "+", RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "0", "]"}]}]}]}, {"False"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414230371124708*^9}], Cell["\<\ This is an underlying problem with singularly perturbed problems: \ inconsistency of ODE system with the initial conditions. We will see how to resolve this.\ \>", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414175136906499*^9, 3.414175179430072*^9}, { 3.414222553648575*^9, 3.414222584083516*^9}, 3.414222621439291*^9}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Numerical Exploration", "Section", CellChangeTimes->{{3.414157166565523*^9, 3.414157179235001*^9}, { 3.414222736005231*^9, 3.414222747698728*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NewTwoDEnzymeODE", "//", "TableForm"}]], "Input", CellChangeTimes->{{3.414156863664146*^9, 3.414156866062421*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{ RowBox[{"\[Epsilon]", " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414230458299837*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Numerical Solution and Plot", "Subsection", CellChangeTimes->{{3.414222669810702*^9, 3.414222685280823*^9}}], Cell[CellGroupData[{ Cell["Plot Function", "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414224152072937*^9, 3.414224167826551*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"DoSolutionPlot", "[", RowBox[{"ODE_", ",", " ", "epsVal_"}], "]"}], ":=", RowBox[{"Module", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"InitCondEqn", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Equal]", "1"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Equal]", "0"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"\[Eta]End", "=", "10"}], ",", " ", RowBox[{"ParamRule", "=", RowBox[{"{", RowBox[{ RowBox[{"K", "\[Rule]", " ", "10"}], ",", RowBox[{"\[Lambda]", "\[Rule]", " ", "5"}], " ", ",", RowBox[{"\[Epsilon]", "\[Rule]", " ", "epsVal"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ndsol", "=", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{ RowBox[{"Join", "[", RowBox[{"ODE", ",", "InitCondEqn"}], "]"}], "/.", "ParamRule"}], ",", RowBox[{"{", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", ",", RowBox[{"v", "[", "\[Eta]", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "\[Eta]End"}], "}"}]}], "]"}], "//", "Flatten"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"vMaxPt", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Eta]", "/.", RowBox[{"First", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], ",", " ", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "&"}], ")"}], "@", RowBox[{"NMaximize", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"v", "[", "\[Eta]", "]"}], "/.", "ndsol"}], ",", " ", RowBox[{ "0", "\[LessEqual]", " ", "\[Eta]", "\[LessEqual]", " ", "\[Eta]End"}]}], "}"}], ",", " ", "\[Eta]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MaxPtPlot", "=", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", "Large", "]"}], ",", "Red", ",", " ", RowBox[{"Point", "[", "vMaxPt", "]"}]}], "}"}], ",", " ", RowBox[{"AspectRatio", "\[Rule]", " ", "1"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"PlotColors", "=", RowBox[{"{", RowBox[{"Blue", ",", "Purple"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SolnPlot", "=", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Plot", "[", RowBox[{"#1", ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", RowBox[{"\[Eta]End", "/", "20"}]}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", RowBox[{"PlotColors", "[", RowBox[{"[", RowBox[{"#2", "//", "First"}], "]"}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", "All"}]}], "]"}], "&"}], ",", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", ",", RowBox[{"v", "[", "\[Eta]", "]"}]}], "}"}], "/.", "ndsol"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{"vMaxPt", "//", "First"}], ",", RowBox[{"Show", "[", RowBox[{ RowBox[{"{", RowBox[{"MaxPtPlot", ",", " ", "SolnPlot"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"500", ",", "400"}], "}"}]}], ",", " ", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", "Large", ",", "Brown"}], "]"}], ",", "None"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\<\[Eta]\>\"", ",", "Bold", ",", "Large", ",", "Brown"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ RowBox[{"\"\<\[Epsilon] = \>\"", "<>", RowBox[{"ToString", "[", "epsVal", "]"}]}], ",", "Bold", ",", "Large", ",", "Red"}], "]"}]}], "}"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}]}], "]"}]}], "}"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.41415858949458*^9, 3.414158757735336*^9}, { 3.414158822540405*^9, 3.414158876716507*^9}, {3.414158912355009*^9, 3.414158992638582*^9}, {3.414159057101586*^9, 3.414159080172947*^9}, { 3.4141591276818*^9, 3.414159208854669*^9}, {3.414159240840358*^9, 3.414159321459284*^9}, {3.414159384918592*^9, 3.414159495877507*^9}, { 3.414159533693858*^9, 3.414159585770365*^9}, {3.414159664774451*^9, 3.414159672722522*^9}, {3.414159762307563*^9, 3.414159800385224*^9}, { 3.414159891691608*^9, 3.41415989494887*^9}, {3.414159925288239*^9, 3.414159930324265*^9}, {3.414159983438526*^9, 3.414159989600893*^9}, { 3.414160022349233*^9, 3.41416014538795*^9}, {3.414160264496005*^9, 3.414160477515918*^9}, {3.414160513720847*^9, 3.41416053241007*^9}, { 3.414160570575239*^9, 3.414160592186646*^9}, {3.414160626158701*^9, 3.414160672982785*^9}, {3.414160719778818*^9, 3.41416073337495*^9}, { 3.414160766408626*^9, 3.414160798869594*^9}, {3.414161002557738*^9, 3.414161004925106*^9}, 3.414222642285834*^9, 3.414222689524246*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Apply It", "Subsubsection", CellChangeTimes->{{3.414224135903899*^9, 3.414224138410569*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"epsValList", "=", RowBox[{"{", RowBox[{"1.0", ",", " ", "0.5", ",", " ", "0.1", ",", " ", "0.01"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"maxPtLocations", "=", RowBox[{ RowBox[{ RowBox[{"First", "[", "#", "]"}], "&"}], "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"DoSolutionPlot", "[", RowBox[{"NewTwoDEnzymeODE", ",", "#"}], "]"}], "&"}], "/@", " ", "epsValList"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"solnPlots", " ", "=", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], " ", "&"}], "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"DoSolutionPlot", "[", RowBox[{"NewTwoDEnzymeODE", ",", "#"}], "]"}], "&"}], "/@", " ", "epsValList"}], ")"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"GraphicsGrid", "[", RowBox[{"Partition", "[", RowBox[{"solnPlots", ",", " ", "2", ",", "2", ",", "1", ",", RowBox[{"{", "}"}]}], "]"}], "]"}]}], "Input", CellChangeTimes->{{3.414158786898216*^9, 3.414158790860723*^9}, { 3.414159027646104*^9, 3.414159042508467*^9}, {3.414159084292093*^9, 3.414159115096908*^9}, {3.414160835493622*^9, 3.414160876200299*^9}, { 3.414160969298435*^9, 3.414161047651475*^9}, {3.414161176645042*^9, 3.414161251482921*^9}}], Cell[BoxData[ GraphicsBox[{{}, {{InsetBox[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0.3029449910863651, 0.0768762397634175}]}, {{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVzXk41HkABnAppdrHuWXHVZhOOlZWcvQmWjlKYne166hxFLq2tKl9lBHR oHrikc1V9BQpYwYl5JiZ1IOQyZUZ00qay/xSVFRjv/vH+7zP55/3tWAc2R2h qaGhsZPk//aKkD5vkm3bPHApeXpmhsIcN+OjEhod4c1PrjSoKWwozMmrpNnh tHvZmfhvFLyf9XHzae5ISUwM+TpN4bfwT4+u0AJgmq3cpJ6kIF6X4pZBC0eF kaGLgZLC9UW+51m0WBxc2cg43U+BqV254gItCTWZ1q+3cikE7rnBfjeehUrJ eUZaGIWFM8wgD/NCVGGcyzGnsMxPJeWn3YQs1NP2e4kKJzs2IWeiFAbd7Rkf 8lUwqtIfmjWLjeBrU8YHw1W4P+zW3unMhV+fZbvTKhV40fkme5RVqCs+/PLz +Bgml7vo3jv0ALtUDuWcpjFoTpXpmSyrBeupsDguYwz2M3vv+5fXIzTYNfVc 6Bjak+w6WlY3ovHngIq5dmNYclkxVapqQjdX41X03DEoPkmGetbz8MGSt/hH sRI35XWtOhf5+GNtVFsHRwkds9vUyIgA9WnjbvtTlUiPqo68Tm/BQLM6oIGh xMctZSMHzj7BFdeaX3sdlYi1FVQt5j+Fqcnx5rDFSkjKBWnPLVqRn5Vpy6YU +BL9InfV6TasLlYdOdCqgLXrPHVkXTvSTY/vcyhRwKPIYj/HqANDnlaf688p cNIs1PLfoE4IeEfurGEoYKP8ZWHfji6InX1Lq10VMNR9py2Y7sLjYe89KnMF 5jTmsq3ynqMht+2MSC1HjF3dwHzvbvAiOVS8SI4yT8b1ho/dGB1f84NZnRyT CmO90WwhogdqDm7Pk6Pa32N2lvsLcBd8bVnxtxxntycXVo2+gGxiaWBCkBwW Yq/+4uQeZDoU7ajYLIfjxqQsmm0vXMsHvrtqLkeQeefULGEvztFrIdYg+60Z w0eZfVim++rB0CsZcuaExO6m90PLMcJpA18Gw6HqIk1BP4J7J2q8b8mgFc8M 2PTnAHTpf72xSpFBozSEPWzwEsyL1467RMtw7Bo7w4D3Ev2sUwUm3jI8sk7V 1j88CNP3yxMe2sig73XMJlFHhCWleHtBTwbRmi7hqXoRyqMHY+jvpagoAH0k RAx39pZAeY8UwWx7fTO1GE42l0r21UqRkHyDKbozhLfvTzwryZPintQsV8dH ApXHbHs9phR++joOT6YliEkKue0TJgVLS9NEREzReow9iQVTk9/eEbOcfS5u I7YfFvONv0igucr5xGZi48p7voeJPxVYuq0nHg7YsX/RVwluqedLDIljc9Kz w75J0MnaajTIIP/pCafiiNN5raw+4tGE2KAM4oAUf7WQODAqyPIB8YKayDft xC6ONuUL1BJMV2dWNhDPFbU95hCXWGnvKiJGV2NJC/Fsm3/4BcRxgsq0QeKI 5tUbc4nld3P9tGYkcMn0Nc8i7oiPEQcS2wkLlcnE846FNh0ibnT7aW8i8ZZI /+JE4p2ubcIzxNydTlF3ieNef649SazYus6nmdgw9fLaWGL6Rqt1vcSchyuL jhKHWBsZKIj94poXHSK+umTh5AzxBP/3C1HE/wGWpYv/ "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c4V30UAHCrUkmShIZCmaUXUZTTUGSvhIQkoyihKBRCEaK8khFC9vpd o7SQPX7r/ozMQuhFaQiJ3vP76z6f5z7P997vOed+z7nbHS6bnufi4OCQ5uTg YF91z48zqj8f0wwxmfRhX3mOinkMikqBtAyX5zMhKVBOTUgmRFWg5OTNF3/X qoBeexclRVQLzJxe1DxergWnHGdfPxA1B+EPivqMH2bQr3jnaJSoIxiqrre/ ST0HaRuMwiJEvUHPcQ/PaIgXBPES0uGiIeDx/NK9rplgsLRKL57+Fgc2jj+l ImIfwOq/QTbaW1OhyK7+9DKBRNhh8mX83b1MkJKJFs7XTQMf6n5I+JkLRqdp Sa0XMmBj2boBTs5iOPT7T23qYhZUDB1tox2gQNEztzNFnjlQeyFlk9VkGczN B77hj8mDmZ0H1xa6V0KSUeqKYv0C4JrPF9i0owrETM2z7X4Wgupf+wqzolfw vLh6r4hRMbSFqFAb5N6CtOuW71IHS0A8ZmI+90s1eB0zypNrLYGJ2cGBjj21 sItUcX2hWQqZ/71s4Y9+BzmhAf4P80uBf0v215GROvBU0Q0jVlAg0rXcKU2q AbLaZ69Mm1Dg16H8EZdbjRD4ztBL6hEFvJXqyoTfNQFflvX641QKOKlsS4tt aoI3wr+8JWgUsFT1v8dHbQILnWbNJbSGuooD1/smyLWx5ytjUIDrSObaL1+a 4NM5swSRDgrcNwm5UC/WDOssGsrreymQ56G1zduzGZqMzQdKxykwWFR3j7G9 BWwrtaI/cBBAn+KZVJJuAb8fMi3/chJQrXBMP06hBW6IHwvR5SIgLa+e75Ra C8RPSXhTuAlweNYQ1affAklfz53wX07AaErT/TGfFnCf8eGcW03AVGTbw8X2 FqDZtJ6LFSZg4QIrSfZGK1jNDtRYyRFgrnomdvetVnCy+nZ2FF3AORqmHNIK NDejJ57yBNgmzF45GN0Kt9XiJ8MVCKipF9MxedoKh/WGh4ndBNzZdvanb0sr aA1JOMwoEbC+c0q/SawNqLe8ahU1CJA/vGLJ6WUbnOfZd+CeLgElefnS3dVt sO/4T/5VegSoCBmbnGhog/C9dN+76ANjCZnyjDbYmP9KMESfAMMoOb3p0Tb4 1ql5/pohAZ7vDRKuC7aDnnUqoW1KwIsrcUqRru3AMI+4+MSKAO2n251LN1Ih 7+LMZWlnXD+Bf2fDZio4Dp/tDUNvi14Y6dlOBd1lq399Qv++3uHAo0CF5pdp +zNcCCg0Cbc9dYgKPdueL4pewP1wfju56ELF97ubMOdGwKBdtdaJKiqI9O4T 8PMkwGeLncRHGxqMPVOtS/bHfBjvseg7SwP1WdP4MbThbc6ILicaeD4wlFQK IGDn54xv7R40WP7d5VIDmlU2Xl0VQoPPxrS2iZsE7NH3tIsroMGUU0SjbBAB 4zdCk7X/0OC8SEaiVygB/1nIu6Rz0CGY4OatQNtPr+cS56bDLk8FlTm0nuSn vWK8dGjsO9LsF0aARPidFAFBOjjP3/h86w7Wl3mb2+IOOggNs0T9wwlQmDy5 usuADlNrhOa0ogh4bq7/NsKYDkd9Ap1C0EdfH/HSNKODBU0+8h3aOlqxN8uS DqGdzYuHogkI37My3/scHer5pgL23cf6836lK3idDuHXtgqIxWK9LkpEGGTS wWRX2qWcOHyek6gmZzYdSvOX8Q6iK6lrv5fl0sHy8pLNhn8JoKb+sdpcTAcj ExX1IPTi4U7ZiRd0eKDnV38yHp8fFt58l0YHdZ+6g98fYX7WTvPW/aaD2uOK 7PlEApivI+6cWKSDXEb+B6kkAh647VhO+0uHd+btH43Qgi3W3D08DOA9vuJg Ftuh9Ytf+RlQFexqbZBMgMBC4vdNkgwY0vl6/GEKAXxjx/q89BigeNzlzq9U Atr+/WA9b8CAsoclM2JpBERq+b2/acyAibhtioBe/bSkM/wkA+JsSO476FVn NjFS7RiwNmeZmlA6AbzkdH2rFwNkXfO6pZ4SwPM2qVgymQEn7G1zxTMJ6Dmg pTP4hAHXLrjIHUIXV01+SExngMaqtx72aOuKg4KC2Qy4+brBIA1dWjjozUFh wPUuD/0tWfi9Jkuq9zcyYGCx4irfM6x/sTZmQgvuz0rNSha9MsH7onk7A6aF u7iPo8se1ie3Mhlg7fK56CZ69T3nvy/6GfBKL8JuCv38en5d/A8GnNqvpVWd TUD0rNkZ018M4M5wzn6PPnf1z8yaeQa07g8gv6P5rxhIhy4xIC39R5hUDgHn Xb6Ge61kwjdNTdtQtOApZSNjcSbQWIyxA7kEXFR5+X6lHhPURg/tCcnD847e UfDcgAnKvWIP4tEb3KdvORszwVL3n9oc9NusHTvrTzJBKsQ9qg29fmOMZ6A9 E7o/JDDX5RPwct5x9exVJmRtdJZ/iBaIvzWQ5cuE8qsP/J6izysllpr7MWGJ 0yGpFL32Iu0UJZAJxx5o69LQ5/r2Z7rfY8ILvqfOvAUYj7f8B0fSmPDPkUNl V9D2p2UFHmYwwUF338qb6PLZo8OHnzFhQOWAYgTabs/18NR8JrxMqfmSjibS hzusK5ggo75Pk4bm1VzKWfkC90/j2dqDPtMj4v/8JROat8fSRtAr1htKCNcw 4dXYkZx59OmQ55cYrUyouhaotL0Qz89t5OFAKhPELlQ/lUMvez0lpMhgQtcP r0/K6OIZiZeRnUxwrrw/dAzN7Ry1QucjE3hurH3jjLbkzun5NcyEs0ln6y6j C1NrC7NGmSC5qzfFB32qe9aMexLXi37SEobOP+GQ9uYXEyQaetdkoFUUtmvC PK5/gQdy0W/4P/S+XWBCok/diWI0nTyzsYaDhOk6s8kqtFXF5vLD3CTIBmmH VKOHEnpNa5eR4Ptk06969M8zVtHvVpEQ+rPQmY4OOCSioLWGhFO5Mc4d6OWS Xc11a0m4UJl8uActOm6+rEGIBP+u6yHDaE1PY/+mrSR4TB/X/oluNF8rdmI7 CRf3eYnNoY3VqJXNkiT8brZuWkA7/NH70SJDwlJNZhlXEQETA6ti9eRJuJsp /2MZ2rumeXfbLhLoTRV8K9F3wrQvtCuRUEuVYPCjBVyX8xruJSFIQcZ/HTpR rz6LqkaCTN0NLiG05O6Qo0bqJNSQCo7C6AKBox9pB0iweGycLoLe+4PzljGQ 8N107oUY+k1H9WbGYRJSNVWLNqO1n9+qMtEiwSVx882taHqipiXzOMYj87Xs NrRVwOKM6QkSriXKl25HD9m9ekjqkcCo8hWSRF884vePuSHG42ilmRT6p5Q6 jWVMgr3n/KUd6IAV824nzUjICzVx2ole/l/lqs6TJFi+ZOyXRse0XcuxsMT1 TSI/sy1avPd4lzUJ/H8eXpVBP439OXzqDAmszj/9bCt4E0HddiSAbqeELLrc wlPcyoEEqd+7tdjW3P/P6/eO+P4RG46w3bhp2tramYSCJwmb2TZeKprrcSVh rqeBZK/3/oN7/Gk3EtYOFzmz7fBOQaXvEgl11nbd7PeZyJpg2FwhYerT6A62 ve/mXe73IuGMjLkxez9LF1zX2F4jYay+/BR7v3cMZPIHfElwcBA7wI6HwJ4x HTs/Es+nmEUJdv4En40OBpBwVVo6mR1PyRnHEPtAEiofTW5kx7ugS1LiYzAJ ++K/erDzsbdq6O3ZUBKoDZrZ7Hy9SU4/M3SHBP328Sp2PulnxR8PR5JgOnHn Bjv/VloDqo73SQjWTdzJro+hnSmskVgSJvmPlLDrZ2ZCTGA0noQXFpE2fOi4 lLHG5MckmFlSgV1/ykZlt8ySSdgp2P+bXZ9XKAZfq9NJeH0mf24J61nAUSzb JxPva8dosOu7eMOY7e5sjF9CpMUseso3kJpUgPEWF97wFR0pZxBmWkwCd1HT 8//Q8n2imispmC+zfpVRtCsQhdcqSeCN9anoQ39aNhppUov5e3bjYyM6pJKi xVuP33e5jm4tWtL11p83jSQMq/NHvkKfbRNxU2gnYbN5S2IJuv+Bnt6KbhLe R68bi0f7a4lwv+khQU3omWgMetOvkSrvfhJuujfuCGefF1Y35YaGSFivt9By A90hXrry9RQJhgFKejZob0ZAjdc0CT/d9umbo9ff1r0u94MEofv20vpok9Hh 8UdzJPCJObhpoNsLhJs8uVnA3LBXWQRdv98/TEaUBbf/eNS14PnqOKGjObiJ BceeWHtUo7lTNvz6dysL0hVjZ8vRhzmKz3NLseAqXTEhDf264aPWwG4W+Hcc lPJmn/9m2txxWizo0/rhI4S+q/c8dLM2CxrpA8/Z/cPmqCxv1gkWNDUwe/5g f+FSXr2mwpAFlqUCtSNoQ0GacLclC6Zqo8QJ9DjdQm6zOwsyPndK6qLFDJ1M Mv9lgQg58/Is9rupY12kQgILBppOa5iy++VBHYvyRBYcli9JOYJ22iV3uiGV BYq/7FdLogm+L47juSwo1r4XOYT9Vr/1qq/CG3ye9el/bNC3dEJTy0ZZ4FfV ZqmO/Zlp62Kz5zMLWJfNiqXRUlf1RAsmWKCjeXFCCN2Svu5hxjQLnDz9hL5i vxdaSAl78JsFhO5p+afonMIKdw/+Dog4yXmNG00XHNdQUO2Algx5KgXnEwnZ 1rnsfR2wCRomk9FXoahcUqMDck1tvoehxdy8FTcd6gDH3TkUa7RjPYfkKt0O iGxd4OVEz/mIrho/0wFpqn7CJ3D+2d6v250R2gHeqeI8jThPRdRqFJ+82wGi q9bN5aO/ZyuErbjXAfy6++kx6FpPfpWLMR1wWtZllzXakZd5XympA4KCWMkT OJ/lKFtp15R0gL5vjM1K9O4I54qB3g7gC+6r24Pzn7paSJyoUidwbnunq4Tz Y6eDqGqKSicMPjVbEER7RRd1bVPrhLbWx/E/cB4t+NQtJnOgE4QPu0WVobfG 7UpXPd4JuoK7A/aiub51FppZd4KMsI678mMCWvNkG6OCO8Gmd4IujvOtzVba PCfZCf0imUWvHuB50RI15BHUBTbBXaXqdwlI4LH1NpXqhvt/w0sM8X9i/UD5 U666bvDn8IstvILzQUCQ+f4r78F8u9peaUcCOHJti4cEe4DMlFBusMD/qcTi KMHaHvgrfeB+lDbWt/xd3nWXesF5Y6jFrBoB63Q9FYL5++D8Yw3/SRkC+nbR yeuv+sB5dHCDhAjOI09AasS2H9ySxo8J8OI8U6y6bstSP7SM9if/maVAYGh6 UF/eAFBvL35TH6VA4fiWJH79QVCpOxfqjP/HJuv49zX+HoThoAj8BigQsYxr Ux+6mOPJ8gl03fzM4jSaWVHSPo5WHep/J7YwCHLN5OkRtBhRaHQJHRMm4NuL HjI3cN7wZxDSnB1LmtHeCZHx5xYH4Wv/1W3P0IWRgdd90XxGHmMZ6NFAb5so 9MKsa1E62tLVRqISbf/N+kAK+qC6QtGqpUEoC1a2jEMv72utL0WPSLy9H4wG +tucBvSCYKFFINq3jrjXi5bQSNxyE/1fQZLJsr+DQFH2zL+OpgZc7LdEH20Q afRAr/C0q3ZH6/lwRF9CH3IyywhG37YfM3dDUww1XAvQsb2UIWf0xBFF/Rr0 ZfdHuefRUmqSip3oSDU/j3NoW/mNghPoyf22amfRj8RXz/xFP/Q+tGSL/h9A DDz7 "]]}}}, AspectRatio->1, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 1.\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, ImageSize->{500, 400}, PlotRange->All, RotateLabel->False], {266.6666666666667, -213.33333333333334`}, ImageScaled[{0.5, 0.5}], {500, 400}], InsetBox[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0.18187718002578604`, 0.08250423797859953}]}, {{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVx3881HcAx3FJUveI8FCP43E8cM2GQolYvGtRIklsGDvyq0ma3exRbf2g SAutNcmP2rl+KIoLhy35kbti/fAjv06Oe8xucve9HzY7ccXtsz9ej9fjaRv/ 1f4kfT09vb2k/x+YNNXXLvP3lf6Yo9Xp1DDYYZkuoTORZuXd2LqoxiZO8bV6 uju23wwwP7WgRtDL4brrdD90ruppWNSqEZH4tuUyPRyKmcH85bNqjLnk7iig J6LFu9PQU6FGuUXIuQv0DJxr90tZMaJGllG9ww/0bPwUZBgcy1cjMorLm/67 EH2bvW5UpqpB02XF7LLmIDduxua3DWqsC1VNCfJuQedvwXWZU+FotxeK/63E SL9zad1jFdbyTceXLOGBrQ2isS6r0Dix40XP1jpE3j/xhhmvQseh61ZRCj6U KemSwM0qaD7wMalOa0JIYpUPVqmgP39vtdW6hxCUHjp78E8lPHRxjWE1j6Dt TOUUtCjxItu9+6ljG/y5db/HlShhc4mar1S1o0qWHbPAVoJ6KxkfdO2A8G7F 9HCIErfkzc+MLwpgcok2F+2ohDHjjloqFcIuWpxgYahEfkpDcjnzKbJDnxRV SBWY3XZP+uXpTtgkjt4RtCuQsVHIXyPoAjfU8uHPHAUkNcK8PttnWOqWKZR9 r8C7QwNlH333HJHdJW8coxRw2r58Mbn5BZ5vz6uY26LArhu2B2vXdiPW/C/v gDUKHGXE2v0R04Pg0pEWi1kKzopPacPBvYh+MMp8METB3GTaSKjtRZroim83 n4JBWxnP/lofmvwC+yOvUEh1bx5ZEfQKnKHh9NRvKNzbHV/eOvsK1fu8BTv3 U9BQlqsni/pBc9qZn7WJQkPYrqWFfgN4qWqyDzSjcDogh8OfHIC7SBN6eEYO 27FA0c2cQRz7VRoaNCiHt2d2IX3jEAa8ajitfDlirHvml/QPQeB8zeZMkRya ZwUT6VnDEB040Cj5Vo5iA1bGfqYIAxVJXecj5DAfb7ihLxSBUWVPybzkWHYy K9zr6xEwfCI/VNDl0Ktk8SbMXuNtW1+R23sZ2KW8ArOO15gbjzOyFsvQ4nTe yPTIKLRJR62Fj2QwDWQ7nzEWQzRhj9scGcTre/uPPxLjTdJCuXumDA9+AVPK GkOGbz6ljZfhC56HKWNxDA0RtYXsnTJk5nCzxFXjaGmePM9xkKF6ilFmvEcC v9rojncrZQg1Nd7SqZVg8lSAhbliCheW6VuJiROcziaZEAvnNQvTxINRrQ00 Yo+JMYHlOwmKt3p8ZkBsWV8dcoS4jO58VUNNYSI8+KDFewlOubnSRcQZxflF CQsS7BOVMK4TV+dnHj9GHCaQppUQT2ZmxBQQ73Z1bb1CHJkSY9dEbHypi3WR 2MfbuWblogTvk3Wc08SG4udPaonD2Tl28cTobbv7lDjrhIjNIj4mrM8bJeYa OQs+J5bfLwtdppOgsWIgIYy4+2TqWCSxp9bpth/xcnZsexrxjPlZzTbibclh N88Qc3mv/X2I6/Z+nHKf+NXhvMnNxNQnLnseE4dflHpsJGZ62rsMEXe5+eZu IGY5rTWjiNdHFA87El+1oWl0xNmL/zg4EP8HC6yYYg== "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwV13k4Vd0XB/CofimFlJlK6W0wVoqEr5BUIkVJGZOiF5FXSkJFKVKoDBES Ml73nmue3cEQUaYyFZUoQ4Uo9Nv9dZ/P8+x99jlrr7vXXrL2bodP886bN8+d Z968v7/7T39urhjco80c/299xaC59gI9yfO9EnKg6+qo3BNSxbYnUY8ZEqpI HpzL8V6kjwMN7fQ4CX1IbY4t+XfiCI45/CwNlzCDk+5e4/jmU+hWvqkXKuGA 0zxCj+bfuYAEEZOg2xKe2KR3Wvs5z3X4NDxiHS3yROyeJQF896/jaOA73nUn /kNpcrzVp9U3sHTC3a/4sRc22USnrNYMhHdLpPfX1ZdgKvidHel6E6YRb52N /7mKXfQlGV+K7yCAj7EhWOIGko/ONKXN3sfmvfdv0c/fgNi8UbtleuF4Feg2 2Mm9AfGQLWOKt8IhN18hQ8krEMrf1y9PXh4BzmyyUsurIIxsfRhxTjYSS388 3L46JBivx6SpeNWHiOq+rMecuwuhErfqffIxsDiemDP2LRLeLHHR/YwEjHaa LUmSfIANW3mDn7xIQJA13+kjeg+AkE307o8JYJxyk8yLfIBnqt99V4onQsBV K9BH7SEuuYcqu/okgn3tjeX/fB+BmVtm3q+VhK2Zy/8nzReDS6tbb9nQn4L/ T8DJvauewFm7dGGdVQqinI5ZKxg8gYy15qS/ewrkWhRsl7s+geXD4QX/BKZA +3n7qc7SJxCRjyrUyExB4fOHzHylBPzqHdp4bzoFw0e+lhxoTEDnflfHqXup ME97VH9hWRICqePnNzLS8NjqmpGjbBLsiyM8K1hp6BN2abDYnoSXtrsvGLal wc1X96WWVRLmeRU+3DidhuDDw68WZSVB85DzxGbt5yid0X0ba/QU0lMaS/XZ z7HedORz9Z1kONowRDbUpEPSb6/GmcRk3AtmJiq8SYdQVsKdJfnJqNWp2C87 lI5ffEeUTPuS4Royu7WDPwNNFfkXetSfYUrYR+SqcQYuqwTMTX18BkNa3HB+ UwYaBVeuVNJJxe9NIddNazNRreVyutk8FS/2dw5YdGSi4Bwnz/NcKsrrNYxN BzLxlOt9vPhhKnRW+VqILMyCt193vOFwKlYcM/70BVlYO5qy6VRMGg4/leHp pWfhYuNORI0/x5qObfO172ZDQIn5sZYvHSrK3kfjY7KRHKoS8ls6HUlRYeI/ UrLRbLThjfWedGSFXBS8XJ4N+fqVF9Y/TMc+my+v50az0csdTaGrZWCm20rk q3EO9lY+E2i4nIndPeu2G/HS0LNGlqRbJow73cNeLKLB0//xCZWnmQhYvKlo 7zIaEhGRFlGfCcuR7xFK4jT8LvXXtZTOQn1IS0+ZIg05RSe8BkqzUJznMzd8 jAYxankPD08O3k00DCan0XAy5LfZB9EcvNTb+3gsi4Ykh4/1HIUcBEcad+5g 0KAgUlh4xyIHDSbcFYxSGnS9bB+I0HKQnJr4x/kVDTseH0uJVKZhWdasUfcv GuysU6zSemhQX8ToG92bixv7paKjB2mo5zm56pFRLlJ23Gu5PU4Dd9A9aKdp Lr4KXD7gsiQXYskPht0sc+FVfnDn1h25oGiREU//zUXImomVJaG54H+iIrP5 Xi7y+vRevNSk48ClTunXr3PRZhjwLXQvHdopcG9tz8Vkdpmo0WE6Zg4Lpb7u zIWaz067mjN0XGqhc6v7c1GwQnmyIpyO35MShhd+5KJQX3IN/TMdEdHFp4WF 6ShJGbsQGcnAoMkIv7MRHV1LlaIPP2FAaGbR01ET8lyPc2VC6Qys37Y+zP0I HVr4xBdazkBqfLansyUdZe2dcYFDDEx97+xQOUtHOR+X66VDYVjkmNyK63RU OcdJHf9KoVjI5qt+Hh2MwXPnrCcpRBuuzvynkI7ksxrFp+YxUWRx68HCEjoC HdstXVcy0eCrOlpUSYeh/fKY65pMXMXy+Qsa6Hh5PFA8O4SJ2ary1uX95H0N XUTmK+bhxMFHZxWXMdDA3XWaTy0PXT6ysoWCDJQZLGEu252HlqqDh3SFGXii n2ombp6Hw3o/JQ+KMWCv8z5C0TcPd7K9H+vLMvBZzVzYoiEPGkq3N5SqMjDx j5Zglks+aC1h4v3HGdDu0+Xe9s7HzbcTYodPMhAUZ+h39no+eHZvOVdmzYDo SrPRddH5aHTrFws7xcAOnnMvY1j5sFpp1irkwoB3Z1TYLakC8JZ2qUb5MTAT Ni7oUFuAmqlXTZwkBvQP/OLubinA0QfiYh+TGQj53zz/1b0FsD+2eXZeKgMy vvxjb8cL4GAUn7slg7yP89om0zWFMJzd9cuLwYCf/qF7uFgImciR2fBqBnin M4Sk1hfhlv2Wf9f0MSDVoPsDykU4u8Cvrr2fAdXEN60OO4ugs7HBLPQjA6f3 LYrNPliE7ky3H98/M1ATbb9e16sIKTk5AWmjDIRpSGg4ccn8fQXyZTMMSF8J OpXvVIw1Ws288SIUth+SMei6UAzphQnFMmIUjOWojTxXi2G67fbLWHEKfi/e D+8PL0ba3QiBCCkKfdJa3j1FxahtyxJ2laXwvPRHyMKlJeBaxl1pV6Cw449t 3pHsEty5emHdNV0KRgcrru0pKMFr9e7gWj0Kp2JXm6hVlYCamrspuIfCPbWe Acm2EqQFDpo82kth0O2ERN9sCRSLXys+NKLw+J35lfMHS+FVXy1z+CgFnqr9 uqFfS7FWzSiz7iwFcaF0Ab/JUvR/UlcbcKKgZL248/y8Mvj6tfrynqNg+Yt7 wWxlGZLPxOlud6FAbd3zTEqzDI9+vau9407B8Sn40u+UodVurm72EoUXN1Qb OZvL0aJhe342mIKGYD3v/e3l4LuZcZnvDoW0aDu1EzrE7Dll4RAK17PvJoya l+OY+ukE2btkfMdnD/GAcjAH6wpUwsl4+Tgx5/ZyXOyveCEUQ0F38Brtf7oV MIkIT32XRuGSUmPdub0VkL1lZFb9nALtgsTHJqMKKF41aU5Op7BqLkci9lgF 3od16DhkUpgW7r6m7FIBDbV7oq05ZLymmrlFVAWYPFaJfnkUVt/7Mv18pALT GqIi86oplNn5Paf/IOt5O2vSia23rThePFWBTb1rLp1ikfi2aRS84K1EZz57 ezWbxFPmtteoaCX2XXZuvlhDQTh94w9VVOL9uZ9aeQ0UFrJOfy0Pq0SyQcf+ 0HYKyQ+mY2siKzFJ/x6zroOC/pnQA83RlThU8lu8kPjaEmZ639NK3Fb9kvj+ DYW5QwucFhZUYnNC0czGLgpT3Ukf97+rBC3ke8D9dxS+/OztaVWpQtKEY1Hj Zwp5Z8Kq9u+ogpVzSs7RQQr+7dop5buqsOPCFLebWDQ/zuW5QRWi8/84DA6R +HqdmLlysgpue+sdJ8k5FjPeJiF3qwrVpzs0Po9RMPzWYObRW4WDtDc0lSkK K+x81Qc+VOHZtPf9eOKeJgXpk0NVKA0OyuafpuBJu9O/Z6IK18bFEvuJn7jt 85Dgr8ZzFf2rt39TmBxmhVXsqIZgslUFNUfiMVRcJ3C3GiIWSyf9FjDh+shk nXNENVIfL1JqJVbT7/dhR1WDs+d82aaFTNTFLVG88rQaatFTQ03E3w4dDxss qEb4suHrYouY0M6fPMLqr8Yb96daQYuZ4HO4nbl6sBqKte57molfCa1a6DNC /PpsjtQSJk4778nbMl2NwlfIzCYOkYkUfyLAQoFhtGUDPxNvrm/pvrSThVlz deGRZUwkqbC3t2qzMJ14N1BZgIl/uy3uquiz0Lql1uE88Tw1fwwYs1D/28hp jPifocZEMwcWhrI8owYFmfA89K+jchgLMmE7ZyqWMyEgkzr64QML+Y67dy8S YULn6PXu/kEWbPusv20j9gizqe8bYWFx42ElW+I2HvHUd1MsyP82PZRPHP/p lnXXUjZOtBbCVpQJJZpzw2tVNjob78nFiTFhO2hQ/Gon8ZRLcxVx+Np1z5u1 2ZBMd1/+mXgysvPGS0M21qX5G20RZ6LskpFm/Uk2RHfVFpYRH9RTyqi6wcYw j2MtW4LUqStLoiuD2dhmvKDjAzGN+Smo4i4bP9Ul/OdLMrFy4xP7sig2akY1 4kHctVRIsiiTjUDREmkGsYDB10WFuWxM/LLkeUms41czkZ/HxoGKLdeGiJO/ +TczK9jQotjH10iR+LZ9u5XbwoZBjrbTTeJ4wUYv2hsyn89MPYG4yTDdIaeH DUbTqpQCYtVie52sz2x8O7/C5jPxzJPXP9Nm2Lhtr2KiJ03214npmCDHAefy uMsA8ZBO1i3+zRy4HNzX95t4r/izdC9lDnqrBYYEZZjg5UaOGGlw4GN+jbmD +JKcp9e0CQc/peX3+hG3/T4X5WDOwfHVcvb3iFVfnyp6acnBdvXiFYnEYwFH 5p6d5iDX0VKzktixd2vQYR8O1tT4ZM8Qs/I2p5X6c0CF3QhesoqJtXfX1m0M 4uD8O4s5MeJuTWGBP/c4KG77lbeFWGPlEhXnhxyMd0T81iKO+sJzuDWWg2yZ sM59xGYx3x5kpHAwtUHPzZaY7j6YL5pJ3mc/d905YsF9798E5HKw/6z+f/8R 1/1skrEo4cDUtGLsFvHGlzWoruRg1Pu2VDhxUEqFnRKXgxLzDx9iiHeb054t eMWBxuduswzieIU0rls7h9QHwxk68cz8hMG3XRxc9nmrV0Rs2fmI36CPjJeY kq8kLqCHKeYOcKBwbRGTSyx6+6aJ9DAHzxxcexuIL9j5ud/8zsGsa3jGa2Il ITem1SwHj7vjN/cQhww4ttfwcmE5pdjTRzxUZj29jY+L71VtqgPEhg+PSj1Z xkXH+UGlL8TPXIy1lqzg4ur2vBcjxLx7DGz+E+fCQj9U4DuxrbR2wDsZLt42 lY2PE5f92P70wDouvAVi/X4SS9crsvM2cpGs4pEzTXw5af2ArBIXr5wjb/wm br8kszh0GxdeY6Z/ZohVTUXkp9S5mD/xa/UccfjGZQdPaXMxnNH76a/H/ixw a9TjIs3wkNkfYuP2mXs793GRMvf47F9nZo/Tk425OMEjKvfXi4O+tgiacbHr Bv/Nv/MdrT5MXj7ORWFRw/1ZYpZql/gnay72dWTq/11/7dIWDVMHLmyEpp/8 Ivbvrz9Z4sSFy0Pe5CninqLqqxvcuPgcJ2E6SbwrvDgh3JMLXcu7qT/+5pMT o2r2Ehdjc7TUMeJJnYwPZ/24cChvNh0mLkn+EnvxBhc/T18bGCS+xqdwJCiY iw9WL7Z++hv/f/9d8uAuF3o9Y9v+7o9AU2bl0wguFFdt+dJN3LJt2JsexUWp WaPFG+KYR4oqlXFc8Bcu9m0h/scmO74nlXzPgM1QLfHXqhHz4Uwuzq2e3cb6 m8//KC+byeUi105rexmx9kiOj0QJFwLvM2xyiY/65lqYNXHR3Gx/IvLv/r3/ JniqleSDnYZTCHGf/lau+1suGqkylRvErksZ28M+cDHk92rY42++x1LCdVNc 5OQabjhIbPRnvLZjlotvNmmL9YiFT20PGOCtwdfgslT1v/m/OW90wbIa/Ke4 QnwdMbMw/wVkaxBe6Nc0Tv7fl2Wmrhv/UwNHI+ajz8Q6Aeq7rORrULoiQ7qL +IVh4fPL22tgLd1lW0X8ob0oiLmvBkrSXm/uEK+cLNWR96iBHk9apTDx2+Nz P3derEGJyXgAL3FCqXaO4ZUa5GxJmf+dnF8KgeUyjkFk/EU+oyZi/ZWVvxJi ajDqc2YymNhzK4sSra5BJE9EzzdyPjqqrkm4X1ODZR+NZbqILXZcubO0sQYp G8xFOcS7NFTted/UgPXIQD2amFc3WXBkpAauVR91NYnDTG84syVrEaNmmfkf Ob/9j7wz11lTi13rnLNPEHuYa+4uXl+LdcmdrruJjx4fF8tVqSX35UH5pcTS dg7sxwa1GF7fHhdP6kn6ef01nh610DysF5NP6s9jjwT+0Yu1cEuTTIwmDvWc mXTyrYVQnbOzD/F5b6rB5lYt5LR89mgTq/nL+RyIr8XJgEC5SlLfWGEL2tbW 1SKgN6e0mNTH3mzWnWbZOtT/e6glkPRhTcMLvm7dUIcL9h777IgrFPYYRSrU QaxtIliTOCGdvfSYWh3Oln9w+b6CCfsUTmiXUR1aDxdzThB/iqsJG7hYh5bd ywfkhJkYDnkRMdtQh5Czd9XDSb3/7dwSu+lyPbo0twf3k/uH2Q6r+0p+9ThS YnAnjziT51PQthv1sP5o7RRMbB31013rbj0+eawpUiKuZEsamibVo3Kree5F PiZurrEb966rR9bs0PL55L6zom3YqEbyBRj+E17zyH1JfveiOcfiF5hm/Lz7 eJbC3iTZM7lijbBVOP/YYITCRRmbte9PvsQfvsXPPHsoKHw1528/2AR/txiL NnJfXSE4xsf61QSHWG311iIKC8pjc9Y9bobvUZanHbl/n1MtfrP4wCv0S3pJ cSMoZOyzTyibfIV7/EcXiPhRmPgiKfTp4Wssaslc6kX6CeaRvfMj9VvQbtXl +9Wc9EeGgU+oTy2QGuxNebqbgmz3/o6nga1Yn6mpkaRI+gG1G5ESW9twXz7E pJX0VydXvZzmed2G9HJV+fPzyfPrQvvOB7Sjizay2miYgagF1p6H5TrwXjRn T1wHAyt6mEm8rA50zB2Vt2AxsNA3wGyn+xuI+3QZ2GUzMO+5dU6f8Fsonll2 djCaAY+YnFDhqrcIYhsYcK4zUCp/i2+5ayf6y03DxFwZWL7fQ+GaQBcO3G4u GCL9cZdi0+tLJV1QZkW9k9BngBYPuQ/W3ZB4ZiNfr8yAVc6O5TJz3TiewRf7 TYoB/8DEgK70HlR1SaVe+h8DWZ9lYgWMesGSNmkL+E6H6XIBde6vXrTZH783 2kXH7YW8Ul3EgkZWs1+JWdMTs2PEYVfsnIeId/R1V0v+7oUjw1n/I7EkI8vE ldjN23/qLXGf2cEzIjO9WGpbaMsh9owKeXhqtheHUmy3xBFnhfhf8ibO9HaJ jyH+5O95MpTYLPwyfxSxhdPJtfnEQbEPPoYTa2koZC+Z64XnwpfRt4j/11XP ziWOUjPh9SRGU3kahzjvqq2bO7E3i3Gnk1h2mUeXK/FQZqzpwj+96P3zIM+J uNH3XLcF8azme2cb4kUeNhUuxDfLxttPEus4Hnl6jdjmJt8eS2K68S6nTOJf IyqrzYm/6CobVRKXhu4JOUwsp7ZOuY345QXLaRNia3kx4S/EyolujgeJH63m n/jzd32RwNf7if8P5O9iFw== "]]}}}, AspectRatio->1, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.5\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, ImageSize->{500, 400}, PlotRange->All, RotateLabel->False], {800., -213.33333333333334`}, ImageScaled[{0.5, 0.5}], {500, 400}]}, {InsetBox[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0.050822483624240695`, 0.08862176769874228}]}, {{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVzXs01HkABXBR0WNJLzskO5o4haYnUbmeKYkzKXRi6qRo9JoclbKRMj08 SqVyMoXotFZMnjmksZnYyqM0KdOM2SZZ8/xRDUnY7/5xzz2ff+6l7z68Za+h gYHBdpL/239v3+sGpa+7eybvx/g4hYnellw5jYFbBZyPwjEKK3Kz+RW0lYi0 Mq8/M0phU+u78ts0H0Q2L6Obj1AI3TNUf5W2FfY1ceuDBinImOe9M2h7kLj0 sn69lkLenKBzqbQ45FmcVkqlFBJab4pCauMgnrP3bO8HCiG8fwwX7DgKyT3t 2wEJhen6I0l1/GNI6O8790sXhXhxVrzG5gSYdYHbwt5SYF2TxATaJaIgMe3F qjYKySYV9hdpKeCHJP3b20Bhsd+VC+XcFLhmdEdMJe7gHVZ+aE5BuxndkCmk wDByLF5yjId75k31CfUUmkYLl4g7ziFgYOUB21ry//XGKpv0i8jlJB3Jq6CQ LTvpXTV2CV0ClovnfQph2/MF/QNZkCBmHzuTwrTx5HC/+bmgJbNDvTgUFrJ0 fY1phZgt+b2114fC8TZXZH8rQtK8ju7N8ylYVJp3T5ggQHSg65fCHzpUK7xb 2teWg+7kz14r1uFpzG2r7ZpKFN2juI9KddDbrTMrOfgI9CpGuDxNB8Ph4hlW C2sx4FLl7hGlg/P4rurg0scw+spK9PPWoSVlZVvTYiHqeTfzbek62GSqh4t0 DeA7l+e6/9RCPSTvfrv0KbTifMlQlxaFqroXppcawal+9uZ7pRam1vepnh4R HPbP62zP1CKdUxWVx2jCCaGnyZrDWgx6FPfsS2rG4d+YBwb9tYhbLqqc2/g3 Fg7P3OW5SAt5qSjtNf0FVtxbt+XTRC1GYsQ5i06+hLP9kE/oRw0cPI3Houpa oAk78o7VoIHfXXp0mUUb1kSH1BfzNThuvdP2Y3g7ateeFZxP0MBRs23au82v oOfsOuW4Q4NZZv0moh+v0B9wvmj1ag0mCnMEC/iv8dwuNPiJhQb7V9Z1TdnU AVrNbn3ZNzWKN+7OezLYgZ29TancDjX0assZvTfeINPORp9brkZVsJ9Rlo8Y tntrOL6ZaiRt4OVW9opxxVLoHcpVgy7zf1/AewtTt03LHFhquLmkZNGWdyLn s9OX35lqhM9vH57wphMrXl5vXT6D7L/IUHCT36Gs6+KnAzoVsiey47Yw3uPO 81tlk9tVmNVddddQ9B7r93Uq2A9VmHQqeavrkS5Y+BaMeF1WwaCILVDMlGDK YCU/katC7C1BxsynEnhYOR8NCFKh3uGCifmhDwgQuggkS1Qw9491PGMqRV3g UkbNDBWkTq/enHgsxcnkIh6zX4mHd8DoYcvw2dGpZ+C1EhECZ3PrMRnoZbEL D1QqcZqXnyz9sxvTYloazmcpUdJnnWMaIId0o2Jf7zElWOamq5t/yHGhsOKC JkSJ1EmGVlLijdKdNX3EomH9aD+xL396Xw+xs0LWaDkiR19ltJ+M2LKiJOgQ sWwDY3IbsWLr5ug5P+WIH6k+KyCOy06/ETkqx0iqV1IscUn66RPxxG3Px0sP EfeejgvPIO7KrO+OIQ7jhNs+Ir7+yM09knidm2Pp1DE5CqLXjAYTT5a+fFZG bLYlJGEVMV4J/2giDp49r3gZcbyoIu0DcStbIXEiVj3IYU0al2NPOtfNjrjt 1H5ZGPF8/2vDc4mNY3c2HCSeHRixaBaxR1RwwRliD4n9djPi8sA1nAfErmlP aoyJ1V7MgL+IjR+m9hkRM1wWMDuJp0aE/mpAzHawmKkm9rrK2PBzmxI3babp x4nLgr4c/078H3Wt3ts= "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwV1nk0lV0bBnApU3oNhSJDKkohUZTSVcZQKUlEUkSSIkNESYYkijJlyMyZ dHDOeXyRIVMDCSllLElkyNsslW+/fz3rt5699lp77/u691Y+dsb6OD8fH5/A HD6+/74Wx0faa0dNtukyDX6ouwZvm2ck5z0guxKukQeFukbtoJOVmsGR3QDH LxnyLzknYPm0qyxT1hjUv99DR80DcdD1R9VNWRuY73XYqnPhChqM5MrrM2wR +2c65M2GGGitMCj5qmQPdybdrvVNLIQHL+faqjoh+vKW+qWiCehbd8UoTtYV rEdftpn9TUJi1pJaFYfjOHRrO6NVIwUW4oyt1RlusB5PPLTRLhXUZMvGT0oe 8G14fWQ6Mw3Xixeu3qd6Gj9fepoVf7qDbGmrqBhZP4Qtzbmf4ZSH4KcpDbYV fohud7uj0pEH28g3/Csc/CH9j4ZRhVE+FnzzCa3MCIB86bZ/1JQLENiZGDiu FAR3u+A9M42F2B/bR/2vNgib81coNa0pgqax6reIo+cxmjZk0xtXhCFOuY9C XjCyBi4cFrKiYd+t7pN7VC9CIMbLUbGaDnXLFXS5hxcxmH3spYgMA8JzT30Y dg+FkJNG87lTDBy597e0xuYS2hSZNV+lmJBWi9e0Sw5D87tYqeUHWAgT5qy6 KhsB73wG36GUu1hjlhBd5h2BNPOE0scDd9EReWa052EE+I0Eet6psrFyrjpT MyAS3h93Wq0vZaPpT75mZ0cUlkeEJnk5lODM1vAbf9Su4F4NKyH/fAmWBB+d Ug27gqPRWUt23i6Bx0+FsqB10fj85w5toLMEC74kb1SKvYpfrOfH0k1KwVvv n7zz3VW0ju2+esm5FE7e+3/46MegzUzUbfh8KdgT4vcaRmLAeNQbYnC3FNYj 0VtPmsTiw4MYG3vxMqT2nTfi/b2OYFsvmkxVGXbI2+f3H7gBx7+/WoXby/Dx kJ6AcPENbDJV1M4YKoPieJBLsUY8FFlxe4vnc3DGQ1eFrzcey2I/OBVZc9AQ XfAiUSgBFq3mHe0uHCyhSUWp6STAIz4khuHHQe3w52HrmASIhQR5nEriYKEr m1aw6SYEI7yM7J9z4BauaK/vehPLjWu2KQxyUJkbJ/Lsxk1EtPiWp01x4PrW 8+TP4ZsQVjKZ93ABFzyn1eqWSbdwIW7CS9CQCzv7HPbUv4kIODHbqJLDxace m/m5ckl4AOZyWyYXUU7Cx/cbJUGVY+pvx+OC43JGjkpMQnzGT+2Xj7gQO20Q GayXjANFzvYtE1wUTE0NqDsnIzgw9Hjudy62+ubr90cnQ4mfdXjvLBcnA0Wn tncnI5KSYupK8NB4+fUhwQskJ6M+I9u0eHAUiOOVF6TgTb1l+LAeD5+vbJfw aE2BgSnfVk/wsCyuqLFZKRXK1ZExYnt4CEnx10qoS8WuiMiKZg8etFmSgvLC aaiwHxhOSufhsWaj81OtNCjXKdTszeHBuTSw8qJ9GuqzysX+LeQhjhrwfstI w1VphaZ3pTyM1Bb3FO5OR6dbjF9mEw+hRkd17QLS8eRr6PCNZh5kmqQSRLLS kVksvsGzjQej5mDTU1PpWOz8cGH/ax7uvDAvXX8rA1+tTuyvGeNho90f0XeV GZg8YnR07hQPLd0lbolDGeD2bNHT+crD9MBi+R8bM+Er6Zp28DcPNh/fR91/ lYklJukv7otSEJ0NczRTzEJJ8pxYrKKQ6nHQSd00C/zfm6Zt11BY2anuLHk6 C6yjjgVHNChso3e59FRlIW6e8gMTHQr36Mm8cs1sfHPxH/TcRoHvSJguwzAb /kOPpKR2UDCVOlWeYZuNvt8Bh9lGFJ5f3HEv7GI2/vC1itTupDCxf/y+ZWs2 Woo6eVbWFDaIdBlsG8zG500nLyfbUDhf/aBa63s2Xq/5tajDloKQWkqttGIO VHxPbV7tQEH5746GAa8cDE6qGh5woXCAltLs+08uZie9J7t8KGQcvrzLTTkX pz9V7g31pTC40Oup3cZc3Em7LavoT+HMBcNnBodzYal43M0wkMJV64kOoeJc aMgUZqldpNAm9Gr/r9pcfCn6NHojlIJMVV3neGcu4reF0CcvUchblfqy/Xcu nIso8eRwClW/DbvTd+XhW4TIkvhoCvPKNByuO+ehx4CRWXWVgoX7kt5LfnkQ 3uQXNxRDoat9ou94Rh7eRoxLK8VR+Lcw9e268TysSLDgmCdQ2OQYfmw5Xz56 XCV9TW5SuCh5+p2UVD7U8jp8ttwi5xdi9H56Sz5eLWQlyyRRUNk3OVJ/LR9r xsUVY1MpyIWa6bvn5GPJyKsxr9sUJIqzr80vzwcC2U/N0yj8Et6vuW8wH3v/ 7Nk0lU7WW1vu27+pAOY6PYm/7lBonJRoDNtTgCqPxEl2FoUK+ZMyKq4FkDye vt45m0JBoPw9zxsFKMlSfVqaQ85LK+zvz/cFcN0nUbg0n+yvU7dVxkwB8q3V 8hjErrE6OZAsRJuuu87GAgpWI++NorYWIrze6qhBIQVjGSSpWReiM2h6dSWx vnHqcIt7IWiaTV0bikg9ZltcXXSrEM/Wy2+Vp1GQbc3rpmiF0BBolYohFvv9 e+2h6kJsWLBR4Svx9EF2a/ZoIcxPrJ29T6fQKi4lpbm9CLMG31+sYFKoN/A6 3n6gCPMTr//yI/6fZxPl51mEvvCJjjrivIeB9pXJRdDZNe+tDYvk41s7w4lV BAUzV93bxNdXrP09p64ItertId3EgaF9d3ZOFEFDulbCppiCV7Hu1Bg/DX6m mwNjiY/13NhxYwkNZ2qK59UR24mM3tTWpMFhsWz9V+LdeoZDL4xoCHwfULvy LgXD4+kbg+xpmPugTsSaeNOtr1HyZ2jYsuMnM4R4+adCNZc0GopjxdY9IV6s wBcsWEKDS9Sw2gTxAkv7FnojDfL+c0v/YVPgDypT2N1DxuePta4l/lEoemZq iobQlIdxZsTjna61twTp4Gur+eFMPMhfLaknT0dG22+ZQOIurcUu3evpqF9a 9C2WuMXJm3vBjI5BnQ+ZWcR1sY8FlA/T4Z7+XraEuLxi+cGGs3TUdj7xrSZm jQTT3KPpsD9Ww3tCnCvzYnr+HTrymsZGO4lTjDUt73LoEIkIlOsjjj17JWPf Yzpm5K/ve0d8OfvNxNd+Om7fs7r9gfhc62akfqVj6ci7X6PEYpq894+FGQib 0Y34SJwfpxU7I8/AZp+zvv/9159gamusZ2DX9XnPhonbd6167WTCwIMUh8xB 4hOs3NB4ewayO94P9RL/FVVUrfNiYCpckvWCONHzdsuXMAYqpnZNtxCvbZby VUlmQNBJ8Hndf+tfEy97kMFAjwQL5cR2MaK10dUM7NjDMmEQT45GuVV0MLDd wX8snTjSnP+f8WEG3oT46/23n/L0CxyFGQZW/5TTCiYuE562txJnQi2L13OC eODhp8IyPSb2e446bycOWOW5e8iSCdu/EcZriBdcGf4i7cxEUGHQp4XEm037 tgdFM0FbGsB+Q+qhrcDuAyODiYCesNZGYjeBzrjeEiY+Jk0+ohPfanjSjddM WL757HKaeM1K0zCfCSZmjl0XsyKuDX+wKm8OC12NN2maxBOG//MTXMNCmmR/ 9UdSv2YPCsSenmdBK+vdF1vi/mXK5DnDwukTKmnriP0uZTho5bGw9qWOtRBx Dm7RbjWzcD/dSohL8jNTdcnwkHwxHMpLP/MTsyscAj5UFeO32s9l5xnkPpHr kpftKIan8juaCXFvkHW9xXAxPnECgyWIRTabS9wVu4tzjMcL8kneXcp1GX5H 7sJhYMHGetIPFnMl++fMYSM9qH/5EOkvjrEzNkMybJy78PhMNnGu6/vmJnU2 Vl37IedIrC597941OzZy1q5KbSf9yjDAOUm6hA04L7nMI/1MN+NgYeK6EoTu UvN2yaVw1KnwMK2/BIfsazrcMylQg0Ytz7aWQdtfKD6A9O+6k5lL7ce5GNNQ ipo9T+GbqoF4sVc5HEOrNmm7knxOMyWWqlTg9u55ezZakvlnnan9d+/jeJv5 xW5y37ZEbGhtWlMDk1P/W8OnQEEpfmyaPlmL4PzcuWbzKIz9GOh/oVUHpXUW xTsneMj/WPlE7Ho9nJ45PfXp5EFMoejT0FADpA93HlO5z0OsB88te2UTZpS9 5sYX8PB9O3PoROhDHNlUobIqjgc/7QauTP0jfHE++v5sAA8DdxuutSs/QZho y8zkYR5mTnamq51vRu8bNdYXEx7W7hD661bZgsPC2sq0dTyY5Sq7ly5uRemY d27CYh7OKRxZ/tbxGYbSF4WtnsOD+vgB0a7dbfAPOTffaIyLReJTwg2/2lAt KKGR8pyLeTXp7BUZ7YgMEhBOrOLCc0PlaxHLDvz8PLKttYALpvmx7OrvHWg/ 2Oobd52Lb2NyEsPJz2Eo8ooxFUjeo/vN5iYad0JKnNWVdJSL0J2RWdzhTvQd i07uteRCuc/iVV7kC6TrqwTn6XKhrxeRKKv9EitY91+VKHHhqPhses7zlwhf dm6zw3wy/5O4Qe+wLrAr31ZafeEgdZ6Tn/XKV/jOdHvV38fBon5eLn/DK9zO MdUcf8SBwIUwm80+r2H5KkhhZxkHfHQn9uDCbixv9ZbVz+TgbBo7bmFdN24f lLO9GMVB1dpoYcnTPQjvSJEw9OZA0uKs+mWxXrwes9FLceCgV6PtedD9XggJ aCwzMuGg5A5WDjn14UBQu/RFLQ4Os3UlFf72oV9/dYuOPAeXInPCehn96P4p mm8syEHxiEK62K4BrHaeFX/zbxn2SYptevhrAJmOK7S7e8oQI8C/tJe4U/Bc Qhdxw/S3P1PEvbNPpjqJdQf76uVmBuDS78t+RizHKbY6TWy6+7F6I/GgzW53 6d8DOPL58qoSYr/U2GSXPwO4b79eIYq4OPZSUCCxav/1kHDi4Ut+jnHEzqXj PZeI7Twcl5cTWxjT04KJDfTV787/O4CxpapLfIgFe5sbS4mP3tRc5EiMthpa E3Hv3ISz9sSBDZxrPcSrG7602xJ/ZKXvE5gdwIb1FfH7iFsvePbZEUtXWYiZ EQudPVLrRby4gO1lTLzdbX/eZeKPPVJPdxCX7dniwSLm131zbSvxmOG6XQ+I d9qbjm0mXqm3Yt1LYqdmloUesdPaxQvHiI1jFzE2EKcoiX6bJZ5JPy+iTfx/ YS8VyQ== "]]}}}, AspectRatio->1, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.1\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, ImageSize->{500, 400}, PlotRange->All, RotateLabel->False], {266.6666666666667, -640.}, ImageScaled[{0.5, 0.5}], {500, 400}], InsetBox[ GraphicsBox[{ {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0.007170499375738244, 0.09059928053234424}]}, {{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVz3s01HkYBnCUosugTmVIVjOplihZ3XtCRaSSEiXdXCKEnXLZWoQUckpC KNdqlWncFYnNVHs0Sa6JmSmLzMX8oqiRzH73j/c85/PP85zX4PjpvZ4qSkpK h8n9n3aeg2/rRds2M1JixxUKClOtdQKFdCYKYrK9eZMUVmenZ5XRzVHTsW6o 5CeFvoXMqBDDzbgh6LlTNEHB/nVn6S36VnyM0bR5/IMCM1HvjkJ/BzIzldTb xylM2J1IO2a4C6rRnOSfcgoHPL7VJtP3gZk27Ob/nQLXWqeqIcsZy3O9LpZ8 o7CSsan4q74rvD3vm02MUVDrvZDnbOgOVvurVbmjFPimcdZX6B5YmP928fwv FFKyteuXHPJEZIXmibARCnYa9zc+zfJC6sZf9guGKVTKeL9R+j5ocZPvLPpM IYk9Z5mjYQB4WaO/O8ko5MzbfTGezoLRIkZVlYjCH6/TuM7VLIjK5BuXEDvH flBhHDoDV0uj3uRBCrNGgyJqss5iu/PBsIBPFELbUkKl+mFwub802rCfguP1 9767DP+E1DwoPP0DhSi1sqWX6TFIqF9TEtFJwcU1l/N5OAXn+EeSlhdTmKmI crNZlI319sFlqQkUljjKBhsSCvDvibvNH7wphDStQ/rXQly+5lftYElhQbmW QFmZA452aC5Lj/zXa817s7EU/au0Ep+PyfDM95auq7Qc16si60abZRg13KTB 9q+CfF9BZAdbBhX5A03dJdXYrHSeJo6TwUJxtNLp4RMcvRF4oNBDBl6MedOL X+uQ3f3IerOVDPpXJfJCWT02ff9yjqYng+SbUNC+8hlGWttPRY0PoUBc00hL akDXyrB8i/Yh0PTuUX19XGgfPv+4oXgIiT4VXjnMF9gTcO+oOGkIY1se9J2M eIkL22u7DvkOgWXGLZ/f8A98G1dbHLcdgvAhN+GtQSMG6l1sqxlD+OHblrk8 /BWen+UxBxRSGFlOn/Sq4YHRmtF9SyCFTZ6Bd8mCJiwMnFXKqZYiRO/I4o9u bxD8OJRre1MKY+n+mZ0OzehMqzpWFCrFXI3PatzxZji1OCB4vxRT6zI5jKy3 8K90Lqk0l+KUeU2Xun0LxqMbNTy0pHiw43jO07EWnGZlaAtkEoxKdDQHUlsx ov716+smCSqcbKakbG2DT3/hgEmRBBG2sdnlA204Ej7NRDlRAgO+3bv82HYY bWMz0/wkWL8mJoVu1oHa74Fad+0kcFv0Rq7c2oEwG+cvekakv/FKb2BUJ1Ri 5Jbz1CVIn+rO2st8B3eLgnlBIjHmCiryVLjvMNdgnJ/YKIbq+ah964K6UG55 psO0UAylQndO75z3mFhZNds0XozgDM6VOc/eg2cf015zUoxao0tqWgHdGJ5b kTrDVgwtu2DjC7QeRCRPmLGXi9Gzork17EkPVsXxlvWriVF8G8w+dz5S5XSO n1iEwxwLLb1JPvLvsdLZPBEiY3Ojeu4L8JFtdTShSAT2oF4mbacQOXyTsuIk ERy1aGtfjguxoTlXMyxAhHhVFd0e4vmMkbVniLny0Z+fiXMVVseCiC16+Q06 P4R4sX+gxIdYp4y9O4DY7uxqp4PEvfscvOdNCGFy6dONDcSs9MTUEz+FGJFV 6k76k/3EyLBQ4rsh2lvHiQciWW5XiNXiw/3GiF183BZXEbfbb6mVEW9ab/xw xqQQ16xb3IXE03pePS8hjp2imVdPjOa6v14Q05aGNz4hDuWWJXQTW7f1jTwi FhdlOqoqhCh/VWNdQtx0/hTfhbjIJLA/l3h68JF6f+Kb2YLZt4m3eDnlXyA2 y3CwyCAu3bXBp4jYx3hFXDKxxMp059/E07m3OEnEzDUM0w7iPf20d/HE7kYL 5kiIt1+NVIojTtOfOaog/sQdWRZN/B9o8gqY "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwV03k81fkaB3AdlJaxjoSQDhrRkbKE9MnQVUgjEjcRLSpkucZS4RzRZiky krWJpkWSs/2aZIkTZSdFtlOcK2RQOW2W7vf+8X09r/c/z+t5Ps/rq+0XvPsw TUJC4jx5/68Oh0faq0e3bRHtXtuYqFm2RcpWLUSoqoNueamnW4eTsbEgK5ej aoKDV4yP7LmVDdFKHVak3hY8i/e3Vjh1A47NXew8VTuMnz3uH/7yL+gka9z8 obUDDw/G1tyLv4tZh4NXffWcEWEzmZ6XV4KxhE6Bb6YLfjnrdTJO8wH2HvpS ka7qhgwf1WYJyzIIbNWo2lx3fNlvPxeoz8Z6uvWDaS1PrB2VT839xEYu7cAd 3cJ9KApxHdubz4HMYPwNdz1v7PU1DmIxuHj0pqO51u0AOFppARa3uQj57ZCD V6YvNikcG5uR5UGvWlw33eUHpapRlfLDPPQbnbNNUT2E6l1ybR/v85BRsKJa d99h6Dj/3PF4nAcHububK3OPwGjpGFu4ig+JOKu/3Qf8EdSUGtPrxAd/osl0 UusYRqIFK6ZD+Qj09maf8z0OlZ25S6zS+FjdMslYVRgA+u23D64W89FtzSp+ KArENW32heYnfKSWKP7ioncCcupyHaxOPrZpFBWN+gdDXLM4CCI+Yuuy5Z+4 hcCtUd7z9Ac+PGOHnFPEIZjOPOqeO8uHiZlhimdmKC5NOyh9kqYgNxHeqGse BuvSgpT6nyiM3axY/LErDPpij+k9P1N4un/h9sqo/+A+9am5TZXCdeVdZy+q hqMy/EWznyaFU81XBe6PwvGGsjFfv5qCe+IbGn3f71Af9U7fq0vB2FrfZnLm d9h4aqV8XENhmTg0rjw3AuuDWItU1lJ4d+9RxTnrSFD5NQFdBhRqDknOug5E osY0YIPtOgp5K50sV8VFIdKPdcGfQSGqMyNqXCsagn3mKbuMKLgm9/MfVkfj nwHpy1LrKTDs9MQJvifRgYr4VOLFsyc2utBOwSHYVHOaWMShQjUKT8Eqp+mD pTGFqgCJB6O2p/HIIKPbnzibvmOCJzoN+x3/aogljuhNM4xPjIFkGcfqDLHL lZ7jznqxkBNlL4wiNnSk31Grj8WsjU2uD7GMZOC7Yf84FLSEyGwmDtvfk+4p xcSM/lspOWKfv+fLqtyYcFrBXNZD5nFSprfr3mSi/tuZvfnElqH2U0liJmyM qz97ESvrX2Z4ZLIQVBmY3ET2pSVyd1YOs7DpRNx/Y4mn3nQH6pjHg30v34NB 3JilXTzVFY8PX3Y5nCV5sWQ4ay6oJkCp5bMeneS51j7tPDskARettOarDCl0 JAaP9tYn4OjpVeJ9xDqShsWMiESsGHjZlUbuUTdXxOjsOIv0mXDLr/rkfp8y TbWSL+AhPdu+XI9CVv9JW958Ksw1GuY3raLg4fln6dSHDOSXnyk3VaKw9AfL y16zAMsWPbT9+p0PXZeJkdqkInQ3yvhuH+IjssUCWdN38NzkwON7z/lQ4SoM LFhQChmq/WhvGfkvg7ZNrZvZMM34x251Fh81x/PUPce52LXnkObXWD7EetZy JUEUjkq4e17x54P2rVheXfcR3iQG5zg682H24wDf9f5jBAneldeZ8dGUYNJS t7YKbgbM9kYtPrQuv/92Z6IadWPthR8X8vH+i3Dg5foaKHMn07omeSgaK2+Q Ta2Fyil19cFXPMhq3JoUiQRQalL8GlnJQ/Ix3pHrOnWYs+Ip19/i4fPWYtHR uHoUHzTP2HqJh/ANAu7y2mfw01veHRLFg/C+IKlduwGnR2PcW314mDnemaN/ shGH41rplD0PBjaL5o+UN2FbUIPwN2Me7G9o+5eptGBsKitTQ5WHSA2f1W+9 WuFWyai+RuPBcHzP0q6dbSiKULfLJrkoyU3JCL63YdF93f0dnVxIVeWU0nPb 8bhWzZpXyUWASfnrxY4dYFQMnXrxFxfFO/yuV37ugPB1kn/kJS7E79XkhzNf wFdd0fVJNBc8V3vJDLtOXGk9t83Rj4u47YkF3OFOWKTkPY9y4kK736G7MPEl CofaVq4x58LSPCFDdcMrRCdpz6iu4sJLs/XbghevEEB72ly8hPRvSBkMYXWB 0WY3lPiJgywp7/DdOt3YWFjOnO3nQGmAd4Mm6IZBwb9nPzzjQDqG5WYR+ho3 1nzdZMLmQOKOd+mgYg9uq0weks3jICy7NEWxpgcjS0ZoFmc5qDA4L6Nwohdf ejKfDgVzoOAQZhgv24fQ7FeN2vs46FvX9iL6cR9yKmxbuXYcPMiHjsi7HxXZ OmXdRhzsLzVT0JjvR+6DgolIdQ6YiX+y+u4OgLbX8VKINAclIxo5sk5CpC+3 SxJPseGiILup/rsQNWONSV09bFyUpqn3ER/W2jrSSSz4Jp6bIk4v5Np1EJsN 9teqzQhxPjt/rolYjVOy6wTxu18jgmuIB912+ivPChESY+JaQhyelZx5cE6I mGvjameIS5KZ0VHETlXHI5nEw8xwrxTiIpPRFzHEHse8VlPEEz+9S44itrY0 vL9kXojxk8PzQcQL+xqflhGnb5ke9CBGW9XtOuIJr0i4E0cJOEm9xB0N33Nc icfu5bhI/xDC7A/aHmfilpiAfg/igyLlelviRWE+1UHEknE5dBvirUdcC+OJ DY9pM7cQs52tjt0jXmHIsLAgfv+rkdMT4h4p3h9mxDrmdKNXxLrrNn/cSOxt oKL4nvhrUa2zMfFVraXiH8SugY7FDOL/AXXYMJ4= "]]}}}, AspectRatio->1, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.01\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, ImageSize->{500, 400}, PlotRange->All, RotateLabel->False], {800., -640.}, ImageScaled[{0.5, 0.5}], {500, 400}]}}, {}}, ContentSelectable->True, ImageSize->{1078.6666666666667`, 865.3333333333334}, PlotRangePadding->{6, 5}]], "Output", CellChangeTimes->{3.414230520756402*^9}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJztXQWcFNUfHzbujgZFRTEQA8EWu7u79Y+t2NhdcHR3dyktJZ0CEtKCdId0 d/3+7/t7b2Zn997Ovdk78Dz2Pp+d230z8+ue2dlHXvv8nbc+fO3zd994reR9 n7728TvvvvFZyXs/+lQsBfNYVrCMZQVqlbTwnizL3sT8XYJNhmXP1c34F7Ra VSjHqx2cj63M9m/Bv4Czv6Pz0b1fd35LuX+9sxCIPrK1ZkeGc4LR2Ftrdqhz NjgLQQ2emB0tXOeY0pbhHAPa1Dkb/dDW3CUDyzkU/+UnK+R8Vi8G1dL8+OaJ c0/RfwnYY+5Yrcj/UmN91P6M/1ZZfheKPYYXyvjfF4zADOvwWqwsK+jeZ5X2 gNUtF/Bwtjzzw+jTGFRQs3aRZi0UF6UnPP6kgxfWHHdhPHjMlQ6bDkqnE4LL EsdPpdl9nC/6AnjX5YTg8qysqzToACuj2WtqjabHRUiPS0sMlKwoMqfzptRX UbPLIFz4Oi7gEFfW914D+41A4aWuuY4jpSqK/kugwPlQQhZ/ebDp5HxkYs9w HaSjJWYtVbOWYnhcdq8dD7y5mTdTvDo76GB4XE7nLbfgzUm86eJpcd4mw8wJ yFsyzOQevDmJN48w85oE5N4ld8jP+K8tsnWmddlxWNPhbfIf48FDHa9G72LS dR1VSM8yrRi7Qq4dJevy48CKToSNs8jD8jHLee3Q3kPHhYfsUkdY7a5kVaJt y7fxzt3Y8iSoaaKg9m/fHwHFO85IgDiNnFdNXMUIFg5YaO3XyCCrevyz+Z8M f8/GPdaB+DJ+zVAlwThoDu45SFVSqtDIb0Zq2WiSRfg2G9tXbvdiw6NeozbX taF2N7bjT/s0x3WIg3pWp1lZRT3iqxFUJbUKpOQL9Zxucxj11qVbE0W9ZOgS BrF0+NKEUG+YsyFR1Ad3H6SqaVVp+OfDfaEWrsCo189e7xe1MinqdFcnanGZ vHK01wdqISVGvXL8ykRRT2owiUFsWbTFF+rVk1bzeYsHL04U9Y7VO6hSnko0 tvJYX6iFjhn1vF7z/KJWcyJqe2Nbqn1KbaIjZO3xgVpIiVELc0sU9eD3BzOI qU2n+kIt/JnPm9F2Rqaog5EQG6R9W/dRzaI1qdtD3axdzt5Ozjt5IO3dspfh i9DFygi5soaOH1Uc0e9Vf2ctrp26VqYbQ37gbsA3vsZ4v6K0Ue/fsZ/qFq9L 7W5q54Fa7+1APebHMfxJlwE80Ktqmaa1msZgpreZLgXrA32NwjVo2KfDEkcf oqNHjnKCSA+m09xf5u70SUGTC5tQr2d7JUJBqqJg3fR1lB5KZ+vaOG/jPAV5 37Z9bHS71+8W2JAMgrRm8hpaNWEVrZu2DieKbRA1Gy0dsRQvcRy2IQ6m83rO 45dwsgCELA6d3GgyLRm2xM2AMaPtb2lPne6UlwQX8DZMh/cfZhLx2rVuF6gX yCWp8HFBoCJSEuwilRYOXBgAfWKn0DxbAYi0Se3+eHcaV3mcQu5LrmlKruvn rKe6p9el6gWr0+wus5spog/tO+QQrQhXRKfSlsUO0fxaMW6FJHg4pCqpndtj rkNtUG0n1plIE2pOoPHVxwsOROIXa0M/GUoDKwzES3zCNky9nutFPZ/p6bx6 PNVDHN/57s5iX4fbOlCrcq2cV9OLmgqcjUo1EmfXP7M+m4d4iU9ieyZcRpw0 6N1B5PqznJgUR4vdn+hOzS+VN2S0zaJAwhBIWEngj7p/SAnUiEgAnhkrgd7P 905AAmGqf5YjAX7VKFTDOouFIHzwgiaxjJraSl7eptDONTup7fVtORAhFqLy FJEhnzIlOnKE6Lff5OvIkQft5aPkSE24adA2/cUZTd8RnHiJZG+b/sz2MzOY /oRaEzKIcvgXw2NEGWRjgi6blm0qjhPCFGtd7u0CYcJTxSchRLFtWqYphMiC DMQRZ80iNa2SyqaEaKP21StRz1EDwp1bRUJlSn1BqNJWq0PPgLcGOHQHFN3D PhvGtTE4k/yFaNS3o5hnvKY0nmKLAvXouPRxNPansZYtMhE4YuJdkJaNXOZI PMDbFNq8YDP0wa+9m/eykkQprgsmXnEPRox69ujBw1j77TeEI5iDOu4lnS1s cGxh65KtWbGFibUn2nIRa9iGUOix/Lo92A2ZK+Ayh1jxd7lPmcNdiZsDwmeU OZyRBXN4M9YcQixgZQ6ogiSXQfqzxZ80+vvR1Kd8H0cac7rOsdOapzmgqobQ /5n5jyUVEaada3c6+tm+fDu3xrrrnR7BIp/aHjl0hB2ycqAyB4zaxWpTyyta 0sC3B7Ju4f8Hdh0IqdjC1nL55cTXPvHC+yNHiqjwiyGDm7BN8zc54Rc27A6/ sHMwu2jQIpWPQjS782zbbGhyw8m2/EZ+PTKDlw2pOMQWP/V+obetFVHSspVA b7b2OtzqxGKxJi0H2oblNDingcxCYgvrgAxgK2cpi6mWv1oGiwmqTIbjqxeo 7oIbQuFp40feD4GssLKOIR8NyWAdds6Z231uBnNAeQMJYRoXVF6HUkRFAlVJ hTngu5OeqKOt23yGhlkd5YxgxXl3Yc3iGY1ULh9xoQoNhw9EyiSBN5iZcn9z KbeLS7mNIsr9Jla50fWG7Vv93+jvZFoRLrKi3HN4G+ImJT0lndLD6VBsUEWC Ruc1iooEIjA5toRaLioSHGvloiV2K1c4o3W7P18voHQnwgRXfKhbhL+HWAoF qNZJtRzzbnllS6pVsCo1tD6mWtZXVMf6kppYFXkN+bn9ze1l7A1Ts7LN7NjL rzqn1nGEXTVvVUfYdnmHCOP2pFon11IxW8bxKCWGWdwh+uXRXxyl9y3f184P wz8fniEgoHWz067opD3j7ICMcRZjzEhyyxhnVcq1vvPlWKkME6KAREdYd9ME 6yaaY11G877uIvAIekJMqNi2nObQL9Ki7QqDPxicwRV+fflXRyqiSrJtE7En 1hUaX9CYtdOwZENHO3ash15KqLrTpR11XCqKpSgNwzgAv+0NbQURWVLQlCZO XYSwEKugBf0XGCgo6FaQOA7boD3oZvF/489RCvO2KB05eIQ2L9rMZCEUoZhH vsEAFrGl6/1dPb2k8z0QjUxIKGViq10kXEgHs2a7EsLUDZERYU7sl9IJu0MH v/7u87fTGa/+Y7UTcEV5YHercHOOFDsPWL8ZWqs9gOtxUyPHNAppTCPA2xDM yTELYWK2taGxjs6+IXfEpL4vKQtJcUolyLb7k92jSybpDXayEDIIqhwi2HfK TcF+QFmD4D4mcEbEsH/HfmuwPzuQu+JWO8t8CTWNwSwtdQ9Ntq5j919c6l5a N3UN623DnA12tBFdV1S0EalWfvshs7He6Sq+x3R2S50DIpO9kP5QnhRlNt47 bMj2EX/CToJNgk2C/a+A5T0HnXedoteSISQJNglWC1ben6D/xpdudqND2cQn DA9yXo3ehf/aaxOmpBnc5REXnk8ydSAYFd/Vss+RiO5WGYNzM7s3xvQWMFMp mcLL1LY0IALxEMS3Lj9Qco1zJsEmwR57sMnaKQk2CfbEAJv09STYJNgk2CyA TYaQJNgk2JwDVnbZ5s/eMR0KNMkGuIlMekLOO4PBSdwzEv8qUeaS8ffVoSxJ JPJkj6wQ5w3F5wRHB8KfTSUGL9c4bBJsEqwLbLKe8gX2UimfVhXKlXLeFTdE 9YrhuR7oz8e/EE4MOyBCzppKA/aDGQt5HlzEkOpnjy3KzJjlZ1mmOe9SnHcB 511Bz+N88XlMsJmzGHQkF3mEJ78r4HlcgixmIzYPFjl6hPTPDQ1EI495QmgE pW4tbHiuqXAezoF0eoiVb29Ki9ZbBEFkzT9xunNNhfjQv05VZiKLkX8EbEiD NLIWiF4LRe/1PteX8HIIfVkTY1BDEu/NG4+4uGdko/COMVXZIDKdtiMhOCbX mgLIbgkeNyITFqh3/DCg1RtAEbkWVTc/koMIchft3oKyxwatMn/Ed+SkVInD BmmF7NPtv8RBZ4+p/he4OkbxNVVzRsDw3OMRabObPg8xFncUGuNVAY12IlV8 ON4ZMWtFogEYyO3Bf5Mgox4kAqKoZs1/l+EfXi4hk7VcwHlXVLPmv/32Dy/X TF2SYJPjuiTYJNicBzbRR3zGvzzlH1bWbmjntciDEQ0ueHqfa3Tp09ct2HEv eCZyC7aBRPjTv3yLf9wHN/q6Ghv38YyJXI39bzlmEmwS7LEHmyzHkmCTYE8M sElfT4JNgj0xwCZ9PQk2CTabwMpnPqfQnj1EkycTtWxJVKECUf78RI8+Srpu WYdVPfqcjh4l+usvomXL9F11FiczWxW1q1fL5wDVqEH0/PNEZcqIEBCkgDgT VJx0EtGppxK9+SZp+/1Ehzk7eJvGjyJatIioVy+iH38keuIJonPPxYlE11xD Hoy/Gr2LMXnPbdYplvcKEf/5J1G7dkQffUR0xx0EPiXLKZQnjyQBpFSuTNS/ P9HKlVJ/CU6MNirMOwTbv/9O1FSAeOstouuuI8qXT2EOUygk5f/000T33kvU uLH6aoDHnCnuQw1i1lYrEgQnNGgQUfXqRM8+S3TRRS59p1CBAkTXX0/09ttE zZoRjR9PoDq/BmLce+ANqPlHUbN+PdHw4dL6QM2FFxLkb1NTrBjRXXcRffIJ UYcORNOnE+3bR2nZZBUxIJYqouB5S5YQ9ehB9PXXRPfcQ3TKKYqoVLaP886T 9vHTT0R9+sjDxWmW7vJUVr7IsFKRdFjErL//Jvr5Z6IvvyS67z6i4sWFTUrD KVVKGk3VqkSDBxOtWUPyHlWvmJG5lnRrCxRFBw5IdcCJPhTh8JZbiAoVcjSX kkJ01VXSymFHEycS7dxJp2og+vtxlei1JTHUtG5N9N57RDfe6HKsFEpNldS8 /jpRgwZEY8YQbdtGJ8cXkS7A/6WQbRTuPGwYUa1aRP/7H9Gllwo3D0e50M03 S6lAOqDr4EEqoYHYQbM2X2ER9NHYsRwEmG48fs6FpYgwtdtvJ/r4Y6JOnWSq OHSIdDdae7A0g7dhWrVKxjnEO5Gr6KyzIG+J6eyziR55hOi776RLLFzIT5Ar acjPHIVC5DHq3VuCATgB1kEhTJnuv5/o229lJlDudJY/ZiYryQkx0Ny5RK1a Sfu7+mpCaLWdBcheeIGoXj3HEGJ/7zcuM9NcKCDxLl2IPvtMphChEVs5Qk9s FbAOWMnQoUT//EPn+eNnvMsSRo4kqluX6JVXpCUL/7KRpaVJFt2uJmqQiw1Z mqSwiLhKU6ZEyhaAFKBtLMKbOF298470MiRQcYrul3s9WBqtjMHOQlWqOCnf MYYSJaQxIM517epY9hWG/Pyu+LFzbcOGUmqXXcZWYPODwgapBdoDFkRXEWUv 9cfPMMUPjBt5AMb90EOMyLIxBQIyr8HmYAzId5s307WG/IxS/GzaFJ0qL7jA lSrDdPrpEvP33xP17Uu0YgVZ5fwxM1BhQrKB/8QxblQpCEYwkNdekyXCrl10 kyE/Q5XI3CHnscfc8SDM6dXOZ0OGsO9Y1/tjpq9iBplh2jRps+++G1NyRcwa 9Y7LrG83ZGaAwoIy1p2fo0qGFBRYXNghHsCLR4/msHOLP5Z6KGRC2OzkqCKR Ga68UpsZoDqoEP4jVHqPIUt9FBaRspwEb6dUkdrcCd4ddf74g6POnZmwxHu6 KhQIbKOEfdepI70DtajwFtuk0XcgEHzzjcwKS5eS9YADJDKs6K7AISgjw0AB iGDlykXFSVGdOBmzY0eiWbM4L9+NszMbdXRQRougAuXVri2dUBiqY7TnnBPp GRDbUIQ9bij0Li6hgy4I/f33iW64gShvXoeFokWlaaEqRSpWefJhf3bU2iV+ MAOLLF8+g/hRVD7zjAw4KmZZzxjy016hQKtl98JwMdHSRZJKmFVy221En38u Q6MwButJf8zYv4azfbu0JVD71FPujBLmCubxx2U4QSoGJy8actJKcbJ/v0yP cLpXX5XpXZNOvviC6JdfZJEkNPOsP2Ya8rZgBs2ULs2xnrti/Efsh/nZ6URU pPJrdwYMNVUM2WMKOC+cGFWFE0XCdNppRA8/LJtyO5+U98dNHaUacDNihGw5 46mmWjVZU6MYe9OQkwaKE4T4qVOJmjeXCSlKNWHEYe6mUVwiR4vEo+2APDip rvSyZYvkBHLHsOT88zPXy7uG3NRW3CCKzZ4tQwAS1rWiUBD9izsoIs9DL/36 8WTCquCPm8pKL8IN2B1QhMVm4JIlpa5q1pS1J/RS0ZCTaoqT2AwSFczCVLgw 0Z0iX3z1lQzbsLD3/XHyveIEGRG9EhIJQpagPqr8QmRDgoE/gRuhx88Mmank UsvMmURt2ngml08/lUUAZlrC/z/yx89XCpnOop0hjYzMzz0n2QXbIitZXxvy 851CgYplvug1O3cmqljRNNN87o+fT13CQ1pr21baNNKAI7yITVeqJMcXotS1 fjDk5ytlAsuXSyuCNcGqhHVZNvyCBSNpBsF58WKyvvXHyYcusc2bJ1vuDz6Q szKXTaP2Qhpw23S6ISefKk7WrSMaIArLH4QIHhD1TrFiEWPGIAPCQ22AgRjK dFHb/ZgJM7znXZekevaUqQqlvZCO5TZjSAq1IySlzLiqAyRSdX2owG3dKiO3 HUXOOCMCDq0C+q433iBq0UIW4iIqsE9lVnK9qeCjVYQ4MGp78EGeRkeJA9U7 NAGNQDNCQ3UMJf6OQoHcjlSIVhFhQoT1DOHjpZeIGjVy6tya/sznFYUJTRws PD1dzlmEE1juJgGOHiOshobMvOGyULQicGxMtyEfV/5AwrUDO0oMxI56/ph5 UTGDqIsBCrIdQIoCOEpsZctKY4XoJkxgsTUzZOZlxQxGsbDBbt1kaL31VrZX mxmM2mCucDcUKWvXZhi3ZsbMMwoTml50SkhWiO8wW1fIRaZHxsfQaNw4bnhV HZ05M7a84Ni//ir7mbvv5p7acvehCMEYGsKSlWM398fMEwqT6JSoe/eIyISc nGCIShVdFfwJvbXIhVqqdWvPKPioHdH2Qxqod1A5uBtDJEcMihDvUcuI+N/G HycPK0yi83eCIYbeJ58cwSTiLssM6QsjHFVzdzFk5vEYzSOzoxC+4oqo8hGX ghAUMDeG84tgYXX0x8x9ihl0QxAbypBYsSFUAvObb8rBJWoNIbbuhsy45YWp CopdXD2JBBipecgQshw4kHDxxermj5O7eBtiA8NsAeYqomPQlf6AAcUpmjHB sJonZM6BLSTMITHdgLzhcZFaLsxzVRQLGK8DvQgNVk9/HNyq0IhQwfUz5mXR hiXrBWRxTPMgqA0b7ElP5mzcqawKJc+MGXKohHgSNaSRYRglXP36klvBtRpZ GXNyg+IE2csWGIrfEiX0VgVK5szhsKL7SRwdM25hIb6iZMCFHhGtHGEJwbEA YXEQKGZ1A/1xcrWSmT14RGWDCiem9UHZi264SROiSZOkdY0w5MQtLKR6CAvy j7hgmKsJTLkwIEL0xLxpaCac8J4rFHDMIBBS4WBoBtxhF5UVqi0MpyBKiGm0 AyFSVl2jYGE8iioNxIAoQZzlNh47JIEZ0S7ISXRmNZW8JlCQOzMYJ8YyKDcu uYQnP9zHwmQQv+HaiKpoEkRNYU0wlLQtDLsnQ3Xw5JNuswxz5IYdwZ5sYYzz ZzOlFRpM3tFwodRBMZ6WFkGDAIi+AnMfFCq7d5M1xZCNi5VNogJBORWnLkDH D5vEVToUbMLtrYn+OCmlOBHUMZWgFrVhpNAN8z0kdgcD0xQ1vLp2lzkntqQw hoF1ostCARApP2RqQK9hd2AoCqb6Y+Ns3hZAy8MKgf3AjmBP9nwEM3AMz2B3 6AeFtOYYciGlVNDpw1EhAxRA2iMYVNC4MoFJIya8MF1clddJyoOT010KQa0H C8Zgt3jxaIXAxZEiMOyFwOYbsnK2go9cjbk2mq3YqIosByPAXAxGsXOnff3Z mI1TFBpIAdJAQaZqGwcNrku9/LIcAqqKw1psyIYtJkRtFHmoWuAKIkxHOTqi F27gQD8Ju13gjw3752URsxD1UTxhYnjKKRE0GCXZdQe0gQHCCkM2bDFBG6jO MfGIDd64ZIwOxw64ghZ164ExGwUUGtSACIu4SoAaQxhSlDZg04g1iDmw3TWG bNhign8gECEgvfhitDZQmqMdtEM7EtxKf2zIW2/yc5eJahhBA70Rcqftgih1 EI4xbEVk32DIgi0iO41Cm0iZbhHh4jCKHHc1vtYfC/J2tHyMBoEKRSZmxHaQ QhGLxITKTxyzxZB6WzLoQuBuSBa6vIpuBYkdY2iPX/h7Ff94T8xjOvFfe0td UJGBcIHqACEKu5EF4ePIG8IxdmhObZwgMlmtox5DgYm7OmK9EokGpo5uAOl3 a3yO4/6QTQw58j6p/O7j+A9ehYoRyyhKkQVgIihedmtgx/3JGy2+Qlp8aD/R lNi2g5EHPBixED2lwL0zmzjmGwGF3DEiAnh0DMwWF326wUomoEI818KIALFC lPi7nH3u+w1136G0NGs6lPzpsuOwpsPb+D9Dve7Otmy4VU/HTqpmLcXwuOxe Ox54czNvpnh1dpCVmy6TdpW0Z/IOW7q6K2k2uZu3rISjDobH5XTecgvenMRb MszkSBw5HW8yzOR8vDmJt8zCDLeNebDp5Hzk7lI1yxT9d0lOX/0b/8KWeMdf ygrhnXoyKak5UKpln13R8+Bg9Bqf9pPEMs85iGUZcGAHnBOD0cAY30eGpwU0 e8POXnmjozXXWeAnYOfDuxQ/1FT0DSBhusLRICJ7vanRnZaiWQtpaWCFFTPE HPdgc3wRxZpyqjvYCF/E/tL8yPgjw9OMaODrQiEHhCkNnxieZkTDtszx1cqJ sLfjX0BzYooDu7bmkFTNmorweIdXKD6WgMNBKB6WgGMbMWsh5zQFe4ezkD9a JnWcHfmcdxGZqLMp+i8H5Y/k6r+xuhn/nAezUwfnYyuz/Xw1K+Ds7+h8dO/X nd9S7l/vLASij2yt2ZHhnGA09taaHeqcDc5CUIMnZkcL1zmmtGU4x4A2dc5G P7Q1d8nAMnqiPoNqaX5888S5p+i/HGTnx2pVfofF+3klZfldKPYYXijjf18w AtP8dz5Le8Dqlgt4kPfAxA5wGJTu2RgXadZ0V/BKZw6PP+ng6S5zXxgPHnOl w6aD0umE4LLE8VNpdh/niz5u+rtkFcp/gsuzsq7SoAOsjGavqTWaHhchPS4t MVCyosiczptSn+57mwbhwtdxAYe4sr73GthvBAovdc11HClVUfRfAgWO0awy ed3kxOMted0k9+DNSbwlL8/mSBw5HW8yzOR8vDmJt2SYyZE4cjreZJjJ+Xhz Em+Z3orv/1HXOek7EYk+rjsHfjPi1ehdTLpucBP15Zm6p9elaa2m0eEDh11f nvH/QG+xu3ax2rRp/ibeudvZkdkvwukgWvli9cGA21zbhipZlaheiXo0sc5E OrDzwB6NOPw9XjrD9J42L9gs1CsEI87a8NcGB+7ebBK9VqMptHTEUup0Vyfm sGaRmjTiqxG0fcX2XVnmUGe4IRYoBFmzaE1aOX7lvvjMZeUbN9J1UmndtHXU 69lelB5Kp8rBytT98e60bOQyoqMk7zXQumViOIOKw+0rt1PTi5pS1bSqNK/n PA/16eqlVLXdsXoHjfp2FNU5tQ6rBhCnNJ5Cezbt0X53r4NmTVka7d2yl9rf 0p4q5alEI78ZydzrvojnQRbfhGGl0eH9h2l2l9mOT6SH0+nnR36mud3n0qG9 hzYZUhZWW+H+NOCtAQyq6wNdmTud5WX6fd402jBnA434cgTVP6s+g6tRqAb9 +sqvtHjwYjpy8Mh6zak6ylKV5P5s8SdVSa1C9c6oR0uGLPH48qCOqEJKaEeP HKXlY5ZT/9f7s3OBsFon1aL+b/SnpcOX0pFDR7TfmtVRlqZktn72emp2cTNp FaWb0r6t+7S27EFeUUUexL9w4ELq+1JflpdNXq/netHMDjNpz8Y91ipD8vLa KhUW0v7m9lQ5UJnqnFaH5v86X96YZE4e39Rm5WNQC/otoAFvDuCEAfIAtvU1 rWn096Np2ahldHDPwWWGFOZXFK6dspZaXtFSGt39XSFQS/flYg8KT7MBHiX6 Z8Y/NL76eGp7Q1uOMwBbJaUKtbupHXvw4iGLaf/2/dYiQzKlQafANuiPun+w QsB1z2d60sa5G3Uu5kFpCQVTJC12hZFfj5SUhtMdeTa/pDkNrDCQZnWchSwE q51nSGwhRey+bftozI9jqHrB6iwEWNDaP9fqvnHuQew5SkMHdx9kt/m96u/U 7aFuEIFIIIJcgal6geos2sEfDqYZ7WbQuunrYMezDAmWX89PhWnTsM+GOV5Z o3ANGl9jPEKF+n2S+FTznvMU5zCBTX9vYuENqTiEA63wJUluKsu5+aXNqc// +tCEWhPYGrYt3wYZy+fkM7DIY2dOUvRBX2CxSrgK04c8MPzz4bRx3kb5qIDM HjFzkYu+zQs309wec2nUd6M4Wjc4u0GQ6UujqnmrUssrW7LCxvw0hmZ1mkUr xq3g/CNoHG8oVumyaXT08FFa9Nsi6vl0T8fEmpZpSuPSx9GaSWt8PuTgMiUM WNfK31fS9DbTWWmwiUbnNUJKtyQjednlGp/fmDrd2Yn6vdqPmZnZfiYtGbqE yykIzvQhRdK989LuDbs56UKncBTOeMK6+73Sj/7u/TeH3qX+WLpagUbo3bJ4 C2cBFMLIy71f6M2mjfoIrIWYtQJcudQ/sz4n3Z8f/pmzCeLf5EaT6a9f/mJX AYu7/tkFBfxqyKU0nhC7wm/v/UbNL2sO/5WWG6ZmZZtxnprRdgYtGLCADu07 5PeRITfzNj+cio1+1YRVNKvzLLYOBBzoqduD3dgAkWiFxQiLBfqiHPYalWpE ra5qxTrt/kR3Pn7oJ0NpbOWxrBdUIgsHLOREgFIPwWvHqh3QC6fW6xSH/JQM /LgSXkeOvGEoIHktMMzkw/wQjrrc14VqnRwJRzAH5KNB7w6i6a2nczktzMbn I2Lu421BVoUwVPbAeb3m0dSmU2lspbE0+IPBnKThvB1u7UAtLmtBDc5pgEAj 8qSkBNUdqmpEiialm1Crcq2o3Y3tAtT57s5CBsh0zco0o97P90adFEChL5wH +WBCzQnAJD4JSxTuJqpWzrvgZVKDSTSj/Qx+v3z0cgFICFpsQaXIRrR87HLa tGBTgLYu3YpHhojiF9LHCyFEaEOAhZ8E2Ty3L9vO5ads+VOkZvCoIAgDL7w/ ckT9sBCD27lmJwNI4W2I9m3Zx2AAbte6XfkYc5CdCTYA8oLYhkGzeAsDAUfi JXkTawiG8DrwG1RbcApJiJfQLrZBlj0aIikruR30ziA2XvESx2EbZM9FfhYv sYZtkD1ViJ7FL5UQZEOGfmoVqyU+CQ0JkTW+oDEbuv0a/cNobX+hs9BzbTGK IA/nAm2IDghYIrNxbAxQtXzVBOcImsO/GM5WKooyTpw71+5kRymtd5T31LIo XxytimYioESOtGKLPKAEDz+BrUD2Ad6GOCEoDaBRCCiBT2kyJUbgKTSuyjgW OKICulK8FxE/zHIOu+UsX0/3tGwD73h7R7Z5lCAd7+jo8YtlOg98mrencQLb u3mvY07C5mnRoEWOxUyqL60EfoNUBEtAbu/xVA/WNrwTVDQs2ZATIMIYvBKh 7RP21CBVy1+N18RLUI9tkK1CWYBYwzbIlgFYsBNpLSnMpbIqanhuQ6RyRIWw MjqQM6ebfJaX6chVKj+Vti3bxs0x0kr3x7ojzHGDIUoEIXqQXhimxMEH+oEy UPGgqkD+GPDGAO4DlwxbQqsnreaUBJiwmj0b9qisGtfn7YJl/46IsdlhZNP8 TUE2uhBDVUaHuB9UXu6yMfFJblEu2F4ujS7F0Z+twygDM3dklNCsmqugGqku tCixaoUxomqA9M5V6kc6jz0O50arP+xWP7+EaTn4EfwRyWWY9GXpag35nOUr Yqhlh29MZ2zhTm44GZHfkhJO5YLH9uLZnWdztdynfB9IVMXQEJ8DycIjej/X O6jCKKyj2wPdkEAtuVaQawDUUSO+EN5ergH1s56kLtbL1M0qT72tp3gNCRe5 HucO+3SYQCDhYYyDc2XMkGvjq47n40SqFOWVjDDwBNsoAsoo0O9GB6ggrRi7 wglkaSqQIQAIobBg7IBn1xYyn4ntBYYuJn/NqABHF9jzmslraEH/BTSt5TQO c13u7cIFDio8FLa1T6mNgjafKtIRSGAxcHZYCdK7bW0i1AeVUcBwm5Ztin5D GW9B1kTHWztS66tbc3CA6FAGdLmiATWzPqAW1rvU1nqT3/e8qZHKam2vaytT W4hrru5PducCtP2t7WWgCXMdZMchvAQXYlVGKsyqYmMZyrtYo7dHDmCylKo6 XbGRX5iHhuLGwxB1uK2DQ4MISrbPIgnGJmlMh+xkbpc/6Fmjc1CICwEVNmhO 1zm24dgVkTQZbMO0dupax1/wQpNh+xJqOXccQ8en++05D1e1fyIkTsR83dD6 blDWt3v9bh5+YIKEvIZALRhkRifWnshBHQEdcXHox0NtucGsMC8R3ZUVVMkW YocqRCGD1BVgbRSkJhc2oZqFa3KagAXULV5XZsGCVSnd+pGqWt9Tdetbfl/v pGrKQqrnr27HUOBRJzvmBKew429ImTqGhXacZgrtAI4KJ1bJoqLKoGRMVsD3 4IqDaeDbA+2aBGkeEWN+3/mWnVpcSnbKHATK6OgQXfviJRKZ9YI/hcunhyXc sLzgbS/t/RFj+vO8L+qJ1h16HH4MmPckf0o7CTYJNteDTfp6EmwSbM4BKy/Z 67/QqJvH6FA28QnDg5xXo3fhv7ZZjtxOss9BZXAriu7c7PqVeJ1ksvI77z6l ZHrrkSmZpvAytS0NiEA8BPGtyw+UXOOcSbBJsMcebLIkS4JNgj0xwCZ9PQk2 CfbEAJv09STYJNicA1a2w+bPgDLt3ptkA9xERjIh550BkXG/iBIXStamRLyW 4JRId67RlEj3izm+JOINxeeoxfRnekyHLqbwco3DJsEmwR57sMkyzRfYS6V8 WlUoV8p5V9wQ1SuG53qgPx//Qjgx7IAIOWsqk9hPGC3keXARQ6qfPbYoM2OW H8qa5rxLcd4FnHcFPY/zxecxwWbOYtCRXORZtPyugOdxCbKYjdg8WOToEdI/ ADcQjTzmUbcRlLq1sOG5psJ5OAfS6SFW/g3ftGi9RRBE1vwTpzvXVIgP/etU ZSayGPlHwIY0SCNrgei1UPRe73N9CS+H0Jc1MQY1JPHevPGIi3tGNgrvGFOV DSLTaTsSgmNyrSmAInJvVJn3SA4iyF1jegvKOy4Y0OUNIHtM7V8gMmHLsycP rTJ/Vn3kpFSpNBukFbJPt/8SB509GvgvcHWM4muq5oyA4bnHI9JmN30eYizu KDTG0wIa7USq+HC8M2LWikQDMJDbg/8mQUY9SAREUc2a/y7DP7xcQiZruYDz rqhmzX/77R9erpm6JMEmx3VJsEmwWQCb6DMg41+e8g8ru64pGpCYlSfvJUJm 5G5o0wueujN8PoiRP2WjROLC83npM8Kfv+8w+IGSaxwzCTYJ9tiDTdZNSbBJ sCcG2KSvJ8EmwSbBZgFsjgwh8hnyIZo5k2jgQKLq1Yl+/ZV0TUw2YJOPYE6h zZuJxo4lat6c6N13iW6+WQggJLCKY0X/hiXXn+WIK2vYNyjsW7cSjR9P1KoV 0YfiwLvuIjrtNIU9hYoUIbr1VqL77iN65RWiP/4g2rmTdA1TNohktSJqxw6i SZOI2rQh+uQTonvuISpRwiGqYEGi664jevNNonr1iIYNI1qzhvIdG6KW8jaV DgurW7yYqFcvoh9/JHr8caJzzyXKkwf3yUrK8ucnuvpqoldfJapdm2jwYKIV K0g3O9ZRZhvgQeEFc+YQ/fwz0ahRWml7EDxfEXz0KNGyZWzCbMovvEB05ZVE qak2wakwNCpThuj554lq1CAaMIBoqeBYnGudYkj1dqW1deuIhg4lqlWLqHx5 opNOEu11gCSqIL34Ijmn6O4r9uBojsKwa5e0i5YtpavcdBNRoUJkMyM0QSVL Ej34INEXXxB1ENROm0a0bx9pn/OlY2ajQiWMnKZMIWrXjujTT4nuvpvolFMc Ezz7bKJLL5W+8csvRLNnE23Y4FdT01yagtShqfR0oqefJjr/fJaeY1q2J8JJ W7cmmjqVII9zDflao1DBiv/+m6hHD6Kvv5aygszcVpwvn7Tit94iatxYRqdt 27T+5cHcJCXJf/5hI2ZIb79NdMMNBA+2kQke6cILJc9VqxL1788uU9qQr+UK y5YtRKNHEzVqJOMC6Bd82KaRkiIfuQUjhC8Ay5Il/IAsq3B8vhIdao5TVNkG i+j63ntSgSef7FiReEt33EFUsaKMdTC43bvV75VGQ0x0JLpQUXLoENFff8mQ Ar0/8EBUSD31VGnin31G1Lkz0axZhCikCwEJf0ljmDJBOy717UtUuTLRU08R nXdetLUXLiwT4TvvSMOBAQlDuhwgEvyehx1ENm0iGjlSZg6ktKuuIpiHjRmW gij58stEdesSDR9OtH49nebAyYZniQxWpCDOQ9IdOxJ99BHRLbe44lkKBYPS NZ55JuIay5fT9RqIWXkSyYwYE+nalejLL2XOP+MMx0TEW7r/frmrWzd5qGCg ZDaZSAyI/oqojSIgjxghVaHRVoECRDfeGB0V9+yhWwxFZErNFEUN/HniRKJm zWR0RJRJS3OoEZmVCUT6r19fmpkwtws1EDObbhus9YrRW5cuUjn33ktUvLij N+HlrLevvpLev3Ahh707NRCz8mM743kbyWVe3i0SKdd0oBYkzZtH4OLi+HLS JZifFf9C3zR5sqwKkGBilCLeslJeE7Ju0EAqRdTc92sgdtCsjY7B0qKFjEqw Og9fRSG1ahVd6Y+lTgoZciae2YiS7NlniS66iIDBRobKCoU6ihyX/B4xZGmY wmJHQkjlpZeILrmEOw8bS9GiRLffnsG3rvXHUhuFDHaBjIvy+bvvpEkKK7WR oXYrVYroiSek2cB8RBnwlCFLAxUWu7yBVDLEsDD7wiOPyPq9Xz+ilSvtn0Qw 5qe5wmTHbmTLjz+WxDvVbgqFw7LggNUhgf3+O6Gted6Qn74KS2zFe/31rrIm YtsIOMhniJQiYt7hj6VGChlqKNgDYi0KeNAv+HCXhTBxmAma1enTiQ4coJcM WeqhsKBNGDRIegmKPhUc3HUurA4yRV5EZBO2fa8/luryNswmjiYMVTVMSzRs lh0YzzqL6KGHiL75RpbDsBthP6bP8O0SY3J2RR1j2HZ96w4MwrAf9sdPDcUP 0iEqkpo1ZWQVpbvlxlS6tOzz0IPBGIRK3zHkp73iZ+/e6HB6zTVRJmdX0m7D Flb6hD9+0hU/orLiUctPPxE9+iihr7JsZ0UHhL4Uho0WRLRkWlg6ZlopZkTb Qm3bEv3vf9KkY0KcHUhjyt5nM2GG9/ygWAAKqKRaNTkTOPPMiEqQFcqWlajh VShjxfEfO0Aig6+mLg0PGSK7FOUejkRQgtnhSwVI+YThzAZmX/O2IOsWIxx0 SaAJ5oLIi0PxH58hqoYNiSZM4GbE+spQ5A0UA6tXy0rVVqlbHsABtSKnIbd1 7040fz7pqiAP4/lMKRchGP09uiv0fFdc4VKuDPZQCCSJsLZ9O1nfGzJTS6HA A5RRMIFQ5BNULaJ6cev34oulLJFFx4zhKF/BHz8VXcgQ7mCwKDHgeU6tG+Zu Efns++9l8lq7lqzKhvxUdYkMRt6+vczrqGJEDe12buST11+XNS5sRaT89/3x 856yBOQTRHqYK5pL0dRZNjMI81hDVYqSQPQ1VnVDZn5SzCDyzp0r5zzvCxqv vTaq8BPVGXdUdiZRzv2xP2be4m0BrrIxGIZY0IggptuugykaxIYWH1W4sJg6 hrx8a6YY8IJJASo+2KIq4r/wx4t6RAXKHurZU4Y9SEiEd0cxInWx1yDDIOoi BDQwZOYLxYxdK7vbJNEb6RQDcYkIAGa+9cdMecUMFIMogJiGJCvc3mEmb14p SQyRMaZDwGyqgaVj5mPFjChxuPRFyYOkh7GfK4UUKxbpZVya+ckfM88rZkSM 4uj/ww+yCsqfP8IMZo4INJAqGBYmY7U0ZOZ9l2bg1IDxxhvSap0SL8xjIEwE EbsRw1EfV/PHifzZnvxwaFYuSghkXVQntq+UKydnXrDBNWvIamfIRQUTlYS5 vUSgRGHXp4/Uem1/XDym9IGuBSG5qbCa556LNi7MqCAsVHUI/PAU3ZUZHSev KU7g9jNmyP6qQgUpGQ99iNyqdUYPTh5SnCC5ABPmEo89xmNIhxNUwkj7sApc d8BUtJshJ+UVJ7pg7Ph8mJtJuIlbJzpP9ODkPg0nqIZEKlGchLi4gF136sQp pachE88pJqDuRYvkfAsxAyNIJwqHo6Iwyv2lS+1KM5Na8S5FOoQEw0UtGEs6 EgpMALhFau/tnBypEZ9SYMRuvlbw7bcyiUbAyC4N10UwT8QkTwXX1jg1szLx dt6GGDbK2Ycfdo3qQzyFcFE4wFC4jyqqhX9wt1BH5MYnn4wuDNEuw/bR4+KS C66niMDe2Z+F3Kzox/gEdoho6VRrUsJI0QjT4pDBhvQ/4DIONHqoJUBnTLkJ 04MTIQ+hZcdVp1/80S8nu/lwKndvsDPENrvOQG7GFQzEVNF9Dzdk4B6lANRj mCqhHkN8jJiNDGYYHCLxoGYTjbPV2x/11yjqcZG0SRMZuGCNOASDijvvlBdF UeYIWY4ypP52RT2EYqcuTKuENh3zQVJBU4qqGYqHmgSKfv4YuFKZD4IyGga4 kNCqO7Z88IEUocij4wzpdxslmjYUCtdd54ykTj9dTibc9dZv/uiWP8qal/WL lItEBX3iEFRAcGMoRCjGmmhI9XVK6ohYGPSgI8RgAQ26bTMYd+NqHvoUJEFU Czqb9CD9YkU6KlI4DppxKBOHQDKoHpH4hLzlj/MakF5OkY7CEMEWNgcRuNsP 1FIQE5o2VKr799uTXmPS5a/jBTlUYbwkSiknlqMnRHAGemGHfxpSfrmiHFUa LmZiEIr4HqkCQ3y1HmaOCaeoncb7I/p8JW/kUMRidACYXOIQVGhIeIjPMJWZ hlRLHebnS+aoXZHiUXQjpuMwNMmIlWhrUPGtX29fHDYm+1xFNkIwYis8E+Zh hxaM8VBCbdhg3yyQOdmlFdlC9TyXAdm4q8Q2P5CPRIp1jBAxPtAp0oPsc3ib xiYCMLhdxCYZGRA1hJCa6U97n6cohhRQpqGKQBy3gywoRl+FGI74BafRKTFD eXKmohNXZeHIMF8bIC4Uo5rasYP+dk6IlCQl+dQQD/JQbuCyqTP9lI4AZSGl 7NpF/JvgmVUhpytq0Auh7sbMGxkQ9gn2cAVm82ZabCg1yVw+DgfjxklF4AKv nVTRLSCpIm+Iqma+PxWfqoiFTmBFqAAQc3EIMhKCz6pVtMyQ2NMVsQjlGAVg xmuHcgxncAMB5lmof4UP637B3oNY+ZvgqVw/ImRh9I7dGIMis4mu0tL9ILiO Usl4XrgcD+BQPNgef845MkZhSiW0bum49yCzqJIp8jBAoJBAEIEBIBzCzkQ1 sNqQ0pMVOFwLwFAbfTXA4RAMPGEQgvNV/ogsrGQplMuh/rTTJERMHeGA6A10 P1uvo7CIohAWDzOEU9thCONjFGyiC13rj8KCikJkEkQb8IwXpjuoYURqt9Yb UlhQUYhyAPd4uc0cVgQJiLpOB86DwnyKQoRgDD0xJ8BuzFRwKQUFxSZDCvMr WGjfMFTErNxt21Om6GF5kJemQGLCj3YI5Td2o1FBE4AKf4sheWlqi8SLS0BQ MewZLoN2HD2xEIMOnAeF9o92i26ap2m4MxJxDdBFNNpuSFyKYhQegrE8bgjD btGhcZwQpaulg+VBWUgBRp5CGwY+8UJ+EGs7DSkLKcpwUQENOW6wBIPoJSAy EdQtHSz3HSi8J+aOQ/z3+A2cFB6w4SoFkEGquAdQuPpuzSmNE0ayYIEUDiI7 hIPLuHPn0p74DMX9zZ0YrJHbnsRbrIMHhBFhy7uwj5Nws0Sh4bYb2Jtw0F3O vjMSIDHjHW1IbbyGy32Xa2Bdls1runtR4/4okU8eUOoeDx50N+S4XUD3LVdL sxZXINlNsKkiGv9nqPdQQVZu8tKxk6pZSzE8LrvXjgfe3MybKV7TKJW0q5yP Nyfx5hG2dGVd0mxyN29ZCUcdDI/L6bzlFrw5ibfMwgzXc3mw6eR85LJPNRUU /XfJf3OVx3VhS7zjL9ak4p16EqN9ztfOITxgC+FdyDlEyRHv+BO28q4p+UUf XjjDeReKhv2V85FFH3DQ87tgBEs4Cos6XWKTN5JZC5yD+dm++fAuLR7eLzUH p3hTEMOns6OKCXpG+oPmkLCzFpF6fi1sVs1pGoi8o5gxHF4oEY+y4iZwIopN i8frj5pDdLzyvC3kgr3YWQjHg11Jc4gONkeCFJeJ7I2G0zLeOSGXEZueY0WO wSd5d7S1yyGBl/nOjIDx2XscYnRnBxzRePDY2gGRzzlSSZqi/zzDhJXn/+zh hIw=\ \>"]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Numerical Exploration", "Section", CellChangeTimes->{{3.414162186636762*^9, 3.414162215836375*^9}, { 3.414222729970998*^9, 3.414222751732341*^9}}], Cell[CellGroupData[{ Cell["Dependence of Boundary Layer on Perturbation Parameter", "Subsection", CellChangeTimes->{{3.414222722925392*^9, 3.414222726866147*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListLogLogPlot", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"epsValList", ",", "maxPtLocations"}], "}"}], "//", "Transpose"}], ",", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", "Large", "]"}], ",", "Red"}], "}"}]}], ",", " ", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0.4"}], "}"}]}], "}"}]}], ",", RowBox[{"PlotRangeClipping", "\[Rule]", "False"}], ",", RowBox[{"Filling", "\[Rule]", "Bottom"}], ",", RowBox[{"FillingStyle", "\[Rule]", RowBox[{"{", RowBox[{"Thick", ",", "Blue"}], "}"}]}], ",", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"FrameStyle", "\[Rule]", " ", "Thick"}], ",", RowBox[{"FrameTicksStyle", "\[Rule]", RowBox[{"Directive", "[", RowBox[{"Brown", ",", "Bold", ",", "15"}], "]"}]}], ",", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"600", ",", "400"}], "}"}]}], ",", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\\"", ",", "Bold", ",", "Large"}], "]"}], ",", " ", "\"\<\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\<\[Epsilon]\>\"", ",", "Bold", ",", "Large"}], "]"}], ",", " ", "\"\<\>\""}], "}"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.414161266396957*^9, 3.414161327384561*^9}, { 3.414161377935914*^9, 3.414161446476523*^9}, {3.414161485032038*^9, 3.414161488685343*^9}, {3.414161531256668*^9, 3.414161536401956*^9}, { 3.414161570161946*^9, 3.414161581462897*^9}, {3.414161692186511*^9, 3.414161885455377*^9}, {3.414161954054614*^9, 3.41416214221731*^9}}], Cell[BoxData[ GraphicsBox[ GraphicsComplexBox[{{ 0., -1.194204037524275}, {-0.6931471805599453, -1.7044236547321419`}, \ {-2.3025850929940455`, -2.9794164312838602`}, {-4.605170185988091, \ -4.937779978854736}, { 0., -4.937779978854736}, {-0.6931471805599453, -4.937779978854736}, \ {-2.3025850929940455`, -4.937779978854736}, { 0., -1.194204037524275}, {-0.6931471805599453, -1.7044236547321419`}, \ {-2.3025850929940455`, -2.9794164312838602`}, {-4.605170185988091, \ -4.937779978854736}}, {{{}, {}, {}, {}, {RGBColor[0, 0, 1], LineBox[{5, 1}], LineBox[{6, 2}], LineBox[{7, 3}]}}, {{}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[{8, 9, 10, 11}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{-4.605170185988091, -4.937779978854736}, Frame->True, FrameLabel->{{ FormBox[ StyleBox[ "\"v: \\npeak\\nposition\"", Bold, Large, StripOnInput -> False], TraditionalForm], FormBox["\"\"", TraditionalForm]}, { FormBox[ StyleBox["\"\[Epsilon]\"", Bold, Large, StripOnInput -> False], TraditionalForm], FormBox["\"\"", TraditionalForm]}}, FrameStyle->Thickness[Large], FrameTicks->{{{{-4.605170185988091, FormBox[ TagBox[ InterpretationBox["\"0.010\"", 0.01, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.3025850929940455`, FormBox[ TagBox[ InterpretationBox["\"0.100\"", 0.1, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.995732273553991, FormBox[ TagBox[ InterpretationBox["\"0.050\"", 0.05, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-0.6931471805599453, FormBox[ TagBox[ InterpretationBox["\"0.500\"", 0.5, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.912023005428146, FormBox[ TagBox[ InterpretationBox["\"0.020\"", 0.02, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.6094379124341003`, FormBox[ TagBox[ InterpretationBox["\"0.200\"", 0.2, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.506557897319982, FormBox[ TagBox[ InterpretationBox["\"0.030\"", 0.03, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.203972804325936, FormBox[ TagBox[ InterpretationBox[ "\"0.300\"", 0.30000000000000004`, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-4.199705077879927, FormBox[ TagBox[ InterpretationBox["\"0.015\"", 0.015, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.897119984885881, FormBox[ TagBox[ InterpretationBox[ "\"0.150\"", 0.15000000000000002`, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.659260036932778, FormBox[ TagBox[ InterpretationBox["\"0.070\"", 0.07, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-0.3566749439387323, FormBox[ TagBox[ InterpretationBox[ "\"0.700\"", 0.7000000000000001, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-4.487387150331708, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.382026634673882, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.286716454869556, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.135166556742356, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.074541934925921, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.017383521085972, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.9633162998156966`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[25], -3.2188758248682006`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[50, 3]], -2.8134107167600364`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.2072749131897207`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.120263536200091, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.040220828526554, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.9661128563728327`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.8170772772123447`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.7429693050586228`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.6739764335716714`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 2]], -0.9162907318741551], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 3]], -0.5108256237659907], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}, {{-4.605170185988091, FormBox["\" \"", TraditionalForm]}, {-2.3025850929940455`, FormBox["\" \"", TraditionalForm]}, {-2.995732273553991, FormBox["\" \"", TraditionalForm]}, {-0.6931471805599453, FormBox["\" \"", TraditionalForm]}, {-3.912023005428146, FormBox["\" \"", TraditionalForm]}, {-1.6094379124341003`, FormBox["\" \"", TraditionalForm]}, {-3.506557897319982, FormBox["\" \"", TraditionalForm]}, {-1.203972804325936, FormBox["\" \"", TraditionalForm]}, {-4.199705077879927, FormBox["\" \"", TraditionalForm]}, {-1.897119984885881, FormBox["\" \"", TraditionalForm]}, {-2.659260036932778, FormBox["\" \"", TraditionalForm]}, {-0.3566749439387323, FormBox["\" \"", TraditionalForm]}, {-4.487387150331708, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.382026634673882, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.286716454869556, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.135166556742356, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.074541934925921, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.017383521085972, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.9633162998156966`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[25], -3.2188758248682006`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[50, 3]], -2.8134107167600364`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.2072749131897207`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.120263536200091, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.040220828526554, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.9661128563728327`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.8170772772123447`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.7429693050586228`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.6739764335716714`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 2]], -0.9162907318741551], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 3]], -0.5108256237659907], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}}, {{{0, FormBox[ TagBox[ InterpretationBox["\"1.00\"", 1., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[2], -0.6931471805599453], FormBox[ TagBox[ InterpretationBox["\"0.50\"", 0.5, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[ Log[2], 0.6931471805599453], FormBox[ TagBox[ InterpretationBox["\"2.00\"", 2., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[5], -1.6094379124341003`], FormBox[ TagBox[ InterpretationBox["\"0.20\"", 0.2, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[ Log[5], 1.6094379124341003`], FormBox[ TagBox[ InterpretationBox["\"5.00\"", 5., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[10], -2.302585092994046], FormBox[ TagBox[ InterpretationBox["\"0.10\"", 0.1, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[20], -2.995732273553991], FormBox[ TagBox[ InterpretationBox["\"0.05\"", 0.05, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[50], -3.912023005428146], FormBox[ TagBox[ InterpretationBox["\"0.02\"", 0.02, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[100], -4.605170185988092], FormBox[ TagBox[ InterpretationBox["\"0.01\"", 0.01, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.506557897319982, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.2188758248682006`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.8134107167600364`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.6592600369327783`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.2039728043259361`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.916290731874155, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.5108256237659907, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.35667494393873245`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.2231435513142097, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.10536051565782628`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.0986122886681098`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.3862943611198906`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}, {{0, FormBox["\" \"", TraditionalForm]}, { NCache[-Log[2], -0.6931471805599453], FormBox["\" \"", TraditionalForm]}, { NCache[ Log[2], 0.6931471805599453], FormBox["\" \"", TraditionalForm]}, { NCache[-Log[5], -1.6094379124341003`], FormBox["\" \"", TraditionalForm]}, { NCache[ Log[5], 1.6094379124341003`], FormBox["\" \"", TraditionalForm]}, { NCache[-Log[10], -2.302585092994046], FormBox["\" \"", TraditionalForm]}, { NCache[-Log[20], -2.995732273553991], FormBox["\" \"", TraditionalForm]}, { NCache[-Log[50], -3.912023005428146], FormBox["\" \"", TraditionalForm]}, { NCache[-Log[100], -4.605170185988092], FormBox["\" \"", TraditionalForm]}, {-3.506557897319982, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.2188758248682006`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.8134107167600364`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.6592600369327783`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.2039728043259361`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.916290731874155, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.5108256237659907, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.35667494393873245`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.2231435513142097, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.10536051565782628`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.0986122886681098`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.3862943611198906`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}}}, FrameTicksStyle->Directive[ RGBColor[0.6, 0.4, 0.2], Bold, 15], GridLines->{None, None}, ImageSize->{600, 400}, Method->{}, PlotRange->{{-4.605170185988091, 0.}, {-4.937779978854736, -1.194204037524275}}, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}, RotateLabel->False, Ticks->{{{0, FormBox[ TagBox[ InterpretationBox["\"1.00\"", 1., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[2], -0.6931471805599453], FormBox[ TagBox[ InterpretationBox["\"0.50\"", 0.5, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[ Log[2], 0.6931471805599453], FormBox[ TagBox[ InterpretationBox["\"2.00\"", 2., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[5], -1.6094379124341003`], FormBox[ TagBox[ InterpretationBox["\"0.20\"", 0.2, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[ Log[5], 1.6094379124341003`], FormBox[ TagBox[ InterpretationBox["\"5.00\"", 5., AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[10], -2.302585092994046], FormBox[ TagBox[ InterpretationBox["\"0.10\"", 0.1, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[20], -2.995732273553991], FormBox[ TagBox[ InterpretationBox["\"0.05\"", 0.05, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[50], -3.912023005428146], FormBox[ TagBox[ InterpretationBox["\"0.02\"", 0.02, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, { NCache[-Log[100], -4.605170185988092], FormBox[ TagBox[ InterpretationBox["\"0.01\"", 0.01, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 2}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.506557897319982, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.2188758248682006`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.8134107167600364`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.6592600369327783`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.2039728043259361`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.916290731874155, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.5108256237659907, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.35667494393873245`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.2231435513142097, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-0.10536051565782628`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.0986122886681098`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {1.3862943611198906`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}, {{-4.605170185988091, FormBox[ TagBox[ InterpretationBox["\"0.010\"", 0.01, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.3025850929940455`, FormBox[ TagBox[ InterpretationBox["\"0.100\"", 0.1, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.995732273553991, FormBox[ TagBox[ InterpretationBox["\"0.050\"", 0.05, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-0.6931471805599453, FormBox[ TagBox[ InterpretationBox["\"0.500\"", 0.5, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.912023005428146, FormBox[ TagBox[ InterpretationBox["\"0.020\"", 0.02, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.6094379124341003`, FormBox[ TagBox[ InterpretationBox["\"0.200\"", 0.2, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-3.506557897319982, FormBox[ TagBox[ InterpretationBox["\"0.030\"", 0.03, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.203972804325936, FormBox[ TagBox[ InterpretationBox[ "\"0.300\"", 0.30000000000000004`, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-4.199705077879927, FormBox[ TagBox[ InterpretationBox["\"0.015\"", 0.015, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-1.897119984885881, FormBox[ TagBox[ InterpretationBox[ "\"0.150\"", 0.15000000000000002`, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-2.659260036932778, FormBox[ TagBox[ InterpretationBox["\"0.070\"", 0.07, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-0.3566749439387323, FormBox[ TagBox[ InterpretationBox[ "\"0.700\"", 0.7000000000000001, AutoDelete -> True], NumberForm[#, { DirectedInfinity[1], 3}, NumberPadding -> {"", "0"}]& ], TraditionalForm]}, {-4.487387150331708, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.382026634673882, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.286716454869556, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.135166556742356, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.074541934925921, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-4.017383521085972, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-3.9633162998156966`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[25], -3.2188758248682006`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[50, 3]], -2.8134107167600364`], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.5257286443082556`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.4079456086518722`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.2072749131897207`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.120263536200091, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-2.040220828526554, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.9661128563728327`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.8170772772123447`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.7429693050586228`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, {-1.6739764335716714`, FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 2]], -0.9162907318741551], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}, { NCache[-Log[ Rational[5, 3]], -0.5108256237659907], FormBox["\" \"", TraditionalForm], {0.00375, 0.}, { Thickness[0.001]}}}}]], "Output", CellChangeTimes->{3.414230633688529*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Conclusion", "Subsection", CellChangeTimes->{{3.414222773800923*^9, 3.414222775521629*^9}}], Cell[TextData[{ "The size of the boundary layer (as given by the time at which the solution \ v reaches its peak) \nscales as ", StyleBox["\[Tilde]", FontSize->24, FontWeight->"Bold"], Cell[BoxData[ FormBox[ RowBox[{" ", "\[Epsilon]"}], TraditionalForm]], FontSize->24, FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.414222778273694*^9, 3.414222830351575*^9}, { 3.414222885349025*^9, 3.414222906119787*^9}}], Cell["\<\ That is, to be able to look at the boundary layer, we need to use a \ magnifying glass to blow up this region.\ \>", "Text", CellChangeTimes->{{3.41422293146333*^9, 3.414222972530487*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Numerical Exploration", "Section", CellChangeTimes->{{3.414222924347223*^9, 3.414222926788092*^9}}], Cell[CellGroupData[{ Cell["Looking Under Magnifying Glass", "Subsection", CellChangeTimes->{{3.41422299388844*^9, 3.414223000137658*^9}}], Cell[CellGroupData[{ Cell["Magnify Plot Function", "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414224344309991*^9, 3.414224362594181*^9}}], Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414223004618129*^9, 3.414223008274756*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"DoMagnifyPlot", "[", RowBox[{"ODE_", ",", " ", "epsVal_"}], "]"}], ":=", RowBox[{"Module", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"InitCondEqn", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Equal]", "1"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Equal]", "0"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"\[Eta]End", "=", "10"}], ",", " ", RowBox[{"ParamRule", "=", RowBox[{"{", RowBox[{ RowBox[{"K", "\[Rule]", " ", "10"}], ",", RowBox[{"\[Lambda]", "\[Rule]", " ", "5"}], " ", ",", RowBox[{"\[Epsilon]", "\[Rule]", " ", "epsVal"}]}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"ndsol", "=", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{ RowBox[{"Join", "[", RowBox[{"ODE", ",", "InitCondEqn"}], "]"}], "/.", "ParamRule"}], ",", RowBox[{"{", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", ",", RowBox[{"v", "[", "\[Eta]", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", "epsVal"}]}], "}"}]}], "]"}], "//", "Flatten"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"vMaxPt", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"\[Eta]", "/.", RowBox[{"First", "[", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], ",", " ", RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "&"}], ")"}], "@", RowBox[{"NMaximize", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"v", "[", "\[Eta]", "]"}], "/.", "ndsol"}], ",", " ", RowBox[{ "0", "\[LessEqual]", " ", "\[Eta]", "\[LessEqual]", " ", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", "epsVal"}]}]}], "}"}], ",", " ", "\[Eta]"}], "]"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"MaxPtPlot", "=", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", "Large", "]"}], ",", "Red", ",", " ", RowBox[{"Point", "[", "vMaxPt", "]"}]}], "}"}], ",", " ", RowBox[{"AspectRatio", "\[Rule]", " ", "1"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"PlotColors", "=", RowBox[{"{", RowBox[{"Blue", ",", "Purple"}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SolnPlot", "=", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Plot", "[", RowBox[{"#1", ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", "epsVal"}]}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", RowBox[{"PlotColors", "[", RowBox[{"[", RowBox[{"#2", "//", "First"}], "]"}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"FrameTicksStyle", "\[Rule]", RowBox[{"Directive", "[", RowBox[{"Red", ",", "14", ",", "Bold"}], "]"}]}]}], "]"}], "&"}], ",", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", ",", RowBox[{"v", "[", "\[Eta]", "]"}]}], "}"}], "/.", "ndsol"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{ RowBox[{"vMaxPt", "//", "First"}], ",", RowBox[{"Show", "[", RowBox[{ RowBox[{"{", "SolnPlot", "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", "epsVal"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"500", ",", "400"}], "}"}]}], ",", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", "Large", ",", "Brown"}], "]"}], ",", "None"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\<\[Eta]\>\"", ",", "Bold", ",", "Large", ",", "Brown"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ RowBox[{"\"\<\[Epsilon] = \>\"", "<>", RowBox[{"ToString", "[", "epsVal", "]"}]}], ",", "Bold", ",", "Large", ",", "Red"}], "]"}]}], "}"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}]}], "]"}]}], "}"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.41415858949458*^9, 3.414158757735336*^9}, { 3.414158822540405*^9, 3.414158876716507*^9}, {3.414158912355009*^9, 3.414158992638582*^9}, {3.414159057101586*^9, 3.414159080172947*^9}, { 3.4141591276818*^9, 3.414159208854669*^9}, {3.414159240840358*^9, 3.414159321459284*^9}, {3.414159384918592*^9, 3.414159495877507*^9}, { 3.414159533693858*^9, 3.414159585770365*^9}, {3.414159664774451*^9, 3.414159672722522*^9}, {3.414159762307563*^9, 3.414159800385224*^9}, { 3.414159891691608*^9, 3.41415989494887*^9}, {3.414159925288239*^9, 3.414159930324265*^9}, {3.414159983438526*^9, 3.414159989600893*^9}, { 3.414160022349233*^9, 3.41416014538795*^9}, {3.414160264496005*^9, 3.414160477515918*^9}, {3.414160513720847*^9, 3.41416053241007*^9}, { 3.414160570575239*^9, 3.414160592186646*^9}, {3.414160626158701*^9, 3.414160672982785*^9}, {3.414160719778818*^9, 3.41416073337495*^9}, { 3.414160766408626*^9, 3.414160798869594*^9}, {3.414161002557738*^9, 3.414161004925106*^9}, {3.414177081358854*^9, 3.414177083741417*^9}, { 3.414177145154275*^9, 3.414177148916313*^9}, {3.414177301153661*^9, 3.414177355007666*^9}, {3.414177474392666*^9, 3.41417747609487*^9}, { 3.414177864968065*^9, 3.414177867984862*^9}, {3.414177983300389*^9, 3.414178014739552*^9}, {3.414178120453376*^9, 3.41417812359066*^9}, { 3.41417816618642*^9, 3.414178239426559*^9}, 3.414223008275032*^9, { 3.414224408867333*^9, 3.414224409761468*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Apply It", "Subsubsection", CellChangeTimes->{{3.414224381810063*^9, 3.414224389634127*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"epsValList", "=", RowBox[{"{", " ", RowBox[{"0.1", ",", " ", "0.01", ",", " ", "0.001", ",", " ", "0.0001"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"maxPtLocations", "=", RowBox[{ RowBox[{ RowBox[{"First", "[", "#", "]"}], "&"}], "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"DoMagnifyPlot", "[", RowBox[{"NewTwoDEnzymeODE", ",", "#"}], "]"}], "&"}], "/@", " ", "epsValList"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"solnPlots", " ", "=", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], " ", "&"}], "/@", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"DoMagnifyPlot", "[", RowBox[{"NewTwoDEnzymeODE", ",", "#"}], "]"}], "&"}], "/@", " ", "epsValList"}], ")"}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"GraphicsGrid", "[", RowBox[{"Partition", "[", RowBox[{"solnPlots", ",", " ", "2", ",", "2", ",", "1", ",", RowBox[{"{", "}"}]}], "]"}], "]"}]}], "Input", CellChangeTimes->{{3.414177176064495*^9, 3.414177186831664*^9}, { 3.414177437470984*^9, 3.414177442854965*^9}, {3.414177496229518*^9, 3.414177530406274*^9}}], Cell[BoxData[ GraphicsBox[{{}, {{InsetBox[ GraphicsBox[{{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVz3s01HkYBnCX1qmJTqvZpaHJWNMq3RiU7PQUUtQUkzZRbC57rCGUVs62 qWhdto2xXYjQ7DCh1v3SuOVWFmll0MVxO+3iZH5fJyXVxn774z3P+Zznn+fl +YWJA7U0NDT20vuUr4e+3FC+e83WB07ec/PzBFmxK010Vy5ET15/XjZ1OL8q oZ9riBrngd9BfWhGS1jHNYeh3Mf+7BxB16C5QTF3M/wTcyoXfCRY2GMfl8/d BfkUX5/znoAvat2Sx/WE50URO/I1gTWLdVXODYJo3S2xaoLgRvfrzzxMo6EY nlR59BL0BpYHtxSeR9vTt0ppC8G69e4vqhQJaHezDKqpIJhZox8Ty0+GDpff /jKPYHs2S2x9PRW5x846vE0n2ObIfZM6egXze5Y/Sr9IMLHnK16WUTqUiRlz b2MIpo+66NuuyMSIpelETCSBjVSTrfTNhnTkbvK+IAJ1YGhooM1NRLD8LDhH CNiV4i+cymTIHRyR2IsJPJeda01zl6MjN06S6EwgmsETgSoX9V45rSX2BD7/ 7px2ilKg6PI7jsZGAqfENvFt/XzEh9UZSs0Inpc8ZXulFqDnWccoWU5waUww 9LPVbdglqPnhSwheybi645V38EeiolSpTXBcIt7e5l0EC5nPPH+Wgf+JmCMx p4tRaGiS1jnJ4J/pGx1CYQkmpZwzW0YZvHk/LNy0pBSnogxm2/oYDDqFjOzv LsVWbmfTik4GluMCRUZKGW4u0PqrsJGBvr5JBPe7csiMwvu8Khl0nvEIaeFV oDrOQOdRIQP28TuS3OkKeOkJOwNyGNyvd/itpLESO/r62gVXGLjvNRkePleF pjrj2ftJDIIDTDftFlfDc39A9OkYBt51IQ1P2HeR9sG88k0kg6qw6R+kPXcx 6/qjoyKYwc1bWYYXZEok6cSP/eRL/zNLnc3wr0H/NutTyw4wKFtVMKC2rkV2 2lRTlwuDAQnrld9sLbSlS5P3gEEYS7Fau7oOHbETHlo2DFI2BAUOxtfjYrlJ 5sBqBknXIh4PuDRAg/hmnFrJgNX8iLd4yT38cjj0nh2bwYKxOInw5D0Y8Vw5 gkV0/9pB0ble6tXRvuo5NQwqXEpHhY2wW8S5+nBajY2+h4oOZDdi5ljZvmMT aszZxAsH5xoRTrxDnYfUWOb2QBT3fRMIAh12qNS48mvhjP2DJnR1Jqu029Xw Ycl4n29sxmiBaeNEvRoi7a78FdR5zjdCx6m/+e+d5Rpq1ykDzhg1h3F3cKS2 CNU78YK6v1vT/yS1l947syFqt/Sj8qfUkrHHCSpqR3Pe1zLLZhzUkro1UFvx REV/Uo8f0vtYR23Kid5U86lvSMyvpdbQ7d6pou4uO6+lpK4lZ4N0rJph5Xiy vJzatmo4P5g698NhwwJqfrGuVRS1seWzllvU7PzNyljq45EHIxTUr66ntGdS V5uJ2+XURWe2veyiLrHYdTqbOisq5MRzaqO/W82zqC+Fp30Yow4479ibSR3i N7VYU9CMlKVYf53a29v4sh515GTtszRqV49dxhxq274t8deo7USR8lXU/Q+r BVepzZ1z1gqov+2xHb5M/T8hPm81 "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwd13c81d8fB3CjKSFUKKPM5FshUuiFlBaVhDISkT0ihFDILiR7rzvscT8o aU+yWlZSCaGS5FuU7+/c31/38Xyczz3nvM98n3W2Hsb2XBwcHGc5OTjYv9Pv Vm2uO6C4818n1Q+HPGx25oRJSvFKLsG0bK/PR8Gd8JStj3ojIYJFq4cjZP8z xPEZLu1bEgo4KvqjX6DbCm0DCqurJDTwWvS6YkuMG5a80AxnSOzFw3+eL3b4 EQRZw4c7SiTMUf3a2Su9IxY29w8ZZ74zxz5r/4iRrDhkbO91Ssg7DoXWcYmN jvHgk/uWFrDeAockV1unzV3BzLzIv0Zy1ugIGu9dvSwRduZUz9wqW7RX0OVv Lk/GVh6elCIJR7zhzfPJr09HWtT7Qq1IR3j4ya0sWZmBP4saq19+c0Rb8oYy We8MPOB2fL7grhPULqgUpyll4tjfhwvs7VwwJSovYpueBd/Ji96ydHco2U9P SlvkwnI8SOFF2lkkabxy5dMrwBWm42bJ52ehvyT/tKtTAe44mai7cHpDuzE9 IymhADKjG/W5nb3Bs+3xT42BAkwM9Z5U1fSB1tiS3p++hQga0Ei99vYc4iZC er1zipDdOb3QZP15ZEV3OoQ+LsHlfJUehaPnMTb1vGvvcAncvTzL/oadR8CS rZGjC2jYuWLCmPbpPBT+SmdU6NIwcPhj7iw9AL6Lfv8+0UiDVEfn9vzNQZAK ad90Kp+OorYKt69aITjvMjAXdoyJuJwJnftuITgwKyee6sGEj7uicFpOCPgf 3CuNjGZi/eKjb6U4QlFwNfwJ5y0mfpS0hT07FQrjRpmFJ9eXInn4YYe47EXc svSeGBouxSv7OucHpZfQlhfxY5d5OWa6MzTq7l8C1/FG1zG3cogcvLioqO8S yj7O3/EJK8cJFaOCsGVhWNq5JkytohyD8yM9ei5hyKiSVnDhqsB46pp9dxXD oUbPe/qguAKczy7JNzMiYJnMs0SqpxLrtZ1+lt+NAFMu8GPYeCX0qw7dz+6J gOwQo639byUup6w9eWHpZYR8eCEtsKIKvHZUipbTZThs+vfci61VWP3n88Kb CpGodv0lrhJQhX82HRmqp0WhtbvnXN2fKkipNAlW3o2Cl/C/ekoLqyGsLq9b 0heFmHGRVWnLqzGr/Tc7mT8aO2UHeQ9KVOORIcPMyy8aOa/rvsuhGjZunC2K BjH4UrVNjwquRlJZdXX2cCxUEuf06T+rEVG1djCZIw4w9Vl8+081/Osi+eLE 4qCu/+JGC3cNrJusXAKM4mB0WXvD4xU12Ni6VNaMioOcUHqqwT81eDB+Kk3g cjys2lcfCbCtwYyiYEiY7FXkLz3cyv2oBvrbSoRua1+F1546hfiWGiTt2kGf PXYVvzYOKPB31mCTpW2n1+WrGM7m2v63rwZn4mukbUau4sTrZWmXvtdgwm/D 6RyTBByyXW64Y00trHufLglclYiPe4Yssp1qETEo9CJtfSICHzS1HnSvRdmw VTa1KRFSTgl/f56txezUd+WpPYk4c2lts1pQLVKXiVk4+SUi1dPjmsuVWnRo OZebdSdCXFTLpL66Frq5PMZbM5LAbf9q78JpUv4lpfUYLQl3fDPMD/+qhY2W tIFfXRLaFIz/uf6nFqE9mlo32pLgXTS/h3dhHe4IucnpcF/DWn8B2eqVddCJ ap894HoN9Zc0e/vViL2SC+12JsNg1Cl8xqsOHbelJCIOJMM03+RgzLk62PCV p5WYJyPp2fJ+kfN1CC19GP/5bDLehF91lwsl9X+a8fOgJeO6puG6BVdIfSeO HwwUuI4HT1OettOJd0n8TPpwHZoKseHdvXVwMGtb5/ftOpSivZ8/eFuHeJdg I4s/1zH4PvJD2WAdeq8N0KRXpcBQRv6y53Adzg3lnKjblwLLnB0Gj77XgRkh eedVVQrCJ2MOVy1mQfiJVKxISCqMTC8EF25hYUd/R/2f2FT45etGCamycGoy dGgwLRXx3DqLQ9VYqBB5r82oSUVZP1+A0Q4W9jnlT24fToVQ0NdHd3exEMyz 3tTCMA2Hx9aoLjJl4fNB6XU5a9KRYdfsIuPPws5PI6FF8ulQOWe4e2kAC0kX ygaZqulw7tl0eTyQtF+hlld/IB0m5Q8P0ENYiOHfK9kZmA5b3kMG3JEsKHW5 ii/oT8eT70pL9K6z4G5GiTpnZcBocabQ70oW7n0LOO9Jz8D3dxFbEqtZWBWF Ht+6DPz2khORr2WhueFJWlhrBvSuNxkfpFjgF+tbnf0nA5w5tPtBTSxU9f+3 ssMyEwEf2hb7P2Hhx6l9guriWfhdb5ozPkDK9Q6v11HMwrqgmL0nB0n70mYq +7dloVJc4HbHexZGh04bWx/JQvOhrLXlQyz0nwlNuhyRhe62yLEDYyw8cKsX fPMlC+kqcuYyP1lIPi8r5N+cDRkr8wqTpRSOnFCSvtSSDd2u3QGRPBT4NFVV 47qzMXm2071hGYWoPzpH86ay4aOr1yfMRyEoxPLaE7kcsMTruBoEKZyOuCYk ejUHsh1aKYw1FNQSOYVvnMzFwoVc0vuVKEjNrDUbdslFi8KbdrV/KPBYaGQI +ufi/I2W9VKbKAzKeEi5JOQiTJJ5b3IzhZiGfqW1d3OxvsFS8pIqhW/f+tZj RR6+GZzoddhBQX91vWb+2Tx83X5UY5cBhcan+lb1/nmIP3h3fNFeCpuCuoKf B+chV4Hn/FNi0fdf7v6OycPny0byB/ZT+MqU2WtcmIfswcS/OoYU0nYmmXC/ zEOvUtjov8YUvti7udmr5eNay+7ZLCtS3xzvqKVmPgqji1M1rSm4J5TZmujm 46mq8u4e4skb42a7DPPx0ezMqxU2FKb4nfXW2edDe0vcmJ8thZlGh9Vvk/NR Qi/4LHKGAgefzV2T6XxkfjfdT3lQ0Cn8T/PgbD5OtRgqbPekcFEjl9rFUYAD 5Xs1bxJz2Q2UqvAWIHabyoJbXhQWNlimCMgUwFr03x313mQ8bY+7tB4tgHOX 9OJIPwrClPFK/doCtIiNeGYEU4j2EHK81UjKp+ae8IVQmFd4eUP9TgH4MxxM LhGPZh6z2fC8AP5v3y49E0qh6aJ5Kd9IAVZ11vPLX6Jgb2it2yNWCA0j9ZhL ERSoISc390uF8G35VlgRS2FjjuKdkahCbLw3dXFZHIU8s3HBU1cLcdt6ed0Z 4phnrg1Hswpxtl1JRCKegnWVB/d2qhBR/rG/L12hsDjoXDr3WCHoaiET/yRS MBe6+DDtSBGS4zu+8qVQGOJrVS40K4KKaMSWo8SePKtzyq2KUFw3N51CHMlZ 7nvPqQi0LxeXiKeS/n3rlp+4WIQriurO0mkUVrZuiUFNEfZ8tMgQzSD9exw4 s6+hCCJrhg1NiZXuP7I1aS6CfvmF+CRi/RuWmk7PinCoVr52aSYFH3rURNKH IqQvKaVPEXeFDxoNCxbDYTyuuTKbxBO68eakSDF6/PL9PxGPBfrKz0kUYxOD 74lYDpk/b14OgY3FkHy+e0M4sfIpjertu4oR3e+80DiXQoJ2glC8dzEOs8YK e/MoGM6gW/VlMYKf6PUWFJL9uKps7Z3eYlS1GDe0E7epiZw6+L4YliWNG/8Q G52b/Hz6azE233338mgRhcPTeXPXl5RgXUm3zjyx8RSn5C+tEsj9esWpU0JB UNDdLnxXCWJT5AMdiLuUe2kC+0uQFyV5LY74qFfNlg1mJRjeY5r/hthk0lbv hFcJ9HcrGjjRKJh+vW/fVFwCtzy/LYF0Cqv4tjD3lpVAS+faq0zi1/9kfX1Z UwJ118h1TcRmbj5+X26XQHfweeUcsfmETLREbwk6LhTU+DIonBiLKAvlo+Fh /VC9JZOCGM/UJO9KGj6Je3D6E/dusFZLX0NDzFfp30nEFk7qzdUKNMzueT/9 mNhydLj9gx4NcaIBiptKyXwMG/zQ96PBwT1nepx4bPRhQs0FGlJvJX/jLKNw bnzXJqlwGtIuNxSsJo6bhNNcAg3a93ap6hHfnN32rppJg8wB6yXJxHv+soIk q2lwPtzVTiPu+k9VLL6eBj4ZN+ObxGMLthxzfEDD/qfeMe+JRfgVWiQGSH/5 DdsVyykUrShxjBuigYoNOa9FvFlYZtHsGA3Tc4nvDYn3iErpvvqXhtADtRMe xD7SIvWxK+hoYXr8qiLu3Lak8Jc+HX3R/CryFSTeHZd1HA7QURkk9nEr8ajW goEXR+j4U+FnpkfMocchWmlNR//piFhL4k0Hf12x96ejTNRX8QrxDSNfpRfB dOjyZv6XTrz7yPRTnQg6uE63ZBSz6zedXLA2iY7RV0yZJuIYm9GArlI6Nj+e uDpMvMrOQUSnhg5m0HTOJHG+/RCrvIGOzkiW7yxxg/PgZNRDOni+eF9cXklh xKfbAe/oiBQ3W6ZMfNbPdEH5Jzpu0bLPbCeeP/8yX2yCDq/+5iu6xKtCOvp/ /qJDi6tg5xFi/egnxmWCDPIusVFyJx5+3rG0VISB1dd8fXyIowV77jAkGGhv 35AQQNyW+XkTTZEBnWb9XZeJPQe/fyrewoDD8jV9scSCsrNZReoMPGO6GCQS m1XwLCvQY0B22fGcTOLZKcF7eXsZiHU5HZ1HnLVtzflcIwZ4jj3eV0w8eGfj SNYJBpTnPQ9UEDu/OHg/9SwDcrttzJuJeUWOBaT4M2AZs3X6LnGlpZXy9WAG TreJnXlIPP3JLTcphoFH8bNdLcQpir6miQkMxJfYtrYRa3gEL09IYYD7d2N2 J/GFX1cC4wsYeBEh9PQ1sZR2qkocnYFsq3DpHuJ7F3M/x1QwMMm4a9pHfPoR LS+6joHwRi67t8SLllWZRd1gYEVf8N53xPRDDXyRdxg4aOW2+D3xgeQ7DyMe MfD1ysK8D8Rfu58EhbcyUN4cLDhEnCDeqRrWRcZTU+DkJ2IV256xi90MWB/9 HjFM/KrkfX7oAAObek0iR4j9xz+bhwwxsHbjabtRYrEtU/zBYwzoHtov9pm4 yWf2UdAkA37HVcrYtm7kCg6cYSDD0kB0jJhjnkct4A8DES51p9gu1BOa8Odi Qji9KILtPZFrCv2WMCH1S+//Hm2RPuHLx0Rk5g0btmMElFacEybvvhR1EbaV jm194i3GxPPZ96Xs9trStULOSjFh1z+yhm2vAX11Lzkmbht6O7L7Kyxt+MVD iYlbpyoT2fFQZ44VuaswsW3j41R2vOZlVhZuGkwsvfUpgD0es5P2gq47meBT VNdkj1eWmvtTZ30m1kV87GaPJwJ8Q532MyHxXsSEPd4fmoO3OR5m4t1hznL2 fIRzR351MGUCI48/sufrSVyq5WlbJg6+yBxnz69zZ66QnSMTlUb/Nb0hXr6K /uyUOxPiWl9cXxEb5zZonAxgIr5B2KmDvb4+3vlmFcqEvlsR6zl7fSk8LbG8 TN7F75zfPyPuq+4RPpHERJnB3jcPiGvEuIt605j4q994gr1eo8KUVC1yyf9L zzTcIlY/FnLEsowJsUhzbordfjN9sL+Gif7hJd+riYfkujysGpn4HdbVWE6c 9EvmivUjJpj7498WETudMhJ/18qEl/WEBns/6TzzKzv5gv29jid7v33JfPbM ZpCJiu5Cb/Z+3AvPxXazTPj6HX8RSCxJT0/5yFGKBaN2wr7EMwL3ZU8vLsXL vtWqnuz18WGlvr1wKSZmpXlOs8+TiJuhZzaVQsQ8QHo/cV3rolkX21JoDyUq CBDHqm2JnnAsxb2TyuZLiG1zjou4eZRia6+sIwcxv2eZuntQKaTnGjawzzdn IWNvz5RSDGxT12gjXncie8LnWSmqpuZp4cS/7j0K/NlRitDhv5MBxG0bJ3l8 35RCM2V+rRdx0F+9DX5Dpag1r5KwIu7OG7U/P18Kh7qw56rEV0ZU311QKcO+ etP5PnLeByWNRF7VKEMCI+xQJ7GTduaW/J1l4PnJjH5ErH+N69KD/WUonDNp ZN8Pszs7ZZbZlaE1bPnScOIzKe7OadfK8M320UU5Yp3djJ8102XY7LMoxYLc T5smLXMezJbBhvu/HUbEazIFDF5zlGMz77FWHeKZSb+037zlaPwaUSdLXJa1 R1NHthw9td+zv5L7VHT6Y+jzY+V4s5A2EUQ8VSDBO0qV4+n6Upk4ch8Ln/0R F3irHIl7HLYFEqvrPlnO/6AcKkZJ6s7EAe+8+NU7y8HlRZ81IOZa+1AwfLwc K942ZXERC153EZWSqsA5gYU2PiQ/UIlskDOProA99TdnP8kfzroY6z6xqESu OEP3cTEFO+8Qq5CgKuxp3cKnQ/KnTz+yW7S1qyH7Q4T3Ksnnfs4Oam/jq0Hf Z/7Xv69RGNB3fX+0swZPvxvyXCH5qPKoKi0zoRbXaWKdQpHs/EjKS8KmDnM1 TydGSH7cGmzi+mAdC5NzooYS59nxlbsU/2Bh3SfP21UkH3/UrBdffZeCfK2y 6XFn8p4ykhocvFiPau/Vn/3tyPo5vX7bAeMGtEW9T5m3IPnLLdfb3cKNcH+8 MIvjGIV6jx9OiS8a4dj10UrGiNyn9ByRiIIbmDlaM1+9h8Qnk/Qr0+4mAq9u tL8NCrVyzP4vW5vQnvphZJsGhX4XninbX03YUdTDpaxMwYOHtoG74RYW9/GG GymS83uzo/1AZDNmmhrUuteT8zHVq6t/323EP7Dr+EDeazz329ct47sD2Z+u kieEKSwYCXfRPncHigZjrjO8pP9KA4YXX93B9rr5QKFFFFaz9tV80L6LJ8r6 7dnzLGw5ebzyWO5dNGhfaqL/y8K8WqT2wPxdcFTHWXdPsiB0+LFhuMM9ZG0Y uXnuMwvXY0tnNB/fQ4C2gMm1DyxY8xSsW7HlPs5eiOWW7GPBkLuNIU5cLx0r KUGs9ee3siJxUGeMpjix2NcjeruIL++K8V5D/KaT0+4ccerF6I+riQ+nnyrq Ia6yj74vQLxLYZ18gfJ93Hp+JYyLWGWdYWUF8R+7q7mcxOvFzm+7SXyTM+Em BzEHb6fBS+LGo4k/5ntZaPoW6rhI5T6qjyTbzRGr1w8ynInTWZm7pollq3hV /Ihf3c86+YNYmKFxI4w4sSc7cIp4KiPhWRZx1Jq82kniymCd8TZin99F0l+I c/xcvfuIK0lOPkF8xTNtboTY6TrNYpzY1XZyGafqfVgdYl77TGxhsTZ5OXFq fWnlKPF+k71rxYiPyJe3jBBvN/QpkiOOyakYGSZW2JOnpEqsL17Fzfb/AB4+ Udk= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0.93}, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.1\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, FrameTicksStyle->Directive[ RGBColor[1, 0, 0], 14, Bold], ImageSize->{500, 400}, PlotRange->{{0, 0.15000000000000002`}, {0, 1}}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False], {266.6666666666667, -213.33333333333334`}, ImageScaled[{0.5, 0.5}], {500, 400}], InsetBox[ GraphicsBox[{{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwV0XtQzHsYBvAcDaVxy0gXqZRbZ1hsRNhnctuylaS0xFjRKTpd5EjaDklt utjKqsxBGibH0kWiyzKnE+1KoW2yqu0ulS7bt9Q6uaTz/f3xzjufP553npnX yjfEw+8XHR0dNzrMXl4U8fmgvnYLV6OanJwk4B13KdJ3qed8rg8+9IX6QOyV 7HZeFyfavqpikLozbV1mNW+Uoy4vy2qizjGON/yXNxWxXjn3iqint7CUMt48 FOrZagOoS7foskp51rD3ibJv/EmQGhzcVsxjAyG6JS8nCHY52gaGm20Hd+GV 4dLvBKLNsvvZ7a74IAq01P9GsC9J3Xe4bC8GqkOMEsdp3qv5Wm0/H6t+pmln /Efgf+1+n+jFIQhknhueagnYN87Zzo45Atm0kJ2CMYLBOzGmxkbHIC/perdg lEDbG9Rc+edveNy4na0ZoffUf0mPmBxHhv9Gv4JhAqF+gdPtS4HI+3azMpEQ WAybL84eCMKu1EW3g4cIHmz11+U6hmJIN1K8WUMQ8iu7IyX8JJS55uGWgwRR A7eeK+Vh4LbJCzT9tN90h63Ds/7ADr0eQUUfwdkK7v1Ox9NwNextkX4iUHl8 Ma4Rh6O1Yp6NsJeAH2McKpKfgXBobbegh2BJQvObjUZnUXlHspvVTVA7UFNV I4iEpNFKOPUjQfYgK5eVLsSig/yegQ8ETyvtMpK6otBUH9H1rJNgwiEvoMzs HEZuHZtzu4PAfObeRrnreZQ4+7YktxNsa3ZZ1u0SDcV4PFvQRmAwKd2n7I2G iQMnn9tKECH2TihJuYByn8iiBS0E72quzxDbxUBFvu7RqGm+0STa9W0MtDLb WQ1NBN7un8b1Tl+EsMvbS9pIcD5z2C9vTixYK61LUxoIMpJTrBylsRhz6C4Q vifw0JzrULrFQWW6ws5dRWBlfk/i3BeH1Z6udRveEaSXWu36J1WEhsG4H/r1 tL+1asxsZTwiyvkgdQSSTRZDAYp4PA+rm69WEuSXl/UX/n4JDlpBVF4tQauh uLlregJy0vnjV98SFNY9qp37MAEnw8yn+b0hOMUJNmR5JWK/z8J7Dq8JnCOP Oq8jibAw2H/Ipoag0kp60T4jCfMzL9398or2vbb80eK1yUBV25TWKvqPZxzW RHUy7spBql4SjLjkFNSHXkb69/ywmwqCZbk7bCQGYmTZsqeJ5ARTzqy/4VYk RsrDC2u8Kwl6spylvtQn3rvNZFytOFgcTh34w6xvH/VVo4vKLOo2p+JsxsuL a3UJtairfzZjd21AUMpjMTosPIc8qbNPXecon4ghe7z0gQd13PV83kdqbvuo iPGJFxX8ceqv+hW+jO3mfQqzLBbj7WEfU8ZVj+z+DqXeNDM1YQ/18Mib2XNL xFgU8tXfnVpl0rlwCfXUG4ptjGWOYys2Us96JbFgHJtmuv0I9VXrVQ27qY3X +EcUUh9V++5kPMGPjJNTn9ZbvZjxh+jLV5qoc9dPTLhR5yqLcqeUipEkyXzC OG1cUTafmv38WBrjcEu1YgW1zsiaIMYHnDT1W6hHLSadGCNUp3MPtcHu1zaM /weP9ZAx "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwV13k4lF0UAHBJhWQnJbuikJSULMdSZEm2kCX7vo3BWGYxyhIytkgokpI1 28yELAmVsqQklBSpLJGlpE999/1rnt9z37nvc+85977nSLkFW3qysrCwNG9i YcF+5esjlxw5VrU8vjMnzwa7aJv4mtZzmL7S1i8pAi4BbbCPyyz6YDKpLVZ+ 6x3h3xn4mHH0Wo/Jsjbe7FZ23VsnuCOSyN9ushmC7smOcF4JhG3vlAeaTASg //m3/jerJHigxab8wEQGTmfZiugPpUA9a+iY0LQMPE7+Yjty6wpUP/mYGEqV hammK5u8A1PhjkXbxEH6XjCO/rA1aFMaZHpGZ94Rl4fTxLjUUu4MCEhdXM38 oQju1suzrfxXIT0oaJxhcgS+1G3+Kd9+HSa2mjHcC49AMMv1mBDxPDhUqETj XT4CDgF3ho6S8mCgf07LL08VTvkodKqq5QOviv8NsW9HoSxImiFRUgAZy96O cQnHoTk3gc/IpxAyI11HLR5pwW+OCGkTk2L4xKtb91dQG57UHMG9wRfD4TLJ 5AofbWBJxxkdyCuGVyMf1LfwAlzxKO9T/FoMyWL3TR2VdeCX82j4ndjb0ENR quSh6AKvvXxnaXkJGOse8CeInoSp2W79uTd34VisvGCi3knA/auiTq/eBdlH +1qu+Z4EzrZZlQeCpfBXR4ankXkSCFq/nn+yKIU6nT31f6xOwTHhaj/7nlLY pcP9h3rFAHbai6n9q78HX7WXklM2TsONrScvEf3LYYiyeKRA1gjSNsv4dcWX Q0fr93eVJkbQ4RIxPldYDgXaswf7rhvB1FVj2aFX5WCuPTXIq2YMo5Yywrwn KoCp9WZ3TpAJ3EuceWTDUgkJmk3lRR/OgBFf/H6T8Cr4LndBbn6LGeh/0r9y IKUKbAVYS9QVzaA0/M+n+aIqkJ8xujEYaQYvislLki+q4Pm1kTQ2/rPgYT57 UlOqGi5HkU6oSptDzpNzvJ7d1fDidb5ErrUFpBXQ2f027gO1Z96p1dsCgu4L hrKx14BqOxRMRVvAW65HS4Z8NXCjYlJE5ZYF5Ej7OlXI1EDQRQX+nnkLyB5/ GvDZsAb4DjWz/ZdgCYVttqOHaTVgkzL6zbnRCnKcNPfm8NdCDC3n3t4+KzCQ L7t7ULQW7mVYes9+sgL3fzKqzTK1sH6tZ4rAZQ1zyu0NNaq1cKOk6UOqszV8 +Nzym9umFqZa8oaat5yDHdxx63dyaiF00f7RTksbOJ89LVjGUwcFy8LU9142 kEolL00I10Hnz0Ht20Qb6IkN6eIWrwPhDeOHB+/YAD3xTIypYh00cWgwT63Z gBerXLXF6TpglRGtCr1pC2+aZyxplDpIPzeW2z9jB6qPBa8oTKH5M8UJh//a wcIDn9lX3+qgtN/VKpvvPOyLxS2GLdRBq9HXHQ7Hz0OhvznPrfU6mNVavTgd fx66R/XzinnrwWAfT+CGpD041yU3WGrUw38/9XQVbB0glbkj4k5KPbCrJojT /BygKEV/ODS9HgRCnv1ZJDtAipX5mkZ2PRyYPctglDiAc9uB/Mab9WD7wVFB b8kBDnEmHvOvrYe6JwSh86mOwJGw4V09VA/eueXfEh47Af/kp/Rvuxpg+pOt YRK6V3aMSC6fE28AL6Utd1LmnaC0I3j3Q2nkDmeX9J0XwGjhxdtwBeQ5weHr /heg1e/yWqEmsk5MZ6WAMwT0SU0NOTXAkZWys99UXOBjW0vgpoIGCL1Opfhp uoBPGos6o7AB6rVtq2YNXGCi/Plzz9vo+SS27d8dXODEva9u9HJkcefupXgX GP7eKrCzEfm0oNZ/Iy5wRWvafeY1cgHlAM9FV+gJDhj/x04Hy0ptM+crrpB/ 3F2Fi4sOuId/Q+7nuMJTPaaJIA8dqt9RGs9WuMKru0sLO4XocEAs5nT6a1do sTh9e16SDtI3Y7z45NxAxeDX+eFjdOAtohYLvHCDb7ezOJ+60UG5Rqfb/Y0b xNyv7LX1pINZO8tM/YQb7C1P3DTlTYcrE1QV61U3EMvdOfAjgA7bpGLbr4q7 A29iZe4kgQ5/b8WOC4W4Q1X/E3PZZDrM3b64W0TYA15cbGlSr6bDf+YJvQwJ D5h/uv5ao4YOXH+TqOf2e0AzLcdKo44OinYZ05maHiAX55lymEGHQK6iuh3u HtAd26nP2kqH72EtxptrPEBXtrhnfy8dFk+tRX838gRxyT1GNd/owLL8RynV yhPO2Uqe9ZzF1vdvQsHJE/YFDYuJzNPh0PpWQ1+cJyyK6EpGLNIhpFpIYCrH E+5GqG0R/UWHJeEjFSOTnkDYMKr9bzMDVr8EjnWSveCB0a7CE3sY0J5/1+zI ZS9IVMuFXjEGJJ/98OhWphd8mPtS7iTBAHGm+T1KqRds190/HyHNgNMJR8KP v/SCgbl7QZnyDCiQ/c1dKesNbBTDEVdVBui5xullPfeG6mn7GbIxA7iEWuib 3nhDWVKqZb8JA4afrsrjJrzBvVP9g/gZBgQc8uY5s+oNLXaqIQ/OMiDnn9G7 rRI+cOELX/eQNQO+3eAhRON94EUTzb35AgPSR/PKXHf5Qplqk6VeCANMFXZW isv4whqnkrExngHspKzqMUVf+DXxdco8lAExYlfqz+n4grRG7nb7cAYEuZBb jLx9QQh/wcIxigEm084vVei+YHG5y146lgFbl2R/b7LwgwtFujLtaQzo0Lv1 p9XeDz57yI0XpjOAnCX2l+jhB78qh3CUDAasqApv/hnhB7mXyTLHsxgwGbFt x8xNPxivz/lyIwft78Y3ycE5P9i5/eUx1RsMIHLcP1182R9atF9Y5pQxQLhL UOdgpj9UEvPlzcsZUEONPtaU7w8rYUY7OCoYMP3r1L7Ban+QO8bcFlnJAPPp d5tZh/zBXZVvwvg+A2Qfc7a5SgWAxVSkSFcDA3pJXkelmgJgo/xzuEAbA3yO v1CsehwAMTaXzGuRWVdUZNV7A+BEVqWTWTsDjvtv8FtMBMCS/U7BhEcMKD5/ dZG6NRAeOMXzzj1mAEGto2LCMhAquNIOZz1lgMSimHTRbCBogNAF65cMCKt7 MPJnNRBUs4/0fkZ+GmaVYcsSBIwLDwIJgwzA/77MwiMUBEcNgw2zXzGgm3Vl nKwdBKbGX0nPhlD8hXryHTKC4Ng6fYZrlAFNJwhCO48FA6G+MWnbJwbwbPD2 4nWDQQb/5FQsskdbRVyfSTAcZbllvY7MffLjcrxLMMx0aQTNTDLA9Yzp4EoS Gr9WVdbxGeWDi3Ta4Ltg0DEL3mr9jQEVet5shro4eLk6SGFZZIAZ/o3cHgMc 3Jw2JjsjL906ZfLDGAfX7bw3WpCPb5LNzLfGQYCwb3zUDwZ0tk1ILHrj4DsH vntmiQHvNO01rtNwoNpfnsxYZcCOY2fws2M4MOgU4fi1juLp9TC7fQIHivUm Fwz/MMA6R6Ex+zMOFuaJhteQ81Y5WHQWcPDgKf/bo/8xYF9Dd+pV1hBgLezf FLTBAG0VnTKt/SEwpHB4tecfA4IVjkykEULArzBfXIONCbjxh5MviCFw9cBI VRzmDIMvHLEhoMvl+LIX86/z3y+lhEDVW9zwhS3Ij6n/RRSFQMLDtAXiVibg HfpEXHpCQGXav7eYnQmEFF+LQ+J46MJ9USrlQtZetg6UwUOso7XjFOYfJLty eTz8+PDxkNQOJkTYpjvLHsED2x6xvuvIkTLMQJHTeCDvCfqcwM2EqGa2ZBY8 HuZHDWfMeZlAmi3sGOjCg7iyoXupABPmrG7qrPbggdXrmP4IsuPDgtZdA3gY qZUc5RRkgkbq9Sa3UTzETCQdDEReP5hVt/IdD9msXuSDQuj9+IRiEZFQIFz+ zlMijNbzO+Cii18oXOsRjHfaxYRPrv4s8cGh4OuRy5KIbNHjSykLC4XWrxna NciH8r2ilyihoE1Q28y6mwkLmi74uKxQaOEIe1CMHEC1crv3MBTeaKjuGRFl gve2E3qL3GEQPELg3SPORPXe6LaHAmGwnK2poIl8PDy6N1EkDF7f3L3LEZl9 sslOQjoMLuWvBOUjl7dqBJsdDYM032V2EQm0/nCtgkqHMNhURJflkETxmdL5 6XMvDEzrhXEvpJhgJ/qxWbUqDPoGBM99QdaxjI1lqQuDaN9XAqzSTOBrf8SV 2xwG+/m9JY4h1+XryTzpC4Mx3+awQuQVy5Pme1fDID2N65SvDIrHI8Pyj7rh 8FK+vPyTLBNaiazmQobh4PXah/0PMptay+pp03DIr+kAgb1MoJUf1q2xCYeK ClFNfeSSLLG3FP9wWIlVDLmFPOC5vGVPNvq/g8gfm31MkOMsdLX5Gg7Sk9F/ S+XQ/nWe35Y8Hw5MIsdqM3IdRbCqZSkcNu5EPu9H1lxOWpPdCAfPKzdEfiFb vgtLW+YjwPHyS8dPyjOBUm3ckq5BgADCy7q3yEOWP0We0wiwmb5aO7ufCVfH LLfezSLA+MLqh3VkS4/7y9RcAlTfCPvJcYAJfeE+fWrFBPjiEvpeDrk7d/RS MZ0APXOS19yQGeOt36PeEcD4/MKrV8g5fomd8gciwHDxj8JdBSZYL0/WblaO gKO3J2/VIfOTdArHj0QA1bptcxsyLfV31FWtCICdzSnDyAk1/sosFhHwduLm /W2KKD9/ns0bjogAxaJ5Jw9ku4siuISuCPAaZOXkVWJCKC1N61lPBBSeo7OL ItPytm7nGogAWgV5eS9yV93KnYzRCIjSY6ZqIB+eHBgrWIiABZ3iYU/k7SeT DOt3RUL/7bVhBvI+cxahn+KRsPxMrqQdWc8x4tNx2UiIpnFe6EGODPMktx6M hDxPy/z3yFMluvXP9COBhmvT3nwQ5cOWdfGJwEho3FMDJsgjfCFz0qFovOj4 shXyitjXRs/ISMDT+HMckRXU3ljPXowEC1Hp8kDkXK+65J/XIqF8/CJ3GjL+ id9Pro5I0GvbGOtD3ps01qsuHAUzI5Y79ZWZUGP8RMhDNAreCh9rN0I+wVXv RJOMAknZLAdzZPO05PlPB6Lg59xfXyfk6Gz1HVcgCsymmr4QkAduXTMd94kC wb6QiFJke/dLV9mDosBUq8O8CvmzbPC7w6FR8CikWaweeb3UICCRHAX53iuZ rch7q1dTDmVGgcpNwtxrbP4mq+cXm6NAt3Pd5x8yGwkEqtrR+wrT49gOMSFN S8FhuCsKemZ7rnIgl7SzzioMRMEudZ8sAeT+7lrOoako8Dz1mVMOWfYVj7Ec dzTskJteMMHGZ58/fe4SDeVSs79TkQeJ5+1ueEZDTu+b+AzkN9u/fAnyiwbN yySObOR3Cqzb+MOiYfiU3Fo+8oz/8VN2idFgvFUnrAyZba7k0VRVNPzZmrPQ gbyNdNiCURcNlm4bf7qQObnaJxKZ0fBxfzPLM2Q+xbF/Bx5Fg6TNheU+ZPEA Pu2Q19HgQ9OljCIfnyM3baxHg8LboMOLyBqk7cb9/6Jhy7mYp0vI2lzXR4rY iLBaGGG7inxKsWFNn5sIqWv6LuvIlgEzaslSRPggYSzOpoLO/5xNvfBpIkje +mcljBxMmtL7akoEU6d+kggyngs/2GhBBD8jkcLdyFGKqT8cHYjwk+PEgDhy QsBj5dtBREi61vx5H3LRnHKlcjYR6Nrln48is7C8FfXNI8KgqNzAMWRXAWpK cSERZhcL69WRpU8M+AmVE0FJ+q6nFnJJIm7/n1Yi5LmtEE4is+WLXFftJMLK suYBA2TP6nb2oGdEaMR3vTFE3jfE+3XiFREeRT4QNUEula692/2VCCE+wjYW yOxq54VZvhPhxT6z15bIPkabEtSXibDDitPUGlkeZ+FZuUGEqKOH5W2Ry1t+ yGTyk6B8UvmqI3K13eFbTpok6Fhy0fNC5g4Y5b2mS4J04UlHb2y/Yi5SBwxI oFaGD/FBPnR30FnfggSnHd5d9kOuXcaL7/cigWrDs5AgZP5tojQ3fxKE8JY6 BWP7u/vxRj6OBJsc3+jjkA/rCrznJpLg3KYz/0KQG2j1+StpJCAaJB8JRxYs dth+MJsEa+PTS5jD6ZuJ3nkk0P0yUklAVntnZT9aQoLwxDu8kcg5C3+eCZST IAbSmjD/Yi1RP3OfBFmlKs5RyA/2r4i0N6JD9LQjNxpZRKvg8u9WEtws6lAi YvE2P7l2uJMECT/yWzCfiLg6fKcPzb8x00tCbu5UzUmZJMHQw7JaCvLVu5Qz AV9JMH9u684Y5KDLT9nOzJNA05U7ErOkqWMo9y8SqDgeVaIi/1a6e2DhDwnq My/EYh7kWfzYz0IGyWeGLzHHvbpknsFJhtDHQR6xyE703m14HjIc6WOUYla7 trPNUpAMWV6vpjHzRLkSjuwiA2vNM6mLyF/tK5QExckw33vTDvMjzdWpFWky tE/apmDOE4eCITkyzAiuN2IOZUmyYiiS4U1c8hRm00+DnNdUyLBiw739EvLe zj0dEWpkuF+drIT57x2vKDsNMhDus5liHk6sOaSuQwY6KdYLc43v+pddp8gw qr6VjDnJ5GThuhEZLDlz0zC7KdFsxszIkMKneROzBs/bHQ+tyLCE/3UPs+AP qa4COzIsW/Tfx9zdQD9ywY0MZOFvtZgjI42KJQLQ+qPrSjBb2GedZwkhA9tH z1zMBzTf834MJ0PRdevLmDeLyz19FE2G108uhWF+9w8XUxxDhh1pa46Y6R+b 1C7FkaGR/4EuZtpjtu/uSWQwIDyRxux9x+zOSRoZJN4rsGDWScx13JtFhga/ mRFsv3b5fhLYmksGnB57DeYlY8Xn0wVk6EhMvoi5hLtd/d5dMox9HdiDmbzI 8eNyBVqPSeEUFj+bQat7vjVk8CubvoeZPeeLsEITGYanVvZh/hih0re9DcWf o3sCy4+m88T4ucdkoDFkr2EOEONZqeolw7p64W8s3079s6ugDZLhs03XHczi H4vdgofJEJecaoZ5oETt5aGPZMh9LJKD5a+q4oXq+hUyVPyXu4Hl9w7ue55X f5PBXss0DfP0wo894X/JIBP1SAxzbn18iho7BX5Os6hg52PjRJVPoygFDrZq qmDny2DQPy9WkgLn40UrsfNH8z3wwmgvBegOv2UwS+SWKo8epMBrx3bOCGTd 1Vs/13UpkNc+3hCGnHzFRf6xAZqPb5cI5kEZCfsUEwrcag2KDEV2tyxoET1H ARbb6EN45Pj7OXGaPhS4lBpOwe6XPoNzDLZACmy8nu/B7h/hcYGvL0IosPXJ DUHMpVwZJk5ENN/LusIA5Ge+KfwUGgVG0wWzfbH1y1KL2hookK3W/88Ni0+z 9mBiIwVsG/ykMN+03Nhs3koBzkiCjiuycmy098QTCgiuzRGcsXwcDzu4aYwC pTMPuhyQs3N9H+ptigG2XZ/nrZDFdli97ToTAyxJwjF6yB1yijOrljGgfvOB hi52X+tt+W+vXQzE9zxbBew+jGBKJLjFgHaDgRv2vTD+JOptEBEDQR+2iR3H zgNzarW7KAbaD6bvUcL2y5Ug8HQ5BqaoG/ZC2Djp7N61tRjQ0Fh+LoC9/5r8 Mfm/MfDMv+MEPxZ/r0Clk2xUwBHX+XiQqfkSFiXcVJDxOVjKju3f1rhcDxkq XN9PDf6Dvqf6Y6Zyn02psPGkIekDVi+c5XxtfpaK+kvn0ffIbp1PqA8tqDC9 m7D/HTK1Sm80y4YKvzrmOt4iP4w5nqrnQoX3OPXJl8hHZWWXC0Op8GN4+9hj ZLnAP632eVR4ERZCv4u8/V+ZzcAXKnA3elN8kCNptknMtFh4VjTQO4jqodfP 8zlpqhdBSf7S+iFk/be7qGf6LoI/Dy47HdV3tuZf19jDL0Fv4PTZMVRfxlxb 9KzijYO+zA+KSsg5V9KkdMviIFjcSDEG1cOW85SJAbN4UBTSrsHqaSmxe1lG 3+Jhm7Ou9nbk7AdSxq3pCVBa9VLPANXnYjJDK6JKiXBZ77BvKqr3szQkvvt0 J8IgKTtjGPUH1W2NM7UBl+FCj9QbPuT3/LSxyW1JMOSV9ssO9Re1L+v6+WqS 4NTVYfd01K+EagfxK59LBi2/lTPPUT9jFO1udHQhGYwCfByw/qdTquzSsZwU WOzceGWC+iPLXPk66cNXYHexIjUD9VP9D7WVN3quAE6Zc2AU9Vs/TO/cf4VL hblfBTmCyHKVp2SzttPg6g3FGw6of9sUoVZgVk+Dpl3WElmo35u+aVTmhqyS 57gNc0+3I4OAXLXbcyET+arwpYGbyI2ihDbM8ox+tgVkUfFcZ8zmqz6BaQ00 4JJ9V5iBXBSarz1Ap8F1VQ/JdOT4/GqTKeQ39AB2zH6PH9mtIe8+Fr6Yhqwq 8BUvyaABXT2hHfPTOtVSHLIa3HPBvPijl4ePSQM3k7kiGvLQro979iJv7l25 jLlJd2W/OnKF2QYOc1zG7pOuyDssuXUxi6h4R9Yi7zl/6GMq8oZddHwX8uLo 8WeYP1FTM0eQnznq1mKuHKiv3PSABmkulrGYM9a6G4WQSZ/sfTETJEe79yMH ebhbYLY/Pf9KC9l72l8dM+BYPloge/mESWH+H1xD1zs= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0.993}, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.01\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, FrameTicksStyle->Directive[ RGBColor[1, 0, 0], 14, Bold], ImageSize->{500, 400}, PlotRange->{{0, 0.015}, {0, 1}}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False], {800., -213.33333333333334`}, ImageScaled[{0.5, 0.5}], {500, 400}]}, {InsetBox[ GraphicsBox[{{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVyndQ0wcYxvGISOESIQxZhUIEgxjgIqRoUX4vpexlGCGA0gMsWwXZQ7SA jLJCCNZ6RcYpWuqijAJFMUXAQkWxTcUTSLhw0NoCYbUiCvT9/fHc9z53DyMq KSBaiUKh+OHIlvSLjntJxI6LI++2t7cVIFV3L9KYrifCxXw10oJGY84T2V2i 1SdCewsd+7q0/HtZHzE6m2H5Hv17JdF1RfaUaJ1tCl9Hq0UY+AplUoJVx55d QpsPq+hXyhaJ1Jz0RDm6LS9vs0y2Rai50g88Rp+J7eWt76GDcCgxswb9/Gub vYZzesDRpzvHopek1ZPbVSbg3KM874R20vTMoSnMwCqnW2iI7nHjMRqeWUDu SZe19S0F/POWnem90woeberbv0D3GSnJb2uy4RPWNLcT/Xnx8p5DWwchukkR cxk9cdeD4afDAe5V++pMNLtpn8NfKvYwon2UCEN3hJ73a1ccgoF4+0FHtM5z woGq5ADTBaH6JmhfrSK7uaUj0Ol9qV4JHaVlp+ynRgDr4OLUzKYCAk/ZxK1S ncC/3rt/EB3JUeHl7/gUis3yelvQUxPCO39QneHymw8jytFucdMVicqfAe1I lWYS2lgiH3+s6QK95dMJXDTV7FrjUUNXeCCl8m3Rs8HMpRW6G0zdj/bSRdsk hN9KMnIH62C9mTfvFXAyir9gresB3LHs/An0PUeNO8pUT6haO3fvITphPedl k44XqP7wNr8JrflNS9mXNG+oTzEOLUIz9Sq+22fgA8KwAkkMOiDbymXG1BfG B2akHuhEsSBGrusHZ5OLF6zQK3M31m4yjoGJqUujOto2W3yRv5sLIjGTv/JO AVnJNL/YEi6IY4frXqDT+ba+r6j+QOflFXej/2zt0ThT4g+v4yGtDk3fMFSN 3h0A+bu0Vc6jWzunHp0rC4AbBgvfRqInoy70me4KhCinLLEr+uH2xqJFWSCk FOp9ZYHW03gpP6YSBIHNHTwqmqkuoE1UBIFybfzQ/IYC+rfM01foPBCZPRt8 ipZEGjUdqOCBdJo13Ia+2rGgNKQZDIfTm5Nr0RPZpvsLqoJhhKltlIVuZttW jKjy4TSwgk+gmePGzIxKPrimRHMI9EdLCYXOaiHwq0OV7l706LpQN0UQAjuK p+p2orltHzAK0Ky5w1dISxLzWDVonlvtJdKT0jinNvQtFe8q0vMDkLCCPl7S fYE0TbjwIKU6BEZLRVGkfSw9o1OFIbBR7rmf9Ji8L6kQzZ6/bk46qI6TI0LH +FAYpE9omAra0RJalwHpU//+172K7qw0p5Ku+Pk6La0mBEoF2wtKaHquod5F 9IAi7G/StZxqRi2awv1xjnTdzVz7DnQO/bSM9O3KgIg1dKrw1RhptvsvCcqi EGhb/niUdAeFSNdBL/sLh0nfT7Us46DPann0k3aybqh1If8p1/pID8zpNASh V3/b+om0R2NZyxdojl1YF+knoZSONHSGqLOd9P/0p2rR "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwd13c81d8fB3AjIsoWQnZm2YS8rr3uEBlJJFFp+6qkjTIyU1kVlYxC1r1X paUURUMqGiqEpEKFJP3O5/fXfTwf93Pe53zO533e5xzVtdu8wvh4eHj6eXl4 qN+ExqxV7h23l71t7u5lbVtj2z3P5YjYh7O2Qde+eItL2SK9UMm09X2lreef iZkD/xhY/znx2KX3N21XfBu709i5Gs9Tbbm57x/bpsb9faabsgXCa+QZme+7 been6zNlxvdBo0VQLvX9N1u9q+Hx114cAydCOTjp5Xdbfae+ab/zKdAQXPC8 MXzEltUmLP51Syo4JcYKt1aP2o4V8Ozh50vH66GQUq7HD1uT1qb7fGKZUNtx +17pognbiIiaUEidQM3+/X+T38/YvnGfiuO/kwtj217fzWH/bH13JL32WpiH 2hnXKsaXf7bb9ESklPfn4TWSjRL38iBaskdAzyIfr2/79Lkn8OJ27a1x44un 8bpx2O3pWX7cXf75d+7GAry+ryDzpm02ul5nj1jQz0OhpO3OI3EhiAVFtDz4 7zwCEg5tbfAWwgqpBDOV/PN47dL/4EyXEDIebJ7Q+0zcXB2z5pMwdiBpOzf2 At48dP3waVoEzWJh5R8uF2Hr+us+kzLi2NIr9Wh3ZzH0Tb++tTQTR72//uzd E8X4zLNw3Z4V4jimO7uBIVuCdXmxkVPHxXHrAt+mWO8SBLS5pU+LSeD7IHPz vNYSuJh0NvPMkQRftfSTt+xSqPz7aS08IwWfsY+Lrmy5hO5HWnfdlKTRmsKf NpNwCfk5/u7JNtKou/4xXu/8JcgaN/iL7JXG1m1+XcovL0E0LG7n3ElpRAfc Ed1ucxmTDyWuSIzJwDjMuKmXrxzPTi1WU+ifj8ATP+mm0RUYWyh39cYsOQTF pYfLp1VAsozXM0RdDsF6Nbt6LlTA63rH/tI1cqjTO8ij+qQCHe9juszfyOHH 8Ueh3hqV6NR+kOH9VB5Tmo/Yl1oq8eFa8L+Uawsg6L9o/ChPFXgc3U4Zdi0A bahyVZdwFVTbjA06Jhagi1fm+UKpKqx9L7BqgZkiTukOLknSrEIffzmn7Ioi 2MceGDxxq8IgfXLL/SIlMDq9800zqjDSnfH2X9pCWP0edmyWrsZM7wjNpmoh onj3iq9TqoboZ8+L0c8WYgfHZfCHZjVO7BHiTgqroEf4xL/v5tWojms+uIOu ggMxpjGr/KsxlO0qEfpMBSsVKnjm5lYj8LarqfMbVVyUtF/lJFmD3sbo8L4v qlgx2yf1kHwNIppKc2KnVXHkjSu7WqUG0Q+F/t5UUkN5baLC+OIanOxobrJY o4bSc7+LhDxq8HjQ1U/nkxomNmjMW3O4BjQJtxjR7+pwKKO/MB6ogaz9p3tp M+rQXH/fu3u4BsORh8Uk5mmAo2QcHTtWg5yOq0UyBhr4+Pfgy7q/NfierftE eZMGaG4rexqlanFWWVTDaEADfvwqfCm2tZjWe9Lm814TxWXD18TTa9EeuEmu 85smRitaLXuyalGaOjs0YEYTgjeKd1fk1GLFd0wGKWnB5Xikr9H5WlyuqVLb sEoLMpYpm77X1SJg6fHdMa+0kL/hQ4pHVy2uOvuoFjxZhFGFjqh6pTocZZe3 b/mwCBBtNdZWq4OXxqx4m9FFCPowzM7UqsMwb21/l6Q2rsuL63stqYPKDfFy aV9tTGXSryfRSHuTVvPkt9o4Wbjg8OsQ0l7Fgb7zsw4WGhUctS6sw8L0vL8O UzroOKlf/OMCifd3tFJSRBefdrinFpfUke9QKFGlr4tEdam26co61J+aeTm0 TRf9UV2PN92og/LcayFrxnURIG5/fWVXHb78Ntztwa8PA4Mmi6K5bAw5r6t6 JKWPwMDmB7XibAxmZX/20NCHadYF5VtSbPQZzKyiO+lD0ZNu1SLPRnfIIxoj QR83dT6+uqzJxtOWsDksEQNIDuwIvmLDRl1u3hkvqcWocTmf8nw9GzX9bS/b 1RdD7+z7+PAINqpMeMW9TRcjKm/P11+b2ahoWx/r7bMYc+zdNOZEslHMa7Z+ RfZimO/7xxXax0bOxieGvguWQMLryMjadDZuKvL1lEsYIkW4yvJyLRvrXj+b EyxviNMZq12r2GyI5JwzkVA1xIUr2g01XDb8peyO7DQ0BKc76d2V62yMCR/S tmUZYlIlO+zYXTa0Jv5ufZJiCF7zl3sftrOR9uz3n9HZRmgYi3578Dsbpukt GkViRmiXd35iMcrGG3ouw3e+ERRPnE7+OsaGdrNlwTUtI6yh3Q7zGmej8eZu +zgnIyhceveb9y8b45d/JUrHGWGur/vvKWEOgo6OyljMGCGqguu9Xo0Dnl7l yHRBY0S6rZH9q87BedAfD8wzBn/O/QsZmhz0TxYfzVlojIcvOnWqtTnYuilw 4jfNGNLP6UadiznY7/mgsyHOGN1tVgW3rTg4rXAm317YBIVpW4/MW86B7e6H E3kSJmDt0xEK9eLgw/MJ7x/yJjgq97eS7c2BRqqXaJGuCdylFkT5+HJQ/m/2 fgG6Cab6I3QPruKgoS8yqDnNBAFqDw/vD+PgTaWrKlPaFK8ettw2i+agSK08 SU7RFEHMt6doe8j4TomN9aibor1+Qsw9hrzfgZeNu01MoS1fOOa/jwMtxrp1 57xMYd0vWxF+iIPtXw6W/MwwhX9JfqZDIgeC2lyD/LlmULo0821eNgdP8hVO hcmYwS5o9PAocY7YgZklSmbw2XVwuD2HA70Jxyf39M2QzQ5gHs/jwPN++/Zv HmZILknYyn+Wg/x132rtkoklUjdXFXFgeE7TalDQHFcOzGKjmgPJWbvDj80z x7CXPHOa+Gd48/HFsuaQOzL2i1vDQb3+pi9RmubweRe6S7+OA1p91WleR3PM eAevnMPlYPkT638Kh83RNe9cYV4DB5F/l99j/DGHR0jqH+kHHKxYc2FkhM8C Oqe8T7CJze/+VDwxxwIlvzcH+zRzMJWYvfO1vAVytEQyj7dwECv9Tmu9pQW+ zpM8zN/KQZbehqRDOy3AMEmLvf2Ug7qVB5i13y0Q46MYUNHFwfFVBpXTExa4 FI2bdq852Lb67VxnHku0fDrr/YJYN8SqrVPcEuENibJTbzgo3DDuMWNkCR4j B0Wrbg5Sdm91c4uyxPd+HdWTPRysOxnk+H7SEq9Ei5pvDnFgnz23SJt3KRyO mEdZf+FgYW4Df6TwUoj5xkRyiV+fVrg7S2EpGCrZERXDZP6LXtrpWi9Fv0lF SOY3Dmxqmdi5fykmrJOXWI1xIP3M1kqEzwqtYzObZH5zID+kXnxf2AqDqWbq u4mV+YUlYyWs0MLft6qTWNvs+edJFSucZh1ekTvFgXXu+tx+WOFeYcpOmWkO 1oZkTN7ZbwXttMzx8RkOqkY/cqJ/W+HCE97utbO4YM95oGbKa42yvr5BNvE1 9fK070LWcOouSRAS4OKez67wcDlrLJkUjisnfnV1juwKC2tskuk/9F2Qi5nD JjuX7LRGQISl7FphLhiSR0z6R6zhFVC19e9cLpgPH7S7/LbGjf2OQ27ziGPn RJbx2uB2iNDUScpj6VWbJW3wPiCwU1+MC8/2PIMfJjbgnH5f4CPOhdfxqkU8 u22QUF/yKkuSC3/JtwsU/togW/ljx31Z4ofK1/cKLIM9bfSL4Hzi2JCAd3OX 4dGoVJkz8cqx/pxC5WVQ/bZ8fhNxQPuozCLaMkRJTjy5IcfF6uOzxU3jlkH3 mI90gQIXayVNZjGFbWHq+n5aXZmLvVdD1ydK2ML33ga2P/GJNSceNsrb4lvB M41U4vuVvzIsdG1xxvyLzi9iXY96JVUPW3B1ejrvLOTiR9wyi58ptkjrOafF VOUi/pdLRJ44wKO5aLaZBhdnTke3dcgBAcu7/UOIOQ5lhmKqgKnW1OZU4sHM OROkPGLQufJdHzF9cVvcFi/gbrvBUIYmFzLrvc7QTgCzEtmT77S48N68eMMP ERqqF1UYM3W4iHr0saBFjAaNiqSR7cQndE++KpCi4Y7EzsNZxB2Df5zpC2iw KacrdRKvCGvRvKhLQ0xGq32wLhe+Qet6fd1oYGyI+S9Mj8yfZ17QtaM0iA0M dnsZcBFzhXEqI5kG99CIsO3EefN4H4en0VAfeLoplfhN6/plUqdoGJ76JNVM HOhmprj5Ig3TzHdfrRZzEWT/tEvpHg303Gf35JdwEWIq6HOY1w6uCUeNbhiS /Fq7ofiSgB0EvZw2dBKfznw48VzYDj/dsqJ/EHd+S8vTkrTDw3NXtHSMSP6U zf/wSM0O/0lX3jxOTFPW2STraAcJ5V6RYGMuFgrRD18+aofbbZ+S35lw0WBe 2d6RbIdFjBf+P4kDwsQ1ZtLs0FR+RlDElItTjR33PbPtcNplNZ8l8bz9q0XH S+ywMVHmYAbxzOjWbFqLHTQV/aqtzbh49yaz4oWIPUKvHpHbZ06elxUTqBez Rxjsh1OJaZ4pgXlS9vinHFlaQFx076hI8AJ7KO+qft1IHFGxd+Ogrj2Glvvo CllwMXkgTPOPmz0cnAoz04gl1ZaeUUm0x2t7B6tjllw4BnJ+8qXY42rcnxV5 xDtPmdA/pdsjek/hqjLizjmL/5Rl25N1IWfwgLjgh9pKkxJ7yPLm9vIu5UK/ SVTG+b49fmzJZ/9H7EzOcZtmOSAu5dF5NysuxneIzhQKOWDkU+d+P+KLey23 vRR1gEDhuGMY8az0jOV2Mg646fAw+xDxHTZNdr6WA+6XXvDiENvwnytodHFA cW+ZibI1F8ZnQ2rkjzkgZWSV3wfinpJUdVa6A7Qngvu/EGdWXz0Rn+WAlY/K 100Qj9yT2P093wGSQwlL5tlwUfHljnVTuQOs1sjwWhNrL1Vr2v7YAZoxIyWZ xEodPa8eSDiCKbDuuMkyUg9eCFz+LOOIO5E3hJYRn3ipfUBEwRFevxJ3OBOL dm3VYKk5IlK/UWEl8dS7qe0vjR1hJvCsbT9x54DknE/ejhDc+ff+Par9H3sb vlOOMFDWTXCz5eLpdJiYRp4jxjyTti0nFp1J7HE664j3Mkn0lcRxPE8Sk4od obHvYt8G4kiBVS/EuY7gu/c9LYHYU+y/rQs7HeGWdq2zkVhE/UKhjYITru66 XGoELl4v+bhnvrITpp9ce2pBfMlmofeYqhOKnA6OLCN29c0XKNVxgkKK33x3 4qNJWRFSS50QU5rLv5aYbyTOdMjPCSJ4FZRBPNmwrjn7pBMSak8EDxA3t5w/ F5nrBH7bTZnDxNkvP8QwzpD+jmg1jBKbjwQa8F90wvrYbdN/iP9T9zm+tc4J wbmuOuI0Lr4lOQU6PXfCyXN8NhbEn3y1RsbEnTGmPRp/iNjYRKpXRcYZRyZG 7Y8QHxLjecmUd0ar39ffScQKzV3XL6k6Y9a1H15ZxMylqQlrjZ2RGa9Tc5G4 fsFP5XZvZ+yKuKLfQpz84Q6j+pQzlti8ZIjYkf2ooZL2Ps8ZmwZTrcWINXLz TeYWOOPzD5a6FPHN5TvlN5Y4Q85J5qMC8Y9G7U8q9c5gZWfJ6hIHXkzfl9Hl jBiTF9tdiBdHrL68TdEFcvbxSgeIxbzCinxVXHDdqUnzMPHI0i1nlmm4YGBJ lU48cbXw/nQRfRfoLMnRSCY2LTv9X4m1C/Yp0gZOElsPvrF+H+CCpEcbi8qJ XcMDWpm5Lrjn+Ev1FbEOc22T2RkX5PUGlnURzzGPuKl4zgVb1SUN3hK3CsRU DZW6YPXfPTofiVkXc08crXfB4dWPx4eIffs6A2++csGcQf7Bv8Sha/2+Gsi6 Ymngb2dVe5Kfdr6uvAqu+OYu4KdObKvqc6FDyRWhYmLrNInlPnit3KvpChjq 7tQhbl3NbGo2dUXW9o//GRGbr3Q6E+rtinU9G/ppxMKeJozcDFd40eLqVxPv WmJcuvmEK+72KW4LJu6bZ8RPy3HFPmlN9RDim22Lr/YXuGK3fnrcOuJID11N 0yuuCHunr7WJ+K2z6t/Hba7oWnrh127iK8vEKmaJuOFay6aOdOK84QZVPTE3 lA6Ors4kjs+POLVcyg1Jnz/1HScO+N108OwCN9i3aXw5SSzI3udlqe+GgDsB XfnEQfpDE5sYbtgXm4ISYtEFTfbP090QnG/o3kA80RLJ/Z3lhvuybxNuEPdE q+ir5LhByCf47k3i+pd7ZbYUusHGd8rkDvG648aDgtVuMBR//6eJ+LpwYapV uxtORTjqPCGOmIzpPCftjim3cdEPxIM1Dt6H5dxx3dRrivL6LaKP1yi6QzRF rv8jFa/nzN2FGu4IWDtc30sc3Hq78oyJOy68GfAYIF5RKHgk18sdN7cPaH+j vp/rcaPMDHccvtDROkXcwLeqfPsJd9zKZh37Q2x9Q32RZ4474oWiXKeJLY3Z imKF7ii1u3PzL7GJYufs1CvucKUV5fM4kPo5otSd+JjEm6ciJ0gskVOWfEjU A/xVA5rixPPUVBfWinsgZ5FvC+U55Tm1n6Q9kOaweZMEMd/thLfuSh54f+7U ZUninwNhi2UWe2AsUVZRhvilhVp7GcsD9xP8bskTt9/JDX/r7YHAP3JMBeIn HhJ/5vl7IHTy7BvKzcE8GlFrPCDU/G9sAfHVhO6dtjs8cJTpIqVMfPpVnvzz 4x6wPhi7QI04J0SyUiDbAy8Rlk35xJcke8t8D/zYqiOpTpz6L3rTmQse+Ll8 9SwN4gOL/G6sr/PA1+sX32gSh+yWCpl+4YFGeVc/HWKt+SmlmvJ0CF2LS1lC fCVn6qyjEh2b5n/7RNlSYePJUFU6LpzfZmtI7KbkHHtOh46o+w3DlDer8wQq WdHR133W1pi4ekmUmMwqOswMDtabEltV9wiYBtNx520vvxlxo/Hyaa9QOrgt O5iUO8wWf87YRMf993M/Uh63HmwU3UfHjezwaXNiG9fAXbPO0GElkS26lLip 5eFm9XN0sETne1BmeiwNtb9IR+iK9kTKwUxZz0MVdESy/vFaEceueKozfYOO 7SleXyg/WOP47kc3HU8FP+fZEHv21DyX7CX/R1a0Ue4MVX1oNEDH1K7b/ygP hc9wtn2nY3P0i5BlxKJb6jO+/KND7PQzJVtirz36jr0qDDxcc28niLcKcmjX NRiYEtXMp3wsC8uytBloDR+/RflehZe5gyEDCdyvs2nEZj3R2hfAwK3XtEzK Xtv4NPc6MLCGd2kN5a3Tx1S9XRgQnilup1wsW6DAz2KgaO6AhB2xnEeTaGgQ A+FZwsmUTTuZwtZrGSjd3VhMeXlYp4BUOAMrA8YbKScf/DLTuIUB8yvPflP+ UysxqrafAaeiDSH2VDy7/K9ThxhYlSQSQ9n0scZQezwDjicXH6e8edCiNzaF gSb2xG3K3YpBL3ryGejXKpVzIJ4qG3h2rYCBf6wgA8rzLXY8Pn6BAa/mXDvK nsvjH9hfZqDT6sIGyneOXLp6/hoDj00lqyl3S5pyYm4ysODTrMb/xyu4UePV SN5/bmw7ZeNrTy/zPWRgwk95jHLRt/Eza7sYODIwoudIfHvvoTyrdwy0h7kt pfxOaE625EcGXmUYO1OWVVfKaBxkQL3zWhBl46rilLxhBhq6AyIos5YZJkWO kOfl0nZSTvRziFWbZMB6+koy5aK+1gNTfxjoSC84QfnODt+97f8Y5F6ucZby 1LGNUbGzmdDy/Hbl//3J/9geIMKEx13T+v/3V7xvi7EYE0ulJG9T3nQ7PbxH lgkp5azHlAWVmvfNXcBEeHHjC8qFe3iyLBcysaQh+i1lq5eWZaHqTLz+ye6h 3GG841baIibaP8UMUhYa/vilbwkTAc5nxyjbXPSSs7ZkQjVpYOr/459vumPA lYl3a2cEnKh8TpZ5mLWSib62PmHKUdPjarQIJqQ1bwtSfre1c+9wDBPud9nT VHtJbbdS+zgmtshr/aLs/PFqR84xJsL4v3yh/GHZ2NDddCZWX6zspxyTp8v7 PYuJVH3hj5QrvfMNnE4zyf31SAdl16rnDtsLmTgzUdJGuUdUNCC/iInuz6H3 /z9/9/cdHS1n4mZHGYdylRr7tGI1E6aTppWU3Q9+rXFhM7GsfNVFygctg96f ucEEd8GB45QVTp761XyHiX+8exMp140+FvnZxETiY5kDlAcvwdL9MRMi2xdt oOyppJo53s1Ejv4jC8pDe1aWqPYycfn0A13K8S8zb9AHyPyeDVeiXJ/ON3T+ OxMR9Axeyqp8ffYsHha+VBc3UfnZEKS4MmYWC3+LWtmUfa+v2HZRiIXIkdyL lJOjmvL/iLNwXV8/nvJYf/HPElUWvA5ZLaOswpoST9FkIWHvJz3KTC7DYLsO Cx4zTgqUyxJ+hlkasfDis/Y4tR7XaNu/aqaxIBV/8BLlxxvfXf0czAJX+aoA 5elnhi/bQllw6O79Tq1/Xav4ser1LBSsbemifGSOnl7MNhakhe+XU7a5HH16 zkEWlCfTWJQvD0sd1DvLwuL60kSqHnWuWJ8vdp6FWeIlWykL3rjG/XGRhcGN YSsor00NGblewYLef+oLKSssvhJCv8FCs2BlNVUPE7e5O255y8KzY86PqHpq vOd2vN9cT5iVyj6n6q9Y2ae7EPOEv86WGsrDnXP4tSU88aE1I5NysaXP4Ulp T+ywo7EoL5j8vD9X0RNldKdma+JZu6V2v9HzhB5dqpqq/y+iwjcGu3ti1y/5 YEvi6O2izPUJnnikcsnChFhaSFhhT5InLkdLClGuKhDoTz7mCekkRie1vw0+ ntlfme6J3qc20ZT9DUYrfmV7YvCzIMeI2GLoxdz4Uk+8mDisQ+2P46EFbYUt nhAtTxnTJ97pZ8x4LbIc1vNukWsjFwNVV8W2JiyH4vxCYTli8SkFobC5Xih9 fmbDbKp/9ru7+5K9YL0+aGycOj+uPXhTRcAbejct9PuJb/2b+rYo2RszQWLR z4nni3X2sARXQLpc/zJ1ftOaly76JmUFPkUuVK4kbpzR2Dkm7gOB3GcNecQd IYrndFN8kCBWkJxIfKbuK999CV9sU9jJjSJ+s0dFOzbNF7/lDDXWEl80NE55 KOQHQbXmXhYV/5WS1q5UP/z+/EvUhlh5JCLOXtgfFeJ746jzddtkpmxkuj+S G2PXy1Dj795AqyEuc+lbTXn4HiLGiEceOa2gLJr59UZkhj8mngnZUabruIX9 l+mPgedpCpQDxVTSa4ldvEbEKW/+NV7/g/jpk+WzKafcKRKNOu6Plc3SP6WJ T5fsNa8jXuWwa4hyearXmp/E8TdefaDc8J9OsmmWP16YL31FuXUlT10UMetK Xhvl/wGb44RV "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0.9993000000000001}, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.001\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, FrameTicksStyle->Directive[ RGBColor[1, 0, 0], 14, Bold], ImageSize->{500, 400}, PlotRange->{{0, 0.0015}, {0, 1}}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False], {266.6666666666667, -640.}, ImageScaled[{0.5, 0.5}], {500, 400}], InsetBox[ GraphicsBox[{{{}, {}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwd0QtMk1cUB/BuTi2PdbwECxX6SNwKg8RV4wP4jhkEhoWKOJqlyssNXB1S LduCYzJkUATZwOpGocWxYaFAEalpKKMqwsaABlQcVctrFbEBRCiIImFz5+Mm Nze/nHNy/sllHZHEpb5JoVAA79q7s+3PsNniUP7F13jmIFo6WAXXPicm5fE2 0pYn+7ocrmURrHvGAdIs1kbzM91Zot71ZhXpcCI1yapTENk+ZSGkzdEely06 DRElPHD6P7Tf319E3NcZiNaW647/orvKy8uHdD1E28xq7Apa9yCgqMP4kMjk jjstoUcazwmyfScIt6qGtnn0Et/iyYMpYvV54OOnaJWPpuufx3PEuWSgTaGD BkdjvnNeJPJMipZJdHzQu+87iF8QFiFt1yN074pKbNW/InIu9M+Ooftq9EZ7 7yphcLXODaOjFjacIVwoYBJqOh6gF3Pzg5i/vAFB56fuDpF5IxVO3K3rgNs6 vDyI/tpiSpEMvAXpnmm22+gTw3c6D4g2QELjXlo/OkazpDq5kQplOaaVXnRs 09Vag9YB1OKhl93oSmZou3KHE1T4cf3/QP+VNPWRcdwZCgMHmLfQwW8ftWYd p4HbZ/P8G2S+sLxTu2kuwFFRg9vRVAbDu8/qAq0zA7sM6OlG34736lyBlpx3 TI++wWphbz3tBsk500k6tF6gLbaHu8O3Q/SiZvTNcmnxHaoHuMepO7To9u6e CMGoB8i6Btrryf/WFlIrazbBYqx6uhY9k2WW5X/jCZ3d7qM16HdS5lV5MV5w 4Xb/aDVaSMk0CNw2w0hYgNsldGlBQVmbbTNo9jMcleT8LUrGwhU6XN12ZYcC LfKOnCCk3lBNl0l+Ivd/smWTf4QPfMyeT5ejQXA4esKJAWreq6pSMj83YG/w IwZ8sP6ivAQtMB7ZndKwBbSi/t+L0CvHUvsqM3wh4CjfLkMrXr/0ygzzg+3L opnv0U3qU3rn9UzY30iln0HLCAhtPsGE5YeRjjlocep02SELE3pLTA7Z6DFb lO1ZCAt+482GZKH5CXbl3ToWpAmreV+h9wXFHFQ6saEi0Z4gRcf98KM54zgb wk2ynyXog+NehvP32UC/3iRPRz8piVcp93CgN1faKUZLA4fHnqs5ILrXo09D L6zjnT1Uy4ERGNORllqKt3WiE7WLzWsu3JNfWseBTwt8G9b6E+SBL9CTdl7d Wn37tPmwhgPixKjLa3XHD3O70E/7En8lfdJawfWv54Bk55eXSP8PyhYb8w== "]]}}, {{}, {}, {RGBColor[0.5, 0, 0.5], Thickness[Large], LineBox[CompressedData[" 1:eJwd13c8ld8fAHBkb9d1rWtHSFIp34zno8gsWkpCkpREWdlbUVlJRUTZ2eve qyKiQSR7ZRMpZGeV33l+f93X+3Vf5zmf8znnfD7PI2V74+RlBjo6ur/0dHT4 L6i9+qAzc0+rIn90zPSGDXbUte0ZlF3FThScq+Tlx6BvwqiOrcwLI6/v+xq4 dQykpFi6ZksjMKPKjQvve6xAF7t8YaQ0AWuX9mNUjnSCrqPEjL7SHIw6whYt uuIHEh2Oet2lFZjT6xqPj533YX225LuT1yvsuKVctl1aJHSxrYYxYq+x8295 vNadoiASwur2NLzBeiSYHAkMMbCam6wdOfQW4/fQnODgeQBTNfbPJO/UYuse 5ZpH+eOh7smTJ52l9VjBjsALwu8SQTEh5MicWAPWkrzLzkHiKcQmOC2y323A epuXju73fwrWiTqm2hc+YzlnCrN01JJg9elv5jyOJuzgzSV/k8xkUErRvxVk 9xXbKVOX98YhFYzafHMFONqx1uyXqaZH08D/pAt9unY71h/eOj3klgbFbfbm KrfasZjtHM3/JaWBYPsJZuORdixkysPvyFQajLfvsA2idWBfV72720LSIaCz XfjXpS7skvz21a28DCjt2Xm3prIXkwsNsUjtyYLCO74X3832YqtHY0mpf7Ig V7XxYK1kHzb/odX4Fikb0mKv/awL68Os765u5p3KhocGL40/Hf2GGRwwYFVv ygb3Cjnu5v5+7E2MZDwnNQf2J0g9/LY5hI22ukVMOuWCcHrFfmfBYezzWUtf tYhcEPQZfuGsMoydjTDbskvLBX55FZ8btsNYwI0V53NducAR9lXR5eMw9pHO oj9fMw82NLgj3aNHMF+BYJLstnzoz7tv4is+hv1hKugM8CoAy4n8Xf8OjGGB es+D7aILYECymTPYdAxr/mW5XTmjAAYf8TbeCRrDBI3FOpy+FsBQ4CP9uNEx rCNH7k7a9kIYPZWq/TJrHGvRfRv4r6EQfmyU7u1WnsBo3OxxFLpiuHqgg89C fwKbTvbTYWUvhqmby3P9FyawiJxxZlP+Yvj5Xa1oNHYC+/qYfrNCthh+fa3c ObswgckMe++kMyqG2fSP25lok5hxbuXWldhiWDbuI+2DKWwTTIPoBEpANTTq S8O5KSznj+TzZLEScH2tHWbjPoUdSN3fpCRXAnPy2fNRL6ewjwM6kQpqJfCT yb3pB/9PzG+n1rnH5iUwWM0VkvLjJ8Z0ihBulFgC9fsOzbDFTWPuku/2RxBK gdlxKf15/jQ23iVZVSdcCkfSsi3UPk1jykbO6suSpVDLy11vtzmNmTneNlLf XQpVM31p1fYz2LFGqZ0mxqVQmu1u7qExi9GSNw/lBJdCsmhO3fD4b+zkB8nL QZOlUO3AqlHy9zfWxBO3T2mmFObPq/Zqc8xhu/M2slsWSoGYG3+cb/scFnr6 TNa2f6VgoWcGpWZzmMRcwAKBWAYTAV3kpYo5TPSQ4cNBrAz+/e7p9gycx/54 SB29GlMGvIJ3+Yfvz2PZOh3C6vFlIIUdNDVImMcKa8JymBLLQDcy8aNQyTw2 EM68415aGdyTt6C8Gp3HwsLSfQ0pZUC6+C1u48gC9ptxWTSntwyU2waOBXIu YkpxYf+Excsh5c8Zj3nhRcxzezjhnnQ58Ii1JF/asYhdiyr/tShXDnNXan/p H17EmruWuCi7y6Hsb9ZdXi80Xv368ox2OfyncPPDi7FFbKxby/GQbTkcDmLQ ev96Cfv8TrMx+3k5lGb62h2oX8Km6AS1bTLKQaZx6X5O5xJmUBzix59TDoyk yb7IuSXsP/Ef9teKyuFTXqOXmdwyJnh9qKqvqhyOdseXTzxYxi55S51u7C0H M+UdSmwOKxg1i05ClJsCd5jEojRvrWB7BRkYdvJRoKKfMHsjdAXjvdicd4BI AfL9f0Vdz1awq393Ox0SocD4ZOe+jLYVrEKPZiYrRwHXF2EaoPkHC7D64rpT iwIxxFEjD55VjDfj2qfTVylQ86s7L4e8itVr9PP9uEaBhdovnP0Kq9hDn+dN nk4UOOPyqvmw7ip2/mBmdqQrBcSbY0/yeqP/v2qFRvpRID8cLPJGVzHVnFOG UzEUaFhPdhihrGHxqWIvD5RTwNlqKndP7Rr2yzeVUZNKAULN/ung5jXMI/q/ 91gFBSxuNztLT65hl29L+WtWUuAnD537JaF1LJxpcp/wewqwy14K+O6zjhll MmRZtFPAyFTh4RRsYN8SdCqIcxSYLfHoOHh0A9vZxrLSNE+BOGKtwD3zDWzh +InNkEUK9PVaJCi6bGBdnCZOP1YocM0u8plj2gb2YGtMKfEvBe55/86eYdzE qgd2hcSzU+FzOqVyvmETkx9PDGGSocIXxsYp4+5NbP9Y3KOk7VRouTxMyhrf xObU9d12y1GhaweHi8XWJmaQOZ14XIEKY3k2snWqf7HP56xGvXZTYbOMIzo+ 9S/2YNyp9ZIGFZTfX7yg5vEP64pnpVBPUGGPrGfkgxBkv1PhHKeooHon8tWv mH/Ygn+Bv/VpKqgb0Pif5/7DtDJfj/w7QwX9Js561uF/WLbv9U4FSyrYdNBU +oy2sLVtyVmK9lQwXGAOxnjpQCOA1jnpRYWwH5UsPiQ6kJ63WF7wpsLbQddo CpkODFfpKjZ90HyNg0lKCnRwjDFvF6c/FcQzqFSRw3Sw0NvGJRpMhSUz++kV NzqYKDHVXI+gQsqrD2eLuulgj5W64ucnVOgp8h38OUAHViIk5oIEKvBn7bks N04H35oiXkUnUiEi7pnrszk68PaSKDBJooKbo0fUfTZ6UHgVMVeTQgUDMdm6 Kxr0oHOWXvVmJhUWg8KUJVPp4c+TDwyMpVTgblk9oZlJD5Nni0ZrkBUlnDzM 8+ihedyi1a8Mrb/KrDKWRg9hQ1eH5svRfq3JGdG30MOzQp+BFhoVsl0bLo/S McDiJQOLS1VUOG/H/SzDlgFeFEqJjX6iwq2ykJqaqwxwQ05zM6SeCnEMf8b6 nRlAVyODS6aBCvXPhxQFfBmAmdrcaPOZCvsHiituP2SApSPZHW1NVOA5c6rD /j0DkBNWmONaqVCnn8ChILcNbt82xUL7UPyk+e2flbbB280js4LfqGA+bog5 7tsGRYnuX/OQZ4M2bhZobwNnujmF1n4qiLy27tpzfhsYpz+xJgxR4aaS7Av1 2G1Qf8yx5sYYFch8pQeOrm+Dh8RVsZRfVLgyxH58ho4R2J62EkWnqVBacMkh moUROsbOWT9B1jcSSG4hMoJp/J/pqBkquIZ60ZvtZoRdQjO8br+p0LCMNVnZ MYKc3Kya+CLKR1/jxRvNjLCxu1zm3xoVfGZNf6V0MEJvCE3SZp0KAQwd7s19 jBBuoJz6DvmOYn/4rklGsH9jIhO6QYVHPtMFv7YYYVua5nm6v1QoF+Fav7KH CXq8qWzjW2h/LUzibOKZIMbS1eg0Ew1WnNtEY58ygbBGx9Ns5PWQM5nVz5ng lCh/4DoyQ551hXgBE9Bk7ZhSmWlA2HAe7P/ABLq6a0JjLDTYmxSjeO4PE9RW iPeeZafBzW8ttScsmEFeXub2H24aZDgfPMx8kRm+mBcb6/LQoJs+7d3rK8zg oOKYFYuMybvVyHgwg3N0log8Lw04PQTeLscww4DIANdJPhpkc1u8SvzADAwS cclx/DQYPDRWNKLCAutSF498FkTxdBrvfqzGAsUaXNnsQjQ4crW80AhjgQGb hkIj5Pzo2wVlxiwQsHWgtAHZ59uOvNv2LMB5UvFRnTANSB7XsxSSWcDbrntX tigNjuUsJ7uwsILllm+VigQNbOPJr5i5WeHUJnP1ZeRbQTqdSURW+NXu7PkU OcX8AddHKVawyQvg3iZJg1nWXQEimqygKnd4pAU52sHuQt1NVtC/K3LrgjQN mhXbpQT6WGEkjTpmJEuDUdK6Vu4wK7xO3hvgibzCIGUBk6yQ/4DvWzqy+Dfn OIclVnjQoDewgex8n33bW242MF8v5XwpRwOe6UPj9jpsUJFNtVndQYPjBcVZ FflswFRM3O6kSAOxIYZ9/aVsoJrzRDYW+SevWfVWBRtoJcivlyKHua91631g g6QAA7FV5Fcah9k6B9iApnHsRNBOGkh/bnec52YHwp7WlAglGixPrKgourDD uc7Vwz7KNKgVMqw65skOP/LXOBOQY42SDF382UHX9WUxBVmxEGwr7rKD2Pep 23PI1h4RD/XS2CHq8Bsnu900qN8msmLbzg491eI2R1Ro8FRS603Sfg5oTBbc NrOHBk9a3bR0NTngJ/tECOteGsSH5FZPH+aAZP/D/TLIUeOC77WOc8BxTS+y BXJQzkLT0DUOUCp+2vMe+bJKzqDMcw7Q3Oh2eriPBira/Az57JxwjL3Hl7Sf BrvmDcNO83HCF9/CuF3IimlBzH8FOaGbYHVXF1mGcZbdRJYTjPsnSK7IpPp6 /jngBElWRVoj8qZpgKyqByd0iZureB+gwacLUwaVQ5wgIZOy/a0aDfzOGGss fueEThlDzRbkvccKdilOc8L8NXvNUeQUdRdCwionmBn5rzD9h86XwNo3Nz4u iKquNTuKvL2R9cZOHS7oalLs70AOPiD/6GkWF5AqntV2HqTBgV33wlvzuSAz dpfUd+RpmWlv1jIuoL/+0nEJ2Zyv2PpWNRfkS3x5T1BH659Wkz/ZwwUZisn3 TJAHX+i/YWPnhpfHSL61yBpcV0a8nLgheT4hI1mDBpKhBQ2q7twwssTTkIvM vLZYMufDDdNdj3srkFvGg0KuRnDDF3WN6g5k+8qnMubp3CD3tCiVQxOdB8fm y2q93GDl87XRA3miYf/PZV0eONm357amFg2awK+txJgHnO3vWRkgl1BqXzud 5IG9M4qyp5H9Xpje/36BB3bN5oY4IvN5Oyh1+vCAaZendyKypvwz5/JiHtCn VlxbQDbUCfE+yM0LaQ0vphIwdP9zGSvD+Xhh6PWP7DRkbkL4v04iL5irvTDP R+4Yvh/qKsoLqlWlD6qRbQIeReXJ88LYNUe778her3JeiOnwQmVNc7Iy0CBn 99cGei9eGFje6qMhczw5wXnclxc6L2hy1CA7/2s3SQngBQd6YZV6ZNUvPe3q t3nhPsfs2R7kmmujA25xvEAhZ0qtIvdkLs9/z+eF2+oHcvdr04CVTBb5PMIL eumWf3KQDeTK44fGecEoy8G2CDlc5SjP8iQv3DXZ+YGCzHzEj1FylhfWYjZd apEZnftnPdZ5Yd1w57VvyHQ1yXVS/Hwg5/bfAMchGqxdEnPy1uWD3lsOXFeQ /3OmTEbr80ETx/6Q68heXsdsM4z4gFvw+28X5NVI/7Nfj/PBRA2J6oe8Qhk4 JGvFB0/Lq2YfIC+wpJBaPfjgYwmj8Bvkn3niNfLZfPCluDGW9TAN3i3nUIJy 0Xjrc0+4kBNgX15PAR+sHxl5TEDWb9d/HFHOBxuhdMFk5Iz1m9d/vOODxdnL DCrIFwzrhHL60Xxzh96ZIXdMXHHZQSBAhtTPa8nIeSoL9oECBBh4u+PFc+QQ Hz/LbiECXPK40ZqBvIf7gX64BAH26oNkAXL0/tdik0oEaNn51bMK2TCM83OW PgEWr8qSBpDfSpVIy/kTYBXeGwnp0MCV+8TxI0EEqKCUPRZFltuY87cLRfPP Hx0UR47uUOlNu0sA/j0PbGSRrcKLYyQeE+AD/dyevcib00WbQkUEUL8TxGmM rF5R2MUxQgCXtVfvvZFnM0wYd44TgDj1OcYPOe3B7B6jSQJc11c4G4jM7qgc FTFDgBMfRvvCkHvFCnWY1glgvdZNjUH2Ci0o/kfgB4NB3Q8ZyBST/Hvzuvwg lBFu3YTcdyWPmd6AH6IejxU3I/8Lyg3hNeYHbT0tulZkvbIcn90n+OHmwp9H nchdgpnXnKz4IYJv5tkg8urwM6MpD34YYP4lPYfH7xbDPpLFD3rFfcJ8uqie R0bfmXvJD4OBNQR+5JDMKAa6An4wpRDZBJA/d99fFy/jhzZ70qwQ8nnNiJ+W 1fww5jmSKInsxxT8uaebH27N5vruRq5+4nqvhZUIBYaMgcbIPnOXgqU5ibBF cT1+DPmAoZmXOw8RTGZMJEyRC9fV7IVIRHD6Y0U5iZxi9feQjQwRXPj31Z1D DpCJWPutRYTY/1KuXkHWKnp2lceNCMbZKfNByKssMRcu3iJC1RdlzxDkcpug M2XeRLj18PF6KLIS4ZLu2SAi6Kmtr99BJnvIS6ZGEUHCx3k0EnlTvaxbOYcI nVrTJgnIbz7W65kMEOGbR11xAfLp2q8eV4aJwNy2b6QQebqqKyNojAhdd7l5 i/HnUcYZyqaI4DjD7lCKx5tOVy24QoTQvDOsNOTDQf+pjXALwHXNxb/VeD4P 5uxw1xaATS/29hZk2/1FZ6J0BGBN/0lHK/KGCvV2lp4AVPt86WjD45d/P9Zz VADyprVaO5CjScOpWucEQErB/nUP8slFQSEWVwF4FeVgOozclx/O+jRdAFKv HIyeRWb/EVS6nCUADfNnfH4jq8v4WJ7IFYACPvLlOeSkxOvFrCUCMGeUcWAB 2fLOCXPPtwJQvGuoYRl58IJozuleATBjfli6iTxKKNLn4SEB8fGjRLYj6P3N JGf+GoEEBRKy1uzIh+++SPooQIKn9I+lOJDTtx7+9ieToIZZJpMT2W7a68m0 AgnuPSen8iBPfDg82aBLgnY7MRsB5F9eXXfCfEjQL8wrKYkcOawc2OJPggmu thrcSgbhnuRgEozuyLORQnYW/O9qeTgJFo9nP5NGnqMkGo7Hk0CLe5JTFnlp wZJTt4gEtF9B7xSQ/14fe7BtnATa49vu70VO6dC4ZzpJgu2Kfbz7kDHN+JCk nyRgLP71CHcQxxG3ffMk+PPv/TNVZIbcrNOX/pHAXftmxgFk5kkHwTohQdDk KYtWR+a5OJccckwQ7uUODR7C43e0/vLouCCYFtfrHUZmv9X0N+eUIHy0li7E zXg/x/rrOUFIMFT01UFeLbeRJNsLgs/FFO4jyMOsremUAEGo+p0taoBcWlyS +6NIEIz21rUdQ979RuLbRqkgbEzQKZog53+I4uChCsLAaF0Q7qw+h+v7KwWB WbdfyRQ5iVFaOaReEJ5SrwYeRw4zjysRHREEg9Ig7lPIZ+jcKkwIQhB4Oqr3 LLKjUfulDAEh1BdG5M3xfMTv41kXEoK6yEpP3LnyS5czJYSAW5uVeA7P73EP /k0lIdCsZdG3QM544en8Ul8IvAcVnlgiLxz2287oLwQZtTzjNsgsUf1fzwUJ waOnZ2QvIpO7NX2LQoXAI+uAPW49x7+tFveE4ETR+wnciQ8DAkueCEFOn/yY LbL2eFCfdakQnD8U32CHHHP7duyrSSEYyjx44ioer+uGW9dPIZiP1QjF7XrB 5ezijBCo0i+W4z590Ep815IQXKkJFXRAFplRzX9OJwwSY/t7cWedHv8ULiwM y8xypo7IVTI6W2bGwqhfBLE4Ixfyvhp1NRGGdL5OFdzP/yp/jDkhDJJzU+dw h3SLRDWcReOXT+fhNri/IKJlJwzlJgeNbyB3LLw4sN1fGFKCwwJv4uf/HZ3z QqEwELfKKl2Rj37rTN0qEQbPFs5B3IVLua2cFGG4X7d3C7frDrP9O94Iw2LH hLYbfn4iX26e/yQMv3mW3+FmNj95/8OQMNBrd752R5aeTc9J4BWByVNbEbfw /Wfx7svkFwEzc8sM3BOSJpxlJBH4UhRZjfvlqdUbX8giwCR+dRm3yqujagwK IvDJlueCJ35fwpY/OB4SgdUJI0UvZAsR/THMVQTsMlteeOP5deOOjfYQgfWx nle4jzV1ag56iUBzd1krbu0Au8f+gSJg0z9K54MsNxpsWBkpAr5HlKxwL7ys LDqYLQLCSxlcvsjTDGGWd3NFwGVsVRr39/PGbL0FIkCUlP0Pdw9Xn61XuQjo KbHY4n7r8keA9k4ECrVWynDfO7jXT7VfBPiKMo/74euPW5MPGxIBt4C4S7j9 f9V0to+KgKm+xS3cN5+Z7nabEgH/m75JuM/QO42WrKB8NLOO45ZuyDbYzScK xyQ9nP2R35iLCSjqicKER7VDAHLc6fU1bUNRKHpk54n76vHuwbNHRWFWfDYM N9HgQc7tk6JAWy1MxX1djUlzxFoUlh/9asdNJs3YJniKQkefs1ogng++z/pF PqKQ23tNB3c9V7bSR39RyHE6ZorbneniymKoKLAMf7TH3bTUcdc0VhQaXkfH 4/ZvryxmfikKwvmxv3Cf/pr4SCxfFCSOMK/gVmy85aNaJApbKXZ0QchdtSq6 thRR+E+yn4hbuTSju+qdKCgOvNXEPRgb+c+9TxTe3bsVgRtMLI+OcZBBLtGA NxivR3d35mvykCECqxXCLfJhneMxgQy2w9ulcK9oJDYaCJPh1N3MPbgLFbqM CuXIIBD45ARuMtNxQ+9DZDjkciYK9z1tiZdtumj82vV43Ku+s6xKBmQ4p+Wc FPz/+xRZP2hChrSre17ivj/coK9rSYbQ81V1uNff6OjxeJKhRIFxGffVP4Ss qz5k8LvXvo67a+8oU60/sn0MXQheb18GfXAPI8PSVhMHbocnVbp9D8iQ/slW CndXW2TGvkdk2ORNlMOty23JGJVABnVK5U7ckrfX6yCVDAcDmvbj7nFV08nM J8NeKT5D3OVTnQzmZWS4+1r/JO4YG/da9tdkYClUO49bz6Tk0M1PZFCV1r+O m6KwU1tjlAx9gYb3cRtNLN3w+0GGt18WHuAeTHubWjVLhlmWywm4Wcknt2CD DNPzmRm4n/WI7g6mFwNhH49c3HsffbeuZRGDY6k8xbgtub3f6hLFINwl8zXu O+Gc4p8kxYD4+dp73EV0z/0Nd4nBNfZLX/6/Hu99A40HxYAh/kEnbobFj5om emJwqn6tH7fSdYvklpNi0MWaOobb7PvMxskLYkBPC5vCHWAdfL7TUQxMVAtn ced0E9+c9RKDfaPii7g3GjR8LB+IQZbZ2Bpuk0rbgxdzxUBEbOYv7rUr6c9u fBMDo4pT/3Bn8I/TB3CKg6h90jJuHwdGVSZZcfDeJfj/55tWb7eP1BKHeL2Y cdzqP1W3vhqKg81ZniHc2wWOJPCfEYfgFWIv7vVrlz8/dRaH0yGvGv+/v/GY 6Q9fcWD7RqvDHV0l2LH/rjhAqMob3NK8nwda0sXh5KekHNyfMg4898wVB3bz 7HTc1w+m24qXiEPt94cpuKm2fpOOb8Whx5wvHrchRXmeuVccyIez/XHPGiaV FQyJg/mF95644wZZbp2eEIdB9Q8uuPtZRtZfLIpD4BO3y7hvWjxk1OKWAAVy pDHuhK0/gm46ErBXb4KAe6U3xijHUAJ2Oo39/zyfLt/hP2AqAZT6RkbcvA5n R/UtJaBg3noFvw8RbdR8socEXOuJ78Htnelx6GOWBJy55JSIuyDTm8LJJAnP anS5cfNWJsAbZkmYlTNkw+3eRmtwYJWEx1aGjLjVt5YHPnJIQqGV1jpeL+rN XZmDCZIAj5a+4x7ncDy7LCEJq9LZlbhFXC3XBtQl4ewI9xXcdzD0CXBTEryY +orxeuVw+Wfs+T5JaDpyWBGvl4OThpOzmlKg5P4mFa/PxlbzSa3ZUvBS/dk3 vJ8YKR87lcQhDe0Ei+14/zkZFd3l7CQN6m1cjng/OzUkWPGgWxqCi6khHng/ jDRLTlKXgYZ9ReV4P3Xd9W1wKVMG3hPuvHHBHa4eFpMtA8qXF8pwu4wkKii+ lIHeIOt83P8D2NCMrw== "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0.99993}, Frame->True, FrameLabel->{{ FormBox[ StyleBox["\"u[\[Eta]],v[\[Eta]]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], None}, { FormBox[ StyleBox["\"\[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"\[Epsilon] = 0.0001\"", Bold, Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm]}}, FrameTicksStyle->Directive[ RGBColor[1, 0, 0], 14, Bold], ImageSize->{500, 400}, PlotRange->{{0, 0.00015000000000000001`}, {0, 1}}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False], {800., -640.}, ImageScaled[{0.5, 0.5}], {500, 400}]}}, {}}, ContentSelectable->True, ImageSize->{1078.6666666666667`, 865.3333333333334}, PlotRangePadding->{6, 5}]], "Output", CellChangeTimes->{3.414230842171459*^9}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJztXQeYFEX2Hybs7K6ERUBA8EQMd3qcWc9P7zzvznymO9PdgSKfipz3VzGL 4SQtLDkusiJZooQlSVhYEEQlCIKgSxZUMrhkEOX9673q7prpqe6tnu7ZncWe 75ue7tdVvxfqvVehe7rvbvFSqyefafHSfx5v0ei2F1q0bvWfx19sdOtzLzBS qEogELo4EAh2aRTAfQgE9I3p0wQ3CWSf6lN/YdR9+BMKFLS8iqjDjMN31M7v x5+gcX64cRh7XlZ/AD+/yyAE40sOkpxIqBOK5z5IckKrs9sghCR8TCfyY+qo ypZQR0E2rc4eJ7L1j7FBwCiKv/woEDaOtS9BFaiX75+89hD/SSM/TxX1dvwJ UydDbUR7+A0aJ+z3spIDMBV2A0UOEMK9zApSJkmAkCG4oGUnByAzpyNrCChh zifcWsME7wZKpqBrUKGqJaMKUNU1lMyvwm6hZA2QpNVkvsbr83QUIAponxhW phNBLonOWacnQc5MNdtQLFmKGk2xCCFjL+u0s7GA8ZaTgAxZ1fTMmGZekdgS eo1UqBYx9p70CtwTsoxpeUgjC1V5Y5hyW8pECsXv/YJbyBToqRZAIf5T3SJq aaH8DCGyBS8ZuM1KVEGzH+lQuWhyKJZekJUcXqYLWbzRyA1KsOy9TBd4YYmd 3eDRXgbuPe7WViYestFokg0gcy4TinPkTO+ETInmHoIq+KRszzmyzDu9QRZ+ qk1SKj7lyXodR6Eo9kLxNZJEOe2TX0RicdfyyTrmJ9yaLnW5UDoIcituyNZC aaJ+ZUyI3GPDsa3lCa6l56bNgFDWFbjBM08JXeTJqIu6Utdzm9e8zpMZEttn uMDj6hperCuexlkyHC+x/nEdETIvdJ0to56gWHqmN5ksdTlS5q2uQS1cNm3S o936rBvlQy5QaO+M8jdNirOh5bKRGyFNF+jSMwuWuZDkBly4m2s82ot4guKN Hcst91n6pofSC1fVsp/s+l5Mr1me157Kga3s4pCXbEUcpJpT+dvV5FOecVII AM+MqcArBXqJoJNd0CsHr3BwuajipLFskdRKI0K2ggRIm8aRdRqpzpX2LZ/q FlEQofysIO+axXBIYcCT5bhGtmKNsCGmKg9xT5FzqRRqiIhV1cNUQ5WH6W4M R3qYrJFk3bDjuqK1nPMV7eZGZkd1Tdwc6Wuq65xvwvVziP9ot+XeZlS1vLOO iucrlrsmBtbRfQK02z+5aldzprcaKltOJUSdfk4KO2QgWisjgB9+X6P+ifo0 KS0zjWRJJ1qYbxiphe9/HtF8X0vG/4JJpEEtaQ9oMgBKt5ZK7z72aXKabMqe TvKlE605bh36ZP/f9Pd90obm+59DWhUkVaE9IjrMlHwUnZeTB11rd4XN8zbL rhqmndJpQvOdNVXJMt4tN87a6Lul74Ke0BLypWzZwH5Vkrso3TQL+9bvg/zf 5kP7cHv4pMcnAKegsaTehYq0i1zUldFqarRADO0xzxSe//Z8OPXTqbRTuArq m9DGpqUsrm3UqH38wHEY/+B4aBtoCyNvHQkHvz8YOC/dNJM1pYJek5tPJr2G /HEIlH5Tmn56JbTYP+knK1Zb+iwfuBxys3Opa1jafymc+vkUL6BDx5rneQuQ 1aNWQ+canaFz9c4SEAtZ4qH5tDRC4TDilhFkXQyLFe+t4IUusJRHDvTD5h9g 5G0jDaAlfZbEACnJFNag1oxbA7ln5BLUmHvHwJ6v9vBCjSWVZDLpQF9N/Ao6 VetEQKjkzlU7Y4CUZOI36mbAoZ2HYEqLKQTXLtgOPnj4A9i+fDsVaqQolo51 bN8xmPr4VMirmUdYGLVxWEqSRbXt0b1HYe5rc6FjZkdSdPhfhpMFTx47yQuf oyieDnjsh2NQ/GYxdKrayQBc/f5qE6BcRgoNfok+kyJ3cdfF0LtRbwJCfWc8 PQMWd1uMLktY9YxaLyrVn/6f6dRPJdYPWpuK7l1jsFhp4+yNMPHfE6FDRgcC xfHZjP/OgA0fboCfTvzEK9VVNJkdcJczu8C0p6bBhplmYKXmrU7bbDLCh898 COP+Mc5oEfwddeco6r+2fbwN4alSLUWxdWxs6VmtZ5ED6nGCgYdxvKDtAsJm rS6wlSTniT4MPx3/Cb6e9DVMfXIqdK/fPYTwLAbaR9rDmHvGwNL8pcSAKcjr VleU3sBnWq+bto5cqsfZPXT8DpEOMPru0bCk7xLYunArHC+NxVfSoA5tI3B4 52H4evLXFKyYa5kDBjibKPT6VS+y0/RW02FR50Uw67lZ1NSHth/iQFEJsEwd ndmRPUegZEoJTH2CZYYaeTHMMuOYLcxdSI2GZVkfjyM2+mQoq3c2bTPg4HcH qYE+zvsYJjWbBO9e/S50O6tbmJhWgw7RDrTcM+ymYTD+gfEw89mZUPxWMcx5 ZQ51yGxWAztW7ID9m/bDoR2H4OTRk4ETikobIjAF1n6wNl6EunEi9LuoH4kw 7v5xQoSX50Bhi0JYP309bP98Oxdh+yH48ciPXAQlO/C8nQ1Hdh+BL4Z9AatG rKLutOiVIlIYRxv5l+RTimgXahcloapTomX+DD3q96CufNA1g2DEzSMoQjGS prWcRhFb9GoRzH5xNgy6bhAUPlYYRCWZ4+AIYHkB/2KeRs6zn58Nq4avYu29 qWgTK7Nl/hbqEfTv2vFrYd3UdbBj5Q5mNKYtc3/WmcGWBVtg34Z9qHsEju0/ xgCO7jkKpZtL4ciuI5jLiVa6tZQamx+x7WzFZtIthH3MqpGr4IvhX8CyActI NVR16I1DEy2UTSGOFsIvWqjgqoI4C2FGYBYKIg7zfDQQNj46AX4ZB5bNmX2Y lmvGCgutHLzSzkAlk0vQHxMMtHf9XvQzs4FYcGsGCpOBDnx7AI8wlxcpu9Al tM2B/Rv3Q8nUEkpoJYUlsGLwCnIlVGdum7nUEQy5cQj0bNiTLPHede+RVdB4 Pc/pGdSiHZMMJmE04x7alt1Gugg4AMN42LpoK+UGEiFfE+G1eBGwSzdE+G28 CDVMIijZ4UbahnE2RUbELxuoB7WmwDTx7eJvYfXI1bCleEtYa0XM3thy+C1+ oxgW5S6ifeZqzC3QASIwv+18mNhsIqmCIcM6fwaIoRSC+W/Nh1F3jIKil4sY Gqdh4BY2L6SjDI2Gx0iPpS3quIjqspRi1B1912iY8vgUUS4IEx6eoJ+d2HRi AgqWxlp4FJZIEKJtDYSBSU25i2OdsfeNpX381cqiFiTRvDbz6FiThtmAI81+ YTadZ1oH/iLhdS6nlekw0rbaKtpqpWirzXM3622FrhXbVh+1/4j22cgwoa0+ 6/uZZVsxLeLaSrNKXFtp1kloK9bTG3WxTFxbaS2Eli6r7XHEgHg8IVvjyXxJ r7uw40KpzCGJzDIbhGx4yGyAXR/WXdBuQeAKCY30sBmUU9tfbBy+aHXCZhhN 298qdh2isFIC8bF97HLH9gPDx04VdsxNgsbdvrpXxTyvQpH5Y+7Q5NKZFjJj bleRP8jIucTeckjQQnapWPYsiLAtrOlEc09AlWSVXRQU96HR8a+NQ9mNbI4A bO5Ekl1t0m8fTdpozkGVjFbGVR4XAieJrBRcHoouiyzv5ZdelXGcrVQBTpu0 X6mx/fGQj+1j+4HhY/vYFY/tB90vGztmBh3/9znx79hk59DJ4anPosWfLp2P m93gKU2gSEnnSxDNXUCpy2U5r1GdEjtHsZkXmx4XpnuM6/WEpHDVlz9Cngip CqU+/01SOFlYeCBh2FikSDJSHQGcNmm5UmMnM6aowwkFLa9qbOw1cCLopY4B EoSvij9hrBgxIMIGTUt6+mu2qtsWlt0kZin6heXFV64xvZ4s09jLMPaCxl41 23LOlU0xy7L0DBnmE69moz37cm70TAnLBD21Zx5IXwoXjGduev2bYCmjRRTr OrJQg7QWNsG2pjjMiG9GwUrQnIspq+vIpnTLX2Z6iJZoQXkzm+DDEuaCFoyn hePP2td1bslQugnpxqYhiWh0NstKSMsaXluy3ERzbT+ZC4jEbcoRqgApMWcF SJqkde3TjYLM9gC1OC1x6NnQ1pIVJVXQien0iXhB2S+FFZVoNhU2IANhvbr+ SR7aQ0+uXKqlJDFHJTWCinXLLUWnTsgEm8rmQ6bhdI6xR5OFiFUNEy1HUSTT ifq4rXipbOY7AqKmhJbkjMYNaOWXldpb7NWU0JKc/rsB9ZeQKrXCPrbaZSnT MzddX5ZSxXN6c2cq7j9zA69+ccjiUo+S1M09AXUnq6NrWKoAZT1gLuLJxSBV KIcGkv1J1rlcClCn8U2aNG5L8qqaI4DTJoX72P7Yxsf2sf3A8LF9bFfYfmD4 2P5MO2EqLGPg4Uw7SXh/pp2qmba4udSbe0OTccbK1JiWs2/XAstixlOp/T9G /vKw/VGOj+1j+4HhY/vYFY/tB13lwY4dhrp5ynh5PI39eRd4FfekdXo1akhp Vp/Wipkao8Vpopa8vUzzsDLvHIg9kXav5Ehjmv96FXWabH3Id0wPaL4Tun3H j8iZ4hXF8r+8FxQAfhkObr2jRTgNBg4EyMvjvVEW7fFybI+OohJakNOgY0eA O+4AePZZg1Zm3YqiZbqoG6JtBJo2BXj4YTDoaLOIdu711wFefdX4avbEPY6l 06NpTgvRNgJPPAFw3XUArVoJfR6vcK91Qwtpft+sGUCbNmDQeUtVjEyZKdKR RSQ89VR66JiqduzWDagtO3cWOgaV06v/ZmiHNP9t0WW9GVohPfpeZ0PzPczF +8jtUx6NRfPLLnJ1SsFkTzeWIdqX02Dp2m3IKB6Ox5GduIZXhPhPE6+oK/CH 7qg/y+BrehKZ7EqxeDHiI44BZFAvcWk+NyrWM+xqSkaheJr9/QDi0Uwk66Me w9uzfIXrtNwg0H/1s4029lq7R1LGKGk9I/GshH+baPGPk48/J5zJUksv2KiJ EKsrOW7tFGnoGbhzvUSApKrlvAB3pJfIK5mp9M1HU8TGka4r8Uck2lTp+liK 2DjSdYf3er3m6+Bch534E4wvFJXQghKa+TGohhZtXICqMpLLHzRCWKEjND3R s40LKHt4TdZdBiHb2BNDKtHMJM3rtoVl1TQuEP/xbLzpU32qT/WpPtWn+tTU UPfhj/HwLhhmHL6jdn4//gSN88ONw9jzsvoD+PldBiEYX3KQ5ERCHfFQKFMd cUKrs9sghCR8TCfyY+qoypZQR0E2rc4eJ7L1j7FBQOmpawRVoF6+f/LaQ/wn jfw8VdR78Mf+H3pir07ZhWUTD4VqYpZV22OBFAqbFgmpyFllF5apaim9qCZU be1EerFXw0k1mZCOAIS41ctBXEfVZO2W46SazDgKWsrakhZotXAyXRixf1KT WHvQ6UHDkZwBhWKBpOVqOQYVs/Q6FaKZOGFfV8gpu03QXgFzXfmLUhVYi+ts svu6kzKWBbm6Z/hlO001r3gJQ9WoBOYxeZ5zSNNSl6yIczuYQeW+6kZY4cS0 ihYI3G0QLBfvTLaqVXYNy1t965RdN1ORh3OpFGrIrqWb8pNlDdm/B+xrEI3e 9vScE+lNelRzrLmsZWo4Qcl0zNeNzM7rKuxVd4wia1/nKKLNtTFF6gJQlphk Dmmqa7rqoFAj7UJR9npxBR6y1NnaiTKuI1PWZAo+JlBMjeeo7mkQo7KGT1IW mTOkvM+U5RjVuubBnmLwRhXLmXjQVyEUnQev7O6zM21rcKGMC5e6eOUburKm c44ia0RHQRx1XMOyYZPs3FwHscwBqjpGsXCKlIew3bxYVYGQYg0Ssa4nqriJ WMsZkD0j01JZuUWq3bTSEZBoK+f9bM3UqpySwLRsZ+cCibbXAlK2tGaZV8sM NC+AZCtK9kDCH5zX9UIbheU01ci1VEChrgJf0fyytbSkLOVgschLfNkiT1L4 wnk8g0yhSRTWzxRixd6PnNtBAdSNpPKkZbr/TCTsOrZnz5KcDRusZHXFhQl7 ZNPZkFFXxtd0VlbXtPBtyVfs1VAsl2NbTljDHk/YRZWvZTmTNSzlM5Wzx0tY c4X4j3atVuHprFQ8X7HcNTGwjlaLabd/ctW0PwepPjqT6vRzUtghA9FG/r/+ /H8CuqWJf/05f/at73++r7mlJfzr1OkjijGLto+0h6X5S9PvKS1pTPOfuKNO a45b3yd9/6tIWsITn5xlSn7jxfu3vw9tA21h7N/HwsmjJ6VXl9JO8zSh+R6b qowZ75uj7xoNJw6e8H3T90NvaAmZU7aAYL9ixv00g584BTD/f/OhbZW28O7V 78LedXsbS+ql05NiH3OtcPFbxdAu2A4GNBkAu1bvSjuFHbyIIzPWNLB++nro UqsL5J6RC8sGLINTP58iui5lghkVMDfP2wzd63eHjpkd4ZMen8RjWjwHOisO AT8Hvz8II24ZQTlx0LWDYPvn23kB3Qixoj1vAXJkzxEYe99YA+T7pd/HgCg9 75pPzDLIDVa/v5o0Q9/PvyQf9m+i/xvB+ZYixdO0fA9fjv6ScNpVaQd9L+wL u9fuDgggJbHCmljHS4/DkD8MIZE6Ve0Ec16aQ6bDz3mKYulYJw6dgBG3jiCs jlkdYfYLs8mCBpaSZBnaliUGmNRsErQPt4cO0Q4wreU0jB0qdK6iZDrW/o37 obBFIWHlZufCjP/OgB+2/CCwbJ4DzzuMKJR+U0oyoGboD4NvGAyrR61GrTnD s40qLyZU3luyFyY3nwwdMjpQIhh520hYM24N/HTiJ3PloLVp+HJxJhzbfww+ 6f4J9GzYk0TJzcolP1g5eCU1An7qK5pIxzz43UFKUzpmXo086HN+H1g5bCVK KTCVGpFuz8A7GpnXb/t4G+mLeiMyNiYeL3tnGTYyr3SWorg6MCaFjbM3woi/ cn9D4M7VO8P4B8dTqxzafigGWElmfnkpTNpiDsJQ6N2odxCxWdB1rd2V0Bfl LoJFeYvgwHcHeF27J73L8I8fOA4bPtxAztStbjcdHxtw6hNTYcV7KyhRMA1j 8JU0qKVx2Ld+HywvWA4Tm06EXuf24hyi1ADI5YOHPoD5b88nTtsWb4NjPxzj GGcoakJ3XzGRsRFYXoXF3RbDmHvHQJczuwR0ZujpBVcWwNQnp8JnfT4ji2Ji +fnkzzHMlNSqq7Hbv2E/fNT+I5j3xjwa7rKOh1GRXRYtGOBwYnqr6fBRh4/g 80Gfw5biLbB7zW448O0BwbaKoo7cIXne3v3lbih8rJAS2shbR6IrhDS+qGbf i/pSOkYTLOq0CFaNXAWbijZRev/x8I8cM6SsbkPaZqLIBFEypYT6QUxgXWt1 hb4X9IVuZ3XLIAmqUdeL2hdcVQBDbxxKk1P0o5nPzoSiV4tgUedFML/tfJjY bCJJtmHmBtZITD6m3NZFW2H78u2Ua5HVpjmb4Ojeo0HMMK9x0XAyQQmHfZkL 4zaEZag8+wZyaBsiDMRiX0bDbQi2LtxKlkBuObQNwbpp62Dt+LX4ZW6C2xDF 1NzX5tJRVY32xfAvyInZlyUp3JbdaA01Tzm04xA53JJ+S8gGo+4cxXRmmZ+7 S01K4pjpep/bm8YvGBIYj9jCC3MXEuOVQ1aSoCWTS2D1yNWwc9VO8mA0Bib9 A8otegFtq8HJYycpNr9Z8A1l/6X9l8KCdgtgzD1joN9F/WDc/eNg2E3DYODl A6FP4z6Ql5PHYholzqCuCxOc3lHn1cyD3uf1DmFBpnGPBj3IC3o26ElVB14x kGnMfIJZkjkLdKndhY44rSaVwZ7wnUvfIc/Jb5JPx5gf+v26H+13q9cNOlXr FFsfejXqRecQP6zh4zksg0c1NBqOdJEHSpdDWy4His2++Ghrtg1Bh0zWIYba 0VFYo+Ex5nNUnPYUWp4Poarisgzs+XoPefLKoSspNaEHYPCg/J1rdKYA6l6v O5q0qmZdJKNoaGWWxbgJLx/IrRWlRhlx8wgaKaGlh/15GPUFkx6ZxGzPHIdJ PeSGIehnyI0B4jaE52HQdYNgZuuZBm3G/80gGpOIIX+c9zGjjX+AYTWdREdh jYaOMeqOUeiSBm1um7lEm9dmXkI5Fu+sdZFWDWY8PYNo7Ii+hc0LiUfRy0VE n/bkNPpd2HEhdRITHp7AkDgelsUxLx5laDS9HvJ9SiJzNdyeiQoqxcOVWm79 8ciPlNS3LOCJGtPH5rmbeXaKQElhCbUhBuO4f4yD4jeKGRX5RaD4zWLDkpjt mMbMItgSYZjwzwmQf3E+/TIrh7Cp0CV/NwD6X9KfjoK0rQlDbhxCeQAjEBt0 1N9G0TE2MDY47g+4bAC5fUx9GHz9YDo39h9jGUOOj+ewDB6dqdEm/GsC5RUU LEdzlFmtZ5FLxjoKw4GhfxpKR1GNhqMxrQFZYuNGx55UT4o5PClSotQTao6W PFmST0i82NXrCTpbS9Drpq6DNWPX0FGWRtu3YZ+R3Kvx5F5m+F1G2ywKvyO7 j8Cer/YQry/HfAlzXpwDXwzlyfzTnp9qTppBzod2wME4Nhf2rMwZedNEaSEL mwC/GLl6dmImZu3PMwpLgNAu3A7aZ7THB79T9sAsqGePVbj1/rVET2hdI/bQ etcY1rrG0q2lNOCIpWF3Wbq5FA7vPGzQ0EpIY7+J5XYcDlAfzOyPXRnSND40 TkceR3bx+oe+187vO0Z8D2w7wJA4HpX9huoye2t8dwm+T0lkztJoODHU9a1l 3dOJxQT/VVk+to/tB4aPTdgxd+/FPW4S9zPEGrEi88fcoam/V517ovx/5s4l 9paD0gu5Zde9XL8y3DmokqyyPzaJG8To+NfGoewOM0cANrcIyS7+6Pd1Jm00 56BKRivjoosLgZNEVn/3ujeiyyLLe/mlF2ocZyv/Lew+tj8e8rF9bEtsPzB8 bB/bDwwfuxyxLf9bZ3q/UxLz8+Tw1Gfo4l+QzsfkbvCUJmekpPPljeYuoNTl spwzqU63naPYzLnDogm4RtxjXK9VJIWrvrQS8kRIVSj1uXWSwsnCwgMJw8YC SJKR6gjgtEnLlRo7mfFKHU4oaHlVY2OvgRNBL3UMkCA83VIXxooRAyJs0LSk pz9wvbpt4Vq2nE0nLiwvvnKN6UH1mcZehrEXNPaq2ZZzrmyKWZalZ8gwn3hI P+3Zl3OjZ0pYJuipPehA+nqAYDxz04sABEsZLaJY15GFGqS1sAm2NcVhRnwz ClaC5lxMWV1HNqW7pzPTQ7REC8qb2QQfljAXtGA8LRx/1r6uc0uG0k1INzYN SUSjs1lWQlrW8NqS5Saaa/vJXEAkblOOUAWoxc8mDo4aKpqufKUKOjGdfS5R ENIewENPrFBJk3RMfSJeUPbrgUQlmk2FDchAWK+uf5KH9rA5KpdqKUnMUUmN oGLdckvRqRMywaay+ZBpOJ1j7NFkIWJVw0TLURTJdIL+B1bxUtnMdwRETQkt yRmNG9DKLyu1t9irKaElOf13A+ovIVVqhX1stctSpodgur4spYrn9MbRVNzb 5gZe/eKQxaUeJambewLqTlZH17BUAcp6qlzEk4tBqlAODRS1BXPUhPZQp/EN oDRuS/KqmiOA0yaFV2psf/zhY/vYfmD42D52xWP7QffLxq7Es2EZAw9nw0nC +7PhVM2GxQ2g3ty/mYwzVqbGtJwhuxZYFjOeSu3/MfKXh+2PRHxsH9sPOh9b FZu/L7IuHD4MsG8fwKZNAGvWACxfDjBvHsCsWQDjxwOMGAFQUADQrRtAXh7A m28CvPoqwDPPALRsCfDIIwAPPghw3XUANWsyMZgcTZrgoFdzBneynqRtPfj5 Z4D9+wF27OCirloFsHQpQFERwJQpXFQUs2/feDFRxBYtuIh/+xvAzTcDXHUV iQiNGzMzMDtUrw7V0WED2XDGGVyLs8/mp3/3O4Df/AbgzDMB/vAHgvFIsa2c BidPcsX27sWHbzDVAnWoDZYs4cpNm8aVGzwYYOBArlzbtly5Vq2EcnfcIZS7 7DIuff36XJtQCB9uiRrWQ2WhVi1+/uKLefmbbgK47TaO07w5N9orrwD873+c 34ABnD/KMWMGlwtlxEbAxti5k+vAdMlOjct+ZuMGKAlKNH06l/C99wD697d2 g7vu4pa65hqASy/llqhbFyAnB2poRkI3wCbHU5dcwo305z8D3Horh2jalEM+ /zyH79wZoHt37oEYMCjG7NkACxZw8datA/jmGy76sWPKjxMvy0iUWAs10/z4 I8fftg1g/XrOd+FCbpoPPgB44w2Ap58G6NOHmwaPX3qJ69GsGdcLzfLHP3J9 L7gA4JxzuAOFw8D9p3qc/2BkYNEbbwS45RYOgVAIidDIAll17QpBtE0QDYOP TywSpvnqK96SzP/h4EEIXG8olkxX8g5t68OJE9wY337L0T//HOCzz7gxCpnF xo3jjaUbo00bYQyMgNiIuvpq4Sf16nGDVKmiR1Rd9BvyHzyPkXfttbzevfcC PPQQx3z2WWtHwUxbXBxvDZT96FEIPJSacHqbtnXhyBHOClkiaxQBRTEnfxQZ RUcVnnuOq/TwwwD33cdVxeR/xRVxSSdQXYslNBdmWTyHnYOecPRY0h3mhRcA XnuNN0fv3pwvNhM2FzYbNh/Kh7/LlnG5jx+HZ1NjoZZaVB06JCxUUpIYVe+/ LyyUmxtvoX/9S0TVn/7ENceUi5bA7FKtGuhZmQUYGaphQ4Dzz+dFb7iBV73/ foB//5tDvsiC4vXX4400ejQXBUVC0VBETABbt3LRWSx0To2R7taMpEcbcpSl njFj4qMN8wL2L+Zo++tfueboJrqRWCrmRqoPkQg3UoMG/PTll/MkjkbCvh1h MMk/9RRvh7fe4uzy83mngB6NnYS5+8LOBMVnnUtgaGosda0WcHqS/u47znrF ivi8ZB7GYF7CTkZ3p7//nat75ZUA0ShA7dqJPXyNGokBh53X7bcLE+HIAU2E Iwm9hx80iPPH4RTK8+mnXD6Uc/t2LvepUzDLvYVux5+Q0jpv7CpRI9rWMQYB 2NNpMUnlUHDd1XC4isq9/LIwHiZkNN7vfy+GSJi4MVvpyZwl9rgBIBoaB35Y D4MTsxYmc9YwxBNd2ipToeFQRi1TaQ8/L4e3xZhaokVy5nYjRvm8BIf8yLRi WOZ9aLEnZE/A4+VqkZfpEyMWBlQGB79jxwoPw+ElToQefZT3hSzMqFzs2Ill rUCEvIvzQVZ0pGU11gvQsEJL+1QAve2BB+IHU5gKMFR79SL+VA7D1Zz29XHm Cf6aEWroLEXd/Xd+pT9NdpXEtdP7NN8J8Uh7XinNxJDOEgmzC25D+jE/om0E du8G2LyZJx5cuzB6ldjkHDH2zBd2cmKZ01IUguHAA5c9hg0D6NFD9LWYYXGq iZOxX/2K1m3CksQapG1tCAZ5Aj7vPD5UZENwKmSek3XqBNCzp+jG2RCRyukJ 9fvvAUpL4XR+X6Pv+snkX2u/Tq0EnEfEmL3rQYnBpwUrbNnCnRiDMpO2If2Y H9E2YizDaF9ttIB7vDyOLtiXL9poDy3SaDB5MmTQik7IGIzw9Z142vDhSMMh C6dhnOFRkNOMlWX2ZTTc8nI6LdNEY/HK8FjkajSMYTwy09g0kNFYpGs0jHk6 om0Gza9xbUena7khkxZ5uaY4XcLvnXcyTdmgTEPC4RkeRU20669HGg7i+NOz cealf1kGYuZmUwqtPE4u8ChK23AsDb8ZNCvhRTGJ0RFtI1C1KujJjlIdb7PE RBi1oiW8MVQhV/ObxWlZn08l9I/stfc+LcDfmZkmsqQTLcw3jPS473W+h5UT TXidg+FpFtx9N1+hxHXXrl35kBQXAfDqHA5VaZyMny5lw0V4bwH33AN6x8KO +Bavour9UJbWS+lrdNirZfO+zVjSxB4xh/eLxvUE7E1zaBuGkSP5Wh6uHbLz WbxLpnV9vUfPpm2IVNF7/xzcVtMGCLj4oQ8tamjDioMH9VGIfq2lDENS0fyy i1xtBpO9OUGGaF9Og6X7wkJG8XA8juzENbwixH+apJb6Nf7Q0OEsQxrxfFKy WNSQ8DnbwqF4GlV7i3P5yihUD/dkrhqKByN+rRWrBSVnxbMa3+YyrDUItDSV bbSAqjTPOQZIWq5IPIQ4ay+NrFqGhBaWykANVluRs2VhdX6iYVU1lRVW4if8 L9OJjVsrVlOSoQR/xH2eqjK8oFhNSYbSsvl1TUfsA/gTlFTMMLC7SYpEJTTz s5ituQQNDcJWXIKGb1jesK1hHzQIZ8TbpLtxItvYEzbRakP8J8V9gk/1qelG DVT5f2k8zNY=\ \>"]] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Magnifying Time", "Section", CellChangeTimes->{{3.414178264906905*^9, 3.414178274201919*^9}, { 3.414178311837214*^9, 3.41417832703455*^9}, {3.414223036799496*^9, 3.414223038524214*^9}}], Cell[TextData[{ "The previous plots indicate that in the ", StyleBox["\[Epsilon]", FontSize->24, FontWeight->"Bold"], "-dependent co-ordinate, ", StyleBox["\[Eta]/\[Epsilon]", FontSize->26, FontWeight->"Bold"], ", the boundary layer solution profile is nearly independent of the value of \ ", StyleBox["\[Epsilon]", FontSize->24, FontWeight->"Bold"], ".\n\nThis suggests that we look at the boundary layer using a ", StyleBox["\[Epsilon]", FontSize->24, FontWeight->"Bold"], StyleBox["-dependent magnifying glass", FontWeight->"Bold"], ":" }], "Text", CellChangeTimes->{{3.414196168452715*^9, 3.414196211552691*^9}, { 3.414196247558284*^9, 3.414196253288621*^9}, {3.414196290899466*^9, 3.414196359748771*^9}, {3.414196394152685*^9, 3.414196432151236*^9}, 3.41422304576581*^9}], Cell[TextData[{ "That is, view it in a new time co-ordinate: ", StyleBox["\[Sigma] =", FontSize->26, FontWeight->"Bold"], StyleBox[" ", FontSize->26], StyleBox["\[Eta]/\[Epsilon]", FontSize->26, FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.414196466813229*^9, 3.414196505845407*^9}, { 3.414196566626403*^9, 3.414196567936403*^9}}], Cell[TextData[{ "In this coordinate systems, we need to apply the chain rule in \ differentiations:\n\n\t", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"df", "(", "\[Eta]", ")"}], "d\[Eta]"], TraditionalForm]], FontSize->28, FontWeight->"Bold"], StyleBox[" = ", FontSize->28, FontWeight->"Bold"], Cell[BoxData[ FormBox[ FractionBox["1", "\[Epsilon]"], TraditionalForm]], FontSize->28, FontWeight->"Bold"], Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"df", "(", "\[Sigma]", ")"}], "d\[Sigma]"], TraditionalForm]], FontSize->28, FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.414196572028133*^9, 3.414196729625298*^9}, { 3.41419676256109*^9, 3.414196780366003*^9}}], Cell[CellGroupData[{ Cell["System Under Magnified Time", "Subsection", CellChangeTimes->{{3.414223082488538*^9, 3.414223094150512*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"magifyTimeRule", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"\[Eta]", "\[Rule]", "\[Sigma]"}], " ", ",", " ", RowBox[{ RowBox[{ RowBox[{"f_", "'"}], "[", "\[Eta]", "]"}], "\[Rule]", " ", RowBox[{ RowBox[{ RowBox[{"f", "'"}], "[", "\[Sigma]", " ", "]"}], "/", "\[Epsilon]"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"magnifiedEqn", "=", RowBox[{ RowBox[{ RowBox[{"MoveFactor", "[", RowBox[{"#", ",", "\"\\""}], "]"}], "&"}], "@", RowBox[{"(", RowBox[{"NewTwoDEnzymeODE", "/.", "%"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "TableForm"}]}], "Input", CellChangeTimes->{{3.414178349669138*^9, 3.414178532428618*^9}, { 3.414178575525263*^9, 3.414178600095454*^9}, {3.414178633502653*^9, 3.414178677911797*^9}, {3.414178766068377*^9, 3.414178783026292*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{"\[Epsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Sigma]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}]}], ")"}]}]}]}, { RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}]}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231128954398*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Order 0 System", "Subsection", CellChangeTimes->{{3.414196884466272*^9, 3.414196892598787*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Order0Eqn", "=", RowBox[{ RowBox[{"MapAll", "[", RowBox[{ RowBox[{ RowBox[{"Limit", "[", RowBox[{"#", ",", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0"}]}], "]"}], "&"}], ",", " ", "magnifiedEqn"}], "]"}], "//", "TableForm"}]}]], "Input", CellChangeTimes->{{3.414178718240238*^9, 3.414178722141565*^9}, { 3.414198031496089*^9, 3.4141980325885*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", "0"}]}, { RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"K", "+", RowBox[{"u", "[", "\[Sigma]", "]"}]}], ")"}], " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "+", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}]}], "\[Equal]", RowBox[{"u", "[", "\[Sigma]", "]"}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231205665885*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"ICRule", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Rule]", " ", "1"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Rule]", " ", "0"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Order0Eqn", "/.", RowBox[{"\[Sigma]", "\[Rule]", " ", "0"}]}], "/.", "ICRule"}]}], "Input", CellChangeTimes->{{3.414175018186032*^9, 3.414175074967189*^9}, { 3.414178793575595*^9, 3.41417879706553*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "0", "]"}], "\[Equal]", "0"}]}, { RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "0", "]"}], "\[Equal]", "1"}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231225383291*^9}] }, Open ]], Cell["\<\ That is, we no longer have the obvious inconsistency that was present without \ the the magnifying time-transformation.\ \>", "Text", CellChangeTimes->{{3.414196900246703*^9, 3.41419694873904*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Magnifying Time", "Section", CellChangeTimes->{{3.414197121125443*^9, 3.414197124436708*^9}, { 3.414223058742871*^9, 3.414223060344889*^9}}], Cell[TextData[{ "Mathematically, we are using the assumption that the boundary layer (inner) \ solution is analytic in the transformed variable, ", StyleBox["\[Sigma] =", FontSize->26, FontWeight->"Bold"], StyleBox[" ", FontSize->26], StyleBox["\[Eta]/\[Epsilon]", FontSize->26, FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.414197139119042*^9, 3.414197154704323*^9}, { 3.414197201790636*^9, 3.414197300710206*^9}}], Cell["\<\ This assumption would be motivated by the plots of the solution profiles.\ \>", "Text", CellChangeTimes->{{3.414197344050581*^9, 3.414197382738846*^9}, { 3.414197418214567*^9, 3.414197437542293*^9}}], Cell[TextData[{ "The time transformation moves the appearance of the small ", StyleBox["\[Epsilon]", FontSize->26, FontWeight->"Bold"], " in the equations: \nfrom " }], "Text", CellChangeTimes->{{3.414197494509337*^9, 3.414197525751519*^9}, 3.414223125928342*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NewTwoDEnzymeODE", "//", "TableForm"}]], "Input"], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{ RowBox[{"\[Epsilon]", " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231310538155*^9}] }, Open ]], Cell[CellGroupData[{ Cell["to:", "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414197563638649*^9, 3.414197564729548*^9}, 3.414223142256951*^9}], Cell[BoxData[ RowBox[{"magnifiedEqn", "//", "TableForm"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414197553605384*^9, 3.414197555446787*^9}, 3.414223142257133*^9}] }, Open ]], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{"\[Epsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Sigma]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}]}], ")"}]}]}]}, { RowBox[{ RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Sigma]", "]"}], " ", RowBox[{"v", "[", "\[Sigma]", "]"}]}]}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231324323667*^9}], Cell[TextData[{ "which we recognize as a form where ", StyleBox["regular perturbation", FontWeight->"Bold"], " (from Lecture 1) can be applied.\n\nThis is what we do next." }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414197609566686*^9, 3.41419769639391*^9}, 3.414223142257416*^9}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Regular Perturbation: Inner Solution under Magnified Time", "Section", CellChangeTimes->{{3.41419770450203*^9, 3.414197729493625*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"ExpansionOrder", "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"uExp", "[", "t_", "]"}], ":=", " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "0"}], "ExpansionOrder"], RowBox[{ SuperscriptBox["\[Epsilon]", "i"], " ", RowBox[{ RowBox[{"u", "[", "i", "]"}], "[", "t", "]"}]}]}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"vExp", "[", "t_", "]"}], ":=", " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "0"}], "ExpansionOrder"], RowBox[{ SuperscriptBox["\[Epsilon]", "i"], " ", RowBox[{ RowBox[{"v", "[", "i", "]"}], "[", "t", "]"}]}]}]}], ";"}]}], "Input"], Cell["So, in the chosen expansion order:", "Text", CellChangeTimes->{{3.414223188503338*^9, 3.41422320203719*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"uExp", "[", "t", "]"}]], "Input", CellChangeTimes->{3.414197831181438*^9}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "t", "]"}], "+", RowBox[{"\[Epsilon]", " ", RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "t", "]"}]}]}]], "Output", CellChangeTimes->{3.414231353735691*^9}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{"magnifiedEqnIC", "=", " ", RowBox[{ RowBox[{"Join", "[", RowBox[{"magnifiedEqn", ",", " ", RowBox[{"ICRule", "/.", RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"u", "\[Rule]", " ", "uExp"}], ",", RowBox[{"v", "\[Rule]", " ", "vExp"}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"LHSInnerODEIC", " ", "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"First", "[", "#", "]"}], "&"}], ",", "magnifiedEqnIC"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"RHSInnerODEIC", " ", "=", " ", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], "&"}], ",", "magnifiedEqnIC"}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.414197874911858*^9, 3.414197947582309*^9}, { 3.4141979793562*^9, 3.414198016265418*^9}, {3.414198051110632*^9, 3.414198108272088*^9}, {3.414223152794488*^9, 3.414223153165935*^9}}], Cell[CellGroupData[{ Cell["Order 0 Solution", "Subsection", CellChangeTimes->{{3.41419811636818*^9, 3.414198119529936*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ StyleBox[ RowBox[{ RowBox[{"\[Epsilon]Order", " ", "=", "0"}], ";"}], FontColor->GrayLevel[0]], "\[IndentingNewLine]", RowBox[{ RowBox[{"LHSCoefficientList", "=", RowBox[{"Coefficient", "[", RowBox[{ "LHSInnerODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"RHSCoefficientList", "=", " ", RowBox[{"Coefficient", "[", RowBox[{ "RHSInnerODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Order0ODEIC", "=", " ", RowBox[{"Thread", "[", " ", RowBox[{"LHSCoefficientList", " ", "==", "RHSCoefficientList"}], " ", "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "ColumnForm"}]}], "Input", CellChangeTimes->{{3.414197874911858*^9, 3.414197947582309*^9}, { 3.4141979793562*^9, 3.414198016265418*^9}, {3.414198051110632*^9, 3.414198108272088*^9}}], Cell[BoxData[ InterpretationBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", "0"}]}, { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"v", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], "-", RowBox[{"K", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "-", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "0", "]"}], "\[Equal]", "1"}]}, { RowBox[{ RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "0", "]"}], "\[Equal]", "0"}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], ColumnForm[{Derivative[1][ $CellContext`u[0]][$CellContext`\[Sigma]] == 0, Derivative[1][ $CellContext`v[0]][$CellContext`\[Sigma]] == $CellContext`u[ 0][$CellContext`\[Sigma]] - K $CellContext`v[0][$CellContext`\[Sigma]] - $CellContext`u[ 0][$CellContext`\[Sigma]] $CellContext`v[ 0][$CellContext`\[Sigma]], $CellContext`u[0][0] == 1, $CellContext`v[0][0] == 0}], Editable->False]], "Output", CellChangeTimes->{3.414231372090373*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Order0SolveFor", "=", RowBox[{ RowBox[{"Cases", "[", RowBox[{"Order0ODEIC", ",", " ", RowBox[{ RowBox[{"_Symbol", "[", "x_", "]"}], "[", "_Symbol", "]"}], ",", " ", "Infinity"}], "]"}], "//", "Union"}]}], ";", RowBox[{"Order0Solution", "=", RowBox[{ RowBox[{"DSolve", "[", RowBox[{ "Order0ODEIC", ",", " ", "Order0SolveFor", ",", " ", "\[Sigma]"}], "]"}], "//", "Flatten"}]}]}]], "Input", CellChangeTimes->{{3.414198164075834*^9, 3.414198197936309*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], "\[Rule]", "1"}], ",", RowBox[{ RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}], "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "-", "K"}], ")"}], " ", "\[Sigma]"}]]}], RowBox[{"1", "+", "K"}]]}]}]}], "}"}]], "Output", CellChangeTimes->{3.41423138101583*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Order 1 Solution", "Subsection", CellChangeTimes->{{3.414198220441773*^9, 3.414198223794063*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ StyleBox[ RowBox[{ RowBox[{"\[Epsilon]Order", " ", "=", "1"}], ";"}], FontColor->GrayLevel[0]], "\[IndentingNewLine]", RowBox[{ RowBox[{"LHSCoefficientList", "=", RowBox[{"Coefficient", "[", RowBox[{ "LHSInnerODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"RHSCoefficientList", "=", " ", RowBox[{"Coefficient", "[", RowBox[{ "RHSInnerODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Order1ODEIC", "=", " ", RowBox[{"Thread", "[", " ", RowBox[{"LHSCoefficientList", " ", "==", "RHSCoefficientList"}], " ", "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "ColumnForm"}]}], "Input", CellChangeTimes->{{3.414197874911858*^9, 3.414197947582309*^9}, { 3.4141979793562*^9, 3.414198016265418*^9}, {3.414198051110632*^9, 3.414198108272088*^9}, {3.414198261160348*^9, 3.414198282345582*^9}}], Cell[BoxData[ InterpretationBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "1", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "+", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}]}]}]}, { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"v", "[", "1", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Sigma]", "]"}], "\[Equal]", RowBox[{ RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "\[Sigma]", "]"}], "-", RowBox[{ RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "\[Sigma]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "-", RowBox[{"K", " ", RowBox[{ RowBox[{"v", "[", "1", "]"}], "[", "\[Sigma]", "]"}]}], "-", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "1", "]"}], "[", "\[Sigma]", "]"}]}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "0", "]"}], "\[Equal]", "0"}]}, { RowBox[{ RowBox[{ RowBox[{"v", "[", "1", "]"}], "[", "0", "]"}], "\[Equal]", "0"}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], ColumnForm[{Derivative[1][ $CellContext`u[ 1]][$CellContext`\[Sigma]] == -$CellContext`u[0][$CellContext`\[Sigma]] + K $CellContext`v[ 0][$CellContext`\[Sigma]] - $CellContext`\[Lambda] $CellContext`v[ 0][$CellContext`\[Sigma]] + $CellContext`u[ 0][$CellContext`\[Sigma]] $CellContext`v[0][$CellContext`\[Sigma]], Derivative[1][ $CellContext`v[1]][$CellContext`\[Sigma]] == $CellContext`u[ 1][$CellContext`\[Sigma]] - $CellContext`u[ 1][$CellContext`\[Sigma]] $CellContext`v[0][$CellContext`\[Sigma]] - K $CellContext`v[1][$CellContext`\[Sigma]] - $CellContext`u[ 0][$CellContext`\[Sigma]] $CellContext`v[ 1][$CellContext`\[Sigma]], $CellContext`u[1][0] == 0, $CellContext`v[1][0] == 0}], Editable->False]], "Output", CellChangeTimes->{3.414231400886131*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Order1SolveFor", "=", RowBox[{ RowBox[{"Cases", "[", RowBox[{ RowBox[{"Order1ODEIC", "/.", "Order0Solution"}], ",", " ", RowBox[{ RowBox[{"_Symbol", "[", "x_", "]"}], "[", "_Symbol", "]"}], ",", " ", "Infinity"}], "]"}], "//", "Union"}]}]], "Input", CellChangeTimes->{{3.414198322651928*^9, 3.414198341900463*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "\[Sigma]", "]"}], ",", RowBox[{ RowBox[{"v", "[", "1", "]"}], "[", "\[Sigma]", "]"}]}], "}"}]], "Output", CellChangeTimes->{3.414231404057958*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Order1Solution", "=", RowBox[{ RowBox[{ RowBox[{"DSolve", "[", RowBox[{ RowBox[{"Order1ODEIC", "/.", "Order0Solution"}], ",", " ", "Order1SolveFor", ",", " ", "\[Sigma]"}], "]"}], "//", "Flatten"}], "//", "FullSimplify"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "TableForm"}]}], "Input", CellChangeTimes->{{3.414198370462557*^9, 3.414198400766478*^9}}], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ RowBox[{"u", "[", "1", "]"}], "[", "\[Sigma]", "]"}], "\[Rule]", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}]}], " ", "\[Sigma]"}]], " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]", "-", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Sigma]"}]], " ", RowBox[{"(", RowBox[{"1", "+", "K", "+", RowBox[{"\[Lambda]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Sigma]"}], ")"}]}], "+", RowBox[{"K", " ", "\[Lambda]", " ", "\[Sigma]"}]}], ")"}]}]}], ")"}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "2"]]}]}, { RowBox[{ RowBox[{ RowBox[{"v", "[", "1", "]"}], "[", "\[Sigma]", "]"}], "\[Rule]", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Sigma]"}]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]"}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Sigma]"}]], " ", "K", " ", RowBox[{"(", RowBox[{"1", "+", "K", "+", RowBox[{"\[Lambda]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "\[Sigma]"}], ")"}]}], "+", RowBox[{"K", " ", "\[Lambda]", " ", "\[Sigma]"}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Sigma]"}]], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "K", " ", RowBox[{"(", RowBox[{"2", "+", "K", "-", RowBox[{"2", " ", "\[Lambda]"}]}], ")"}]}], "-", RowBox[{"2", " ", "\[Lambda]"}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["K", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]"}], ")"}], " ", "\[Sigma]"}], "-", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "2"], " ", "\[Lambda]", " ", SuperscriptBox["\[Sigma]", "2"]}]}], ")"}]}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "4"]}]]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231409768515*^9}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Inner Solution Profile", "Section", CellChangeTimes->{{3.414198449374436*^9, 3.414198475843533*^9}}], Cell[CellGroupData[{ Cell["Analytical Solution", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.41422322632044*^9, 3.414223236071813*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"InnerExpSoln", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"uExp", "[", "\[Sigma]", "]"}], ",", RowBox[{"vExp", "[", "\[Sigma]", "]"}]}], "}"}], "/.", "Order0Solution"}], "/.", "Order1Solution"}], "/.", RowBox[{"\[Sigma]", "\[Rule]", " ", RowBox[{"\[Eta]", "/", "\[Epsilon]"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"%", "//", "Simplify"}], "//", "TableForm"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414198508530775*^9, 3.414198540214252*^9}, { 3.41419858265173*^9, 3.41419865510844*^9}, 3.414223236072071*^9}] }, Open ]], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["\[ExponentialE]", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]}]]}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]]}], ")"}], " ", "\[Epsilon]", " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", RowBox[{"\[Eta]", " ", "\[Lambda]"}]}], ")"}]}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "2"]]}, { RowBox[{ FractionBox[ RowBox[{"1", "-", SuperscriptBox["\[ExponentialE]", RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]}]]}], RowBox[{"1", "+", "K"}]], "+", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]}]], " ", "\[Epsilon]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]"}], ")"}]}], "-", FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]], " ", "K", " ", RowBox[{"(", RowBox[{ RowBox[{"\[Epsilon]", " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", RowBox[{"2", " ", "\[Lambda]"}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]", " ", "\[Lambda]"}]}], ")"}]}], "\[Epsilon]"], "+", RowBox[{ SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], " ", "\[Eta]"}], "\[Epsilon]"]], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"2", " ", "K", " ", RowBox[{"(", RowBox[{"2", "+", "K", "-", RowBox[{"2", " ", "\[Lambda]"}]}], ")"}]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["K", "2"]}], ")"}], " ", "\[Eta]", " ", RowBox[{"(", RowBox[{"1", "+", "K", "-", "\[Lambda]"}], ")"}]}], "\[Epsilon]"], "-", RowBox[{"2", " ", "\[Lambda]"}], "-", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "2"], " ", SuperscriptBox["\[Eta]", "2"], " ", "\[Lambda]"}], SuperscriptBox["\[Epsilon]", "2"]]}], ")"}]}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "K"}], ")"}], "4"]}]]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414231447329987*^9}], Cell["Plots", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.41422322632044*^9, 3.414223263644339*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"ParamRule", "=", RowBox[{"{", RowBox[{ RowBox[{"K", "\[Rule]", " ", "10"}], ",", RowBox[{"\[Lambda]", "\[Rule]", " ", "5"}]}], " ", "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"EpsilonList", "=", RowBox[{"{", RowBox[{"1.0", ",", "0.1", ",", "0.01", ",", "0.001"}], "}"}]}], ";"}]}], "Input", CellChangeTimes->{ 3.414198749364992*^9, {3.414198795960067*^9, 3.414198801635228*^9}}], Cell[CellGroupData[{ Cell["Solution for u", "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414223282151187*^9, 3.414223290509493*^9}, 3.414223333833375*^9}], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{ RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"InnerExpSoln", "[", RowBox[{"[", "2", "]"}], "]"}], "/.", "ParamRule"}], "/.", RowBox[{"\[Epsilon]", "\[Rule]", "#1"}]}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "0.5"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Hue", "[", RowBox[{ RowBox[{"5", "/", "20"}], "-", RowBox[{"#2", "/", "20"}]}], "]"}], ",", "Thick"}], "}"}]}]}], "]"}], "&"}], ",", "EpsilonList"}], "]"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Style", "[", RowBox[{ RowBox[{"\"\<\[Epsilon] = \>\"", "<>", RowBox[{"ToString", "[", "EpsilonList", "]"}]}], ",", "Large", ",", "Red"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", " ", "Large", ",", " ", "Brown"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", "Large", ",", " ", "Brown"}], "]"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"800", ",", "500"}], "}"}]}]}], "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414198690837059*^9, 3.414198696861361*^9}, { 3.414198758084427*^9, 3.414198770770408*^9}, {3.414198809987527*^9, 3.414198878166221*^9}, {3.414198930892914*^9, 3.414198955671107*^9}, 3.41422333383359*^9}] }, Open ]], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[ NCache[{ Rational[1, 5]}, {0.2}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c8V98fB3AzRFYkmkaSlAYq4i0jycgqKqMkUfEVKlrIyNZQCRVRKPNe 2dkr4zPu55OVUfKVQvlW+CH1e3/+uo/n43w+95zzuufc877yrv/YnObh4uJa z83FxbkePD3GrP1irCf94mEl58pnKOczJKsEeWUhXErSSrDzaVIqKasBTD8D Bz1xDTDr7CYeyxrB2khCpnyJEdi7zb65K2sH+8oHiz78tIUB9VuGcbJu0FKY 2hNGOwVp0ociomX9IdYCZj+F+UGIILkxSjYM+mgRFU3TN8HhaHrB1H+JYH9B mr77zl0Q/hviaLL2KYhKTpMiYsmwwfrbWENMJnwJsLdKM02Dy7Q9kPQrByJ4 9T70eGSATLHEIDd3ASif+scnfP45lAwbdtD3EjB4Ten8vFc21J99vOroRDEE vzdQ84p6CdPKumJ5XqUg/PGExDfDXOCZeyW+akMFXDLYG7Mwlgdaf0+U2OZX wYq9xIlv+gXQEaZBa1atAXr412MJGoWw7vb4XM63WlBcZr+3o7YQxmeHBt9t q4dg+Q0RcTuKIPNrZZtofAO0RoSHWj4uAtE1Wd9HRhphua+vls5sEcR6vnZP U2qGAu+5HDMgYEb/1YhHUAuQZ+5k8d4koCpzPOVyWAtspf3+8hl9U1DNNiKq BeTTTj1qDyVAlJFbl3GvBY5+3KJ/J5wAZZf8J4NZLXC4dKZYOoqAI9eLHOwY LSA0xX+R9zYBr8tLO0C+FXQKXVf4PybAf0dj8YqGVuh36isrLSHAXWN92p3W VrgyFn40qpQAB61rMSK0VvjRt/LEsTICdLQ1XHl6W8H2kGLafDkBPAaZYt++ tcKbiiW/dr4hIME67GyT3FswCvNRi24g4KWP0Xp/37dQb5T8qZlOwFB+YwxT vg0ukU+l7owSwJjkm9ixsQ08Vk8Z6XwmoFbN2DxRrQ3WJAz9N4JOe9kkYr+r DQqikuq1vhDg+qI5rt+8DRgTR/azxwkYfdya8PlyGzhn1y+bnSJgMrbj3mJn G2gkyZoPzBOwcJadsulKO3zyb8rcs4wEOy2nO1uD2iH854PISnQu92jEzrB2 mCMEBXRFSXBOmr2gG98OEYs32XpiJNQ1yR2wftYOVRGtJboSJNxaf/JXQFs7 8Nfy1KpIk7C8a9K8Va4DfjDOr369moTN+wT+uFd2wP9gx6VCVRIKX77a2FPb AYOr0w0UN5OgIWVlbdrcAcZP7mXeR+/9nJS5mdkBK5qoTYFqJFjGqZpNjXZA 8CNn0NlKgm+vRVKgZCewCkIaXm0nofxC4o5Yz04QvRp1B3aToPd+t+OidyeU fPrp8xxdbzQQ7u3fCXPWahNL95DQJqPcaxXUCYwtbSVsdP+b0iDp+51QqSn0 7JQOCVxL33c8qe2ExfS6eW89EkyeyZ8pkqHB7fRKbl0jHG+SqHLzahrs3yLS chu9Pn5hpE+eBh1Dqtoj6PnAd658ajTo4vFQjTYmIc86ytlenwZ2sT+0qP2Y D/d/hxc9aBCdmrLe1pSEIZdaI9MKGghs9dCUtSSh43Aer3MNDRp/JCy4osvM kut9G2nQbinun4u+u8tfP5VGA01G1jW9QyQYi6ns/T5MgxPxQlPOViS8qk7Y eV+YDtet1t+4Y0PC5TUuCh8d6bAhMF2l+ggJrlbbjvSfpMMWNwvtRbRlKHd0 tzsdQgsv8u+1J0H5S8Z/nT50SJ0qay1Ds4vHaivC6GD+8OKSAgcStpn7uiTm 0oFfbiYw/hgJY1fCU01+04H4+1pGzpmEr0c2e6RzMWD/keJEK/SJqeU863gZ cHaMix6BNlP8V1NOkAF9PgtXf6AVom49FpdkwJAAUdHsQgLDruP84gYGZHb0 jrieJEFt4rBwtwUDTPVESs+6YR525jXRVgyI4K7heYw2fGPgp2fLgOuEFh8d fSxe/f1zBwY8UeTbtOM0CVHbhF75n2JAieufxV/oUf+qg5KBDHjW5fPr/BkS 0hYVoi0yGZBnzxbYeBb7c5fV485iwJpAEysrdClN7EdxDgMijXptAtG0p7+P ri5gwCpyKKINvbiva9N4OQNmbZTyPc9h/xFRbyPpDJi8W7Ei5Tw+b7EpwcZ5 BvDJG2i1e5NAvYm+ZbrIABtvOusL+u75DUvofxkQVSe+W/AfEiTbjvH28TGh 6vmKw0YchzctfhdlQvayv5/K0eILyT9WKTKhPevRuWQfzCtH80L6BiZYBLkH v0bfdmB8V1ZhgiDjhhMDLVbCP7l9CxNMNs348F8gQfSCz2eTXUyQOVL59zxa 5LNxv58ZE0aj7antvrj+7n84NmfBhNsJ4ZdN0bFGV3tvWDEhVjlm9ARa+Flh V9RhJujF3lBIQC91WsV86sIEHrt8qS9oQdZUU7sfEzZ9tJy960dCa0iMkfUl Jvy6ZG6chY7cptzQFcAErYJnzpVogfjjtR+vM+EGo/TnMHqJaXPF7C0mnOeW e6nuTwJfTUqBYioTwh8aOdag+/YaHRh6woQlJoFdTHRBxcSH5HQcn2O81Aj6 WImupGQWE7q56f0CF0koyhvy5yKYICzSn2aOjtgcuayqmAmHNu7XdUI75mx7 cbmUCduaAp94oQWfh3R/q2ICS7CoIA7tnKqoPdDChHrZcPF2tIZcB5XUxgR3 mZNdvWihJP9zdp1MKNw0cXIMXXyvKbWdYoK0WUgb3yXMK+bM3/IBJuwvqB3R RpcFvmp88JMJXmu2HUlFx8/aOtnMMKFXXjMsC33q4u/pZXNMOD2TE0hc4jwv i43hf5gwdMK6sgV92uN7lJ8QBd1BSanf0dqjDxXURShIyV4jNIcWd9Ov/CpK wdS/k7o8l0mocrkzcVKKAk+Dfi4ptKT9zkNW6yhYsnL0mwZ6jP3+s7ACBYY9 5Wl70W9swoJblCj4nVq4ygjtYfmuSE+Vgvvbfb1s0Hod1w/Oq1GQ5OJrdBS9 /KDyp9fqFJyz5PrXBV1tfFlqiyb2l6Ieeh6d2LAub2wXBYnf+UN80Z77Wo0z tSlInmIdCEBL6cpeXqVPwcyRWq1Q9NeKOrFuAwp+HlzuFImu3X02+64xBapC LRZx6HMalb1CZhS4+pfHP+C0M97lllng/ZnX2pPR0l5TQWesKOjJn2Y/Qdc8 36DcdJiCZrmzli84/Rnoz/k54O8zH1TncMYzeKxD4TgFdZl9C7mc+cjc9g0+ QYHd9aWDBGf+5Etj9VOY10/l0NecfA41rRw8TUG1bNV0KSfPiaHxWA/MS2FY swJ9JnK+WuccBRkaRYZVnPyVpO9+9cJ2j33rqtESdeqnH/lQUEN72VqDdnc6 uPuAHwXSnvz6dejKOTfh2YsUPFH3DK9Hiz8IGnweQEGA6LekBvTpHclFdlcp MBp9daURXUErDuO9QcHW2ArVJrTYObo9EUzB5NvtORy7CXxVPRlKQbvTphmO yzP4/ohFUJA/XybRjBbVX8esjqRA9sD/Fjjtp/r3ZHrFULBz+E8xx2UBdpdX x1PQcXRkL8fLpP852H6bwrqo9h6nf9eiqDVX7lGgMZFTzhlfqUXmlMoDChSm yvI54xf5Wt3QnUTBxww+P878Tkb0PohIQbtkLqlFlyj88tR8QoHLhQJPTj7C NaK6I2kUnJHTTeXkd+L4JvF7GRT03nF7wsn39azhp30vKPDl1fUpQy9NdC6Z yqagLWFAogTtsi0w6ukrCtzMnUJJdHHHPUfLfApyDFmNhWghz3z1xUJcX/5H uvLQZPqnd8dKcH5mHzyz0IJ6f7KFyin4XiY1kYF26lt5raySApPvRXppaIHl lgor6igQooUcTkI7FnhMNzZQYD/6UTYRXWQW2urXTEFRFn9BAvp4WJk3s52C 4LgfZhHowvWsfcE0CthtY7YhaP43k1LqTAr+DP9Wu4YumFaojO3C8Tr32FxA 856JEzjwEdefMe0fzn5z4M3um/mEeblv4LVF5z2tz3s+SsGeOnMPc7R9z6wt 7wQFw7fcsvXQr0xd06pncH81r+eRR2uoyevBHN5vXKVAlrNfRT+8r1mgYLVN soYkmsFykqnjYoHl/b+tnPfHL6ej8Q1LWfDvWK3sML5fruuvVDNaxoKPh7li e9FLFLvfNoqxoP62ZjcDLTtmx98sxYIr61v+V43W87W61rqWBQVN588+QrfY icmZyrPg0oz+iwS01S5a6VtFFiTF3K8MR7v+NvvZpsICqRQ+vwvoWxEmZzt3 sEDmZe8KEzQjWc+B2s+Cr4f27RvH9+3R64vTNqYsuBUuu2YIPexSdY9lxgLB mBAWhf6lpE1nW7Hgd7choxwtW6C5v/sYC5wfnhKOQLs2qGn0e7NAWzvygQx6 elxOfPQBC0rqsn3X4XmS+PhzS+ojFrD6icPL0DsPFQfZprIg0HmV2AKeVxcI i++16SwwVnLg70JPBgTTUnJZkBVEcEej/+UfjbWuZ8HSTgezr3g+vltXJPRm EvsX+fwqFs9ff+b1Or8p/D/fspCL6OWhBwNVf7KA/zavujPaevTT2MP/saBn R760Orozd0WrLy8b3lovFafj+d6051qEiiwbPrgYvxVAv7Y14U00YoO8mwrd EeuLSLOy8NUmbHjQK15jgHY03CT43JQNKt7seBU0z07hZSWWbOjj2kj76YX1 oCR9RY8DG04T8Z2R6DHGEdXVXmyYFZp/n4v1jJylu3XmfTYkEFeTB7D+CToQ /rR4lA0d1gczRtyxvnH2cNz2hQ3ebwyeNaCVLprJ5o6zoeJzRvgzdFu6xL2M KTbEmTPnXNBSC48j7s6zoWda7VEv1mfZeSVePqLvwGn51eoWrOcYkmM6alrv oPHw9EyCKwnyAwd7MsLfAXHR5SXlhOffrrBE2R1d4CPwcvNerHcd19LnuFld oGOSsWsG6+/ptrhhn5BuCHhYE6S7i4QkPmd/G6UeOOE3+cVSBfMefP2Mp7EH bi0m1uetxP14PcRuz4VeCLlEq6hagt8DOc4Fw5J9YJK/R0d1mgDf5II4yfo+ KDv7VsfmIwFvNkcKSni/BxvzIau1nQRIHPRVuynaD+8azAxI/B7s38JgBVb1 w+VnXFwymQQUPgGlEecBEDHsXeOXQIBTgZbEmj8DcPJ4RQ7rCgHB4ekh/S8H 4Zvf9GlxNwLyxtakiJoPAXuo9nGQJQHWEqK7W+aH4Aw99D+aFgHR/Dyr+tFb 9UZkOtCNc9OLU+grqYZ6b9FawwMNcgtDkLfxb3QDWo7MO+SN/hbgqVSGHraz OCP9ewhslwrbp6P9k2IfnFocAn2+m5V+6LzY4MAA9MZztR990KPB/o5xaPH6 RQFvtIOno0IpegYu2nmgdbXV8pf+GYJb1+wnHdFL+tubitBbf4+t3Y8GRk12 M1rk9ApjQ3RAIxnzHr252uCcPvprboo1/98h0N6XVKqNpl0/N+CAlojRslJH C/i61Hqh3S4dv6SG1ne3zbiJXmkTlLoJTVjqeOaiC/oaxhTR4wbq5nXo5Fsj ovJopV2K6l3oGSU+zbVo580ykuPoFkLh+Cr0w3XC03/Rotv1Q1ai/w/nxOwf "]]}}, {{}, {}, {Hue[ NCache[{ Rational[3, 20]}, {0.15}]], Thickness[Large], LineBox[CompressedData[" 1:eJwd1nk0Vd0bB3AppZQoEhki6iVThUrpK1QieakMDVIZMg+pSEIhFWUmFOFe 916ze++RQsqUSJGS8ZYkhWhQifTb7++vsz5rnXPW2ns/z3c/8se9LB35+fj4 BGbx8f33NHEcaq3+uGPbZjFpfk2HwG1zDKW8eZKKuKLfxRn8aIMNGSnpbEkt 9M8EPe9ln4Tp047SW5JG+CDwTWlktz+sHX5Wxknux7bMDW0bgi6j1lCqrCbd Cr5+mjVvtK5Cc5Ve8Xc5W+TSbqe0vImCYP/FLKvVdijyemC4QigWvRqXDaMl HSBXu6R5x0wiEjKWVysdckQE2/JPs1oyTBaztlalO6Hx2+ewDTYpoD43a4/J ueDuKdvYH7dScb1gyT8Wqz3he5j2I3fsNjLFzSOuSvqhrkKSk2yXjcCnybVW 9/xwdnZ16Mq2bFiFv+Ffdeg0OuZW8HMNc7Bwwif4fvoZbD24MVtBngb/9gT/ EbkAuN+U0PxWR8e+qF7qbnUATL5c9q5UyYW60eqJsGPn8Ox1Gq8tOhcD7DIf mexAyHYoRU3vZcAivst17+oLqLRNXylaxYSq6SqmVMMFbOrgVUyJsyA42/3D oHMwOI8efz3pzsLR8pmSB/tDsNKthBoQy4O4coy6TVIowjb/Gyh8IB+hguw1 VyTDoG5Raa+XXAiVXbGRpd5hOG+hb5LPK0RbuNfH7oYwVPqZfa5bXQTF2ap5 6mfC0WfXpbikpAj1f3LU29si0M0MzTl4qBheWy/d+KN8GSubZYdjzhVjeeCx 8dWhl9Fkb/1uw81iuPySKQ3QiET3lltJT9qLsfBbkrZc1BWo3roodWlHCbjr TicZv7uCNckFB53tS2Dnve+nj+5VbJPP8Wo+V4Ki0cXltUNX8Xhg1FyhsASW Q5FbXXdE4dSHabkti0uR0nvOkDtzHVeMSrq/VJRiu7RtTt+BG/jh2Pqt/3kp Ph3cKCBYcAOmdwSMTg+UQnYk4ESBWgyC7m5yC1vAhpeLjhJfTwzMJ6w0Ay3Z qI2kvUyYFwszx7HbOSfYWM4Qi1DeEAvB4zc3n/djo3rw66Dl1VjoVOm83ZLI xhKHIgZtUxwWhx+aUXzBhtMlWVtdhzg89EiYM/SWjftZ0fOf3YiDdaqXo8M4 Gw5v3Vx/DcbBtT7mwPWFHHDt/lE1TYxHp1VUYON2Dmxs7xSNf0kA88WGebxM Dsa69y/IkkrE5Ms11sJ5HETYCTruM0zEyfTwosVcDtgnvKSohEQM7DFJuvaY A2FPvfDAjUkoeqltEjTKAW18nKdqnwSjcvM5lj842HoqR7cvMgnlzXJ5MzMc uPoLjet3JZH9CDndv5iLuoudB+cGJWMyzMxmUIOLwwLR3DJaMtqr4oaiNnLx 9bK+iEtLMsqW+USKgIuV0bl1TXIpSJsTsb/EjIvzyac1Yx+loGIsTtbFhYv1 +aJzpQVTcXLLmhTlNC4a1evsn2qmYjp6udC7TC7sS/zvX7BNRe8XjIXSuYim eN5vWanwjnTr8CnhYqi6oJtulgY1D9q/q+u5CDY8pmNzJg2dO4bDJJq4WFYv Fjs/Iw09IemxX55xYdgUuNN9PA0a3YF1xzq5uP1yd8m6+HT0qV5YpzfMhbbN H6F399NxS6v1WfAYF81dxU4JA+kw37lsW+E3LiZ5EtI/tW/heKzB0LMpLvZ/ eh9R8foW7twNK9EQoiD0N/TwLtkMLBf7fo6+mkKKi7Wd6s4MqNr6XapQpqDY rmov6pmB2XOoJzWqFLYxO050V2Zg0mOtSO56CuXMJG6Zeib2DXRJNOhR4Dsa qsMyyITf7x9VHvoUdoq5l6VbZSJmxZvgeYYUXlzYXh56gbzvqqcibkxhdN9I hWlLJjx1M0duW1DQmt+ht60/E7EP9LUG9lE4V/WwSvNHJn6/mdCStaIwTzm5 Wlz2DlrWaMr7HKQgP7O9ludxBxmMB9zk4xQOMJKbTi3KQk394f5FPhTSj1zc 4ySfBePa6XS2L4X+JR5PbbSzoBa9vPxfPwpeQQbP9I5k4eCatQyfsxSuWI62 zSvIwtj7V/qWQRSez3u973d1Fnrjez5RFygsq3zUPtKehTKl50JiIRSy16S8 ap3OQoH2hfV3L1KonDboStuTDUt9p9N5lynMKVU7dN0+G4xsZb2OSAomzst7 QvyyUa3k7Dl9hUJH62ivY3o2PtzUCtoQReELPeWtxkg2ukRvbLeOobDp8KXj Cnw5cJ78bWYRS+GCqOc7MbEcdIYMJ++II+d33vD95JYcvHu7dqdMAgUli89D NddyIJJwKOtaMgWp4F26znfI972Z59xSKIgUZF5bUJaD73r/nNxxk8JvwX3q Fv05WNHCG/uQStZbXXaqbxMNd7WmYj7dolD3WaQudC8NDnM/T9y6TeGetOsy JQcaJFWu6+3JoEDzly53u0ED3fdb281Mcl6aoTO/3tNQqJoTO5VF9teuyzx9 igYrDberkdkUHKI23IEoHU863SVEcyiYD703jNhKR+obf4jTKBgtQ6KyJR0n N+3gjyXWNUoZbHamwy3mBUOQTuox0+TK0ng6jkp3jAwTS7Zkd1EMOqI6DIqs cykIT0+vPVhFx+J6+4wHxJPWRS2ZH+l4qzzbPIxBoWWxmJi6fi4eJ0bW9zMp 1Oh5OLYeyMUxTuCLdSwKd93qKT+3XFSfbogLIs5u8Le9n0TuMTMNR6E80h8T rSy7/Fwohf1NNCO+vmrt9KxHuchSiOdEEfsH9942Hs1F4Znwb7PyKXgU6IwP 8zMwrz1UYxPx8e4b228sZ0DVIDjGjdhm/se49eoMnFhYtCqd2GyjwcBLQwYS wwR+NBIbOKZpB9gyoC+zRWyCeFP89whpLwaMLjy9KlNAQWGMrnwilYHOW7wS J2IJGb7AucUMSKptO3eZeKGpbTOzjoEgtfInNGL+gFIZs24GrPrKCh8S/6QL eY2PM3C0yX1dN/FIu0N1/FwmnKpfHflK3M9fJbpRmomEuw+3zSsk9aopcaJr HRPmjQ19ksTNdt6coF1M/BC0NFYhfhTVKCB/hImjPjfDNxGX3VOwrvVlwrgq N9OIOH8okOEcyUTVLpvsvcRZy15OLrjNRNxrm2Qr4mQjddNCNhMTISoRh4mj fC+nWzQyscVRIcCe+GLmm9HvfUwMR7oGHCc+27IZKd+ZkEvij/nPwurc942C LLSoKXz77/2caM2oKWkWnoSE3DtCrDuat15tHQvy1YtGbYhb96zptNvBwiLV 9FhL4pP5WcExtixsTHxTaEI8IyS7+pEHC3XdvqbbiRPcbjZ/C2XBzL3FQ4d4 bZPYKaUkFuj3LKX/v36VGElrFgvZ9wyPSBPbXBWqjqxi4bnVE51FxJ8/Rjjd a2Nh5fvvhdNkf8N38y8aGWSh9GZZ0ydiaWYQW2aKhZSfI3EdxKWCk7bmi/Pw GFYLaoh5DWP00o15ON1utjKJ+MwaN7MB0zwYKw40Bv133pcHv4nb52GRzoPN DsSbd/bqB0TmYR3dIlSN+DnN5gMrPQ/LHa1PiBA7CbRH9xTnAa5Y+ZXUV3zt ky505iH/77FtpcQqijtDfUbzUHRRjxlDXH3p4ZrsWflo+6DH70k8anDXb65K Pu4JC8cqEe96SBN+ei4f2hnGtyNJP/StlCfjTD7Ehjb+tCP2C0k/pJmdj53/ Sh3TIr6DeEZ8Uz5khWvO9pB+m6oMMTgoXQBd13UyCsRF9w6d+VBZAOa15rMR pH93SnVIS7YVwL1zXYY5cU+AZY3JYAG07b1FlhPP37xbpFC4EM7vS3ropP9P lOmw/I4W4lTYlGcFyQsJjmjfrFlFUBHr+NBI8udw1NT+gWVFGFi6K+oScZbD +6Z61SL0cT5HbyVWFS8vv2ZThAeRZZx8kl8GZ+wTxYuL4B/xkxdO8k0n3Zqe oFGM52K7Z8mS/DtmRz/C6CtG6UA1Z4LkKdVv2PxsaykK/HWr6TdIfbjeWmE7 woFSbhfHidw3E6v1Fhd4lKEp5CWt8Sjpz8k8kRVK98Cn/tDp5Q7y/7/21L7C Crz/rTcnWI30W5hWS73KAxw9eboiVZyCXMzwJPNzNex7TY/nkft9+Cev76Xm Izz2kLA8+46LnE/3nwhfrwFv4XqWbiMXwjK5YwMDtThduLfMv4iLKBeuU6Zi PYwXqUmfSubih37ewMngBph7dGk5BnHht76Ws6zmMWZoPgVLHbngFdZea5V/ gmx/pZ5yEy6mXNvTlM81IanyfG+XJhdrt8+bcbrfjJrTZbi7nItdWfLOJRIt SLu43yaazGdnZY4qvD38DGtDelplBzlQHTkg1GH2HLGCq2TXtnCwdPG4YO3v 55BXb1mpweFgzoM0EoytOLrGMWwsjQM3rfud803bsKDV/nZuKAd5u49nVv1o w3rjFde6nDmYGJYSGUx6AcO0h68bzck8um/X7ASjdojcae4p1uYg2Dg8gzPY DsFLNdv3y3Ag32vyOjv8JY5tCAjwFeBAd2NYguT6V7ieFO8cOczGYdlnk7Ne vMKnlzepg2QenngS3e8d2gHJx3MqFMvZSJlj52ep+Br+SYcU8jLZWNrHzeKv fY1tG3wO5UeyIRAUun+zTydeXRw2oXmywce0K+pf0oWMQou0g1Zs+KYWRS95 1AXdaOmseVvZqFwbKSjq2Q1dXXqghgIboia+qheFe+Bes4JaSub7HrXnLwIq euD9d4I+NlaK4ttQHLDrBV2i4tfljlIcKdIRlZnpxfYZfZm0B6UICb8T2sPq Q2Gyyi8ajdThkEya8B4e9izi0/KILoWFqPCmht88VGjrrlY9VYqrAvwreoij djTwKxPXTk78GSc+dGA/T4lYp7+3RmqKh99+nilyxFLsAnNP4k2crAVLifv3 mzmLT/PAXi80NulbCr+UqKQTf3hgavSUNRAXRIUE+BMHwCWhlngwxO9wNLGx +Q/vh8Q2LocVyoiHPEVU7hPr6aoWLpjhQanQKL2QeG5PU10JcaZqQUgiMZ4/ YNQTe2/VPRJH7F/LvtZNjD0Nm28Qf8pPsxD4y0Of29uvkcQtQW69NsTSeeKO 54nn+R6t9iAevpe1PYBY32lf9kXi+080ZM8Ql+7d4pJPbPtpd4cX8bCBxp6H xMq/X7HdiRU3rtJ4RfxrvkOMC7HdWoklw8QNkl/cnYiT5YQm/hInK1/YfYL4 fxDDDpM= "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 10]}, {0.1}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV1Xk01PsbB3BbaLlEdQsh2xSGClkK77rqiFCWlMgWyj6YslWWaJ1KkiSl okW2zMx3vsq1z6VTVKQoW7miEEpTt43f5/fH5zzn9dezned8NPwjXQIlxMTE jpP3/2gf+L6t7sMm64VTF9xz1CqspWyUWf1K2uCOfKI3DHFgnJ+Tx1MygaJ7 vdb227kYXKqdEsuwho3R7qr5iTewpbWTe0VpIz71zGazX9yCNkf15oy6HYZL H0aVpN7FL/s9F/0YTjj4X3jUlSulGEnrEPplO8PR4BorSe0edgR8q85UckNi /n+HxNZWQGijTDfmueNipcnJMF0uVmlZ3fui7gHL9uo5eVNc5En4FukUeGKf xx6HHVd5kB1IveHO8Ebmv9mVyYZ8PHjT3tro5gtajTphfocP1rYAe69sPyg6 n5j6IUeBUSdq+tLpj9+Lr+XdD6TQu/KYzWmlANxuoDQ/lVHIyl9Sp+MZiCyj S7ZVYxTs5e9a1uQFwXFx8Ja+ZQKIJa277963F8+3hA6+chBAMN6yZkI9GGLl jsafowQI8/bmHvMLQbr5O0mLcwJoPpkwXFYQiuQA+asXigXoskoprhwMQ7N1 l8/jegHOlCqucGZEgMta7pzUIcAm1cLCD3sjkdtIv7IcFOBwU+78ejcWHKjm qvhPAngc/tfptIgF9fIc1qVfApiYMk97ZEfB5Q+nmYlZNOTH2Y91zKKxxnfM X/gHjZGb1bM/d0bjko3YOZeFNP7ZLb25Ji4GgxuqVrYq0bi2aOvRk0psiJ+R lfVRo5HYelHo/oANJS09a6YmDff0NxJanvsx8+KRh6sOjdVWuhsmfu7HraXy OuPLacwTRSVV5R2A6XWJYEU9GsMlD6qPWcViJLOR065PoyFA8pdrXyyC2r+q WBvQuLLUYe2ypDgox3ua+xvSiOvIihtTj0fKnarvditpuHJ6BZV18ZAu+1Yz TWy4kSFK80uATHFi9PFVNGb/ijB2lkiE788Fwo/Egzw6SrUgEYHDTR4mq2nU hord+2BzEF8ylnz3Jc7VshunBg/i25WholjiA93nmKnphxDn/Pp5IrHz+dch TozDqDTbvINFzNyiVaTcfBgcDeMbO4hlJcOGh/YmwXhqboMxcfTu15keUsmw /VIeLU3sc3+6otYtGfn6C/TbSD0Oi7TadG4mo2Hr1PILxGujbCdPiZKx5MBb tivxIt0Mw53ZKWBtGtvTQPqTSOc71gyl4MKETRCbePJNV5i2WSq2hTOPaBE/ ztEonuxMRfNx8+YEMq8UWd7yE0ppWC6vZfEnmaee7bnjXFYazrZ03+YyabSn R37obk5DuEypmROxtiSz2PBAOsSsAuyOkH00/S407Gg/is9+haJhXbK/qew1 6pwT+Gh62+42g0ZOb4INNX0G23YJIpYuo7HT43r55KcshKg8vCm5gMbcmRQv W7V8ZKpr2p75IYCO8/j7xlOFUJTWqzo/IEDsEwvkfCmCS372u4yHAizmK/SJ i5ejfuEEy/4euZcBm5anllxIWpVwf14QoCHkiorHGB8lxiualx8UQMSwki8N p5EmnWE5P0AAie/F81V0HmAVx2vfpJ0ApjO+AteyvzFvfKGIs1qAljSTJ016 tXBS47gVKgmgnjH6vWi8Dv7i+0J4MxRGv/X3vVjVgDt1K98eHqZQOFL1SO5M I2qNvOT+aqUgp3p7YnBQCKsYW7lkHgVOMBV0TbsJo2fVIhMuU/i6vnhwX1Iz wnx2HQ1LocA2EvL/bHwI1bmp08rBFPrLhKfaNB7herCcQb0ThZ8hHZd1Ex7j VLaH4YAJBf0NMtNBVS24lZ+RUbuUgu0Njb0Vi5/gvCezKEuCQqyqj+Zbr6e4 N8XTZIzwwRzbPrfT8RlMdv2IMGrnY4H8pKzwxzOcjLkZZVrJh1Tt5XKtvDYo BFu++JrPR6hJ1avZW9oRomA+UZbOR7Gd/7War+3QO/65+20oH6JR5flD2c+h 3J2j2+bKB+VqK5m1sQM9bwoMKi34SNqcns8f6sDThtxMTw0+NHrtuwrSX0A3 Ztuj+Nl8rDVLy1Iyegm3lyGVZyd48FJ7+l38+UtULIqS8e/kQfTo9AArpRNv ZHrmMat5yJHyZrtod8H6pVEMt5CHBX3UDQlhF6RiNpfwODzMOpTiZhH1CnkN DZdLonkQK/IuH1B8jcDxFWN+u3iIzi0/rdjwGmKtU5/l1vNQrX9cViGiG+IJ h1pMGTwo2EczU+V6YCw5Ja0ix0OPwbPn8X/3wAyt376S/+HeVWgPevcibMd5 u7PdXOwuN1VQne6FjPWSiBuNXCSnX0/pudsHdqe4XWkRF6XvVS/LOfRD0bEz jX2OC2cFOfPmH/04sl8h1jiWi5OzJFR6iF3Sr7quIhZ+F/2eJNa8oL/KgNh0 oLdR+Wc/6vibPjCIlXmlWyOIp6fiPZWJB9wc9y761Y+E6AGIE7NzONl7fveD FcmTfXqA5Ockx8cRr09a/+4x8VAy2+s0sfzZ1vqHxDuDvTRp4rKy4YQGYqu1 zLI50/0Y/ajykSKW7nn8TwVxUFhaWx4xntXeaSI2PahQdok4Tsg71U0szbl6 Mpt4pOSy86yZfhQWV9pkED85FNq7k3hgZIw6QiwT7VMXTsz9EZ+ZTLw+yLUg lThljkzkIWKu07rgEuJlehorYolH/1rpUE88YVEmxSbWNtNa+ZK4xm7dWxax t/5ixVHiMx4Pq8OJL6rPFc0Q7w7enhtC/D/8UBnq "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 20]}, {0.05}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV0Hs01HkfB/BJKrKmpM0z00qiKZfQitKWd0sd0UXiUTaNVShsUWvRbTWi pbCFZ9hMS7q5NszvN7/flsSTKVGEJuQ2NasbDj1nGYvwfPePz3mf1znvc97n fEwPROwO1uJwOEHk/kmP4A/N1R+3OFP3s8SjwW+dtV35kSqeOZ7MbKh7opHB PjdbQvHW4HNAgXAwlkHvV+aiGIEzxhwuR3QvYbGtoU12lbcZ6xQTgVs2sjBP Mb45beKO/TmtYVkuLD57HMwKFOxEQXrSo82uLPoSlIpAsRcGJLr8RcR7gkYr 03k+4O06ST8gfYUrn62R+MIuQPtRALGd2cayYRM/bHXYHTn9LQsddXy+r0CI crcIR2fibttfXFN5QQjyKcutAIvM3H9VL98XDIGwfew7Yo95RRseSEKQ68bx GXdmwQw+cxgyCcU5/V06TsRppQtWegmOYpl4KJLZwCLvS8/zF3hRcLlt41Lu xOJUQ5bC914UQpJ9JbuIfRNfa5nt+wkXwn/WDK1j8cXIsbgKSTRabBuLbIhj lZmxAyYncPCPI4Yljiy8MjrCdgp+xrm6kt5b9ixEOtSKZF4CFP2Wv0hWsbB0 u5wki0wA9b11tT1xS2LEx87aBFx/uWqs3pr8c6Z1sU10IkRVduFjViweT96w UbacBzIcPX0tyf5fYgeTlGTcXe9iNH8Fi+zuk67yqTRIk/1un1vKYq/fNemn /2Xiyoqk2jBDFnrTIn+3JbnIQ/PhkXEGy70GP9RcvAF9wauucTWDmEYnZA8X YnvVljl/P2FgRBv0zJghRcWa39PLyxgwatdnzzfIMOm/T3lAzOBh2NXFfgM0 bnm3fUg7zWBEsHFe6REWcQIIY4IYaI0Vz1+8/B4sS/Qu7PFg4Dj9PeN95z5m cxWLhlczeJawpvGxZRW2On8TrcdnYHKpf6xwsBr+pkYpfA6D/lFVz0u7h8h/ 3aP17r0cN/oq6rlpNbi7W8+usEEOrvHtod5eBdZmaGzfU3KkhMpD8swf4620 4dKbHDk0m4p7D8fVIiROt+CFSI6orxX0oponMLJavTQ+VA7VHcXFZtN65CRX 7lzpKcdEmDLH4uRTJDI6u9wd5LD6ds5USMUz5FVBJjCWwy3f9FC5USNST3XW T2jJEWMcsOyN/3MUGR7cnNpHw3rg33ptO5pgc7Lw0m8tNAznfdJRjDchIcMn 4+ofNLSrcqRmkmboJfdr9ufRCF9T8Up3WwuCVr+fv+g8jWL3A3kPNC0wL7g2 ufUHGiP9/PnvxC+wcMJt2zofGnJvt5mZm5Vo5Xh7mqynEbc1MZd+p0Sd2p1+ aErDtNuj/XriS5hlTPe/1qWxfm1CJu/rVnhqeB2aIQr+S56PzXjRimKHpRZ1 bRRG6lPVkaI2dKy4aJNRSSFbWxi127wdTpo3mbybFAx75PlainZMpY828FMp zDoj8nE69gpi9bFKwx8pcAqFUvWCDgRw2/XrvqNw/Io0dcHDDowP5C+M3kSh 0ipJx+BoJyZ+sx68KqBg4HHcOp7bhVVm+SvjuRS6VjW9OHG/C6sDTvOEwzKU /Q7zXmE3QmJcwjWdMuyXOhoYT3VjhrD2V12FDGcTr4m6inoQMVoWtrBIhtIP xjnc7SroHzl/q/OyDF4G3HW14yqc+U919pUYGS7M0lrcRbz95o6fsogVYyOT n4i/knd4ZRI7qrtr+BMq3FMOz00j5lOlnkeJ/za0OCMiVvvsOPTlZxWi0i8H HiaOyk4RH5xUIezXA5aOxKUpZ0/EEjvlDs22J353Nso/lVhXevpPW+K9of7L WOKCRrHEgnjjeus7c6dUeKv/lGtMPLvr6aNy4sAU+79mEqOpquAxsZ2k+jmH OFZBXewk5pTsKJmMlqGvJMdr1rQKuU8PBY8SN54J795L3DVX0tZHPOd4QPUR 4hK+Bf2eeFOI9/V44lOWzKVeYtnOb0JLiPkeTe49xP0uttv/S/zRb7+gk9h8 rZltK/Hd0D6tdmKhldGCfuKkEzEqJXGWid7INPGeZO37zcT/B+yaE/o= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, Frame->True, FrameLabel->{ FormBox[ StyleBox["\"Time: \[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"Inner Solution\\nComplex:\\n v(\[Eta])\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm]}, ImageSize->{800, 500}, PlotLabel->FormBox[ StyleBox["\"\[Epsilon] = {1., 0.1, 0.01, 0.001}\"", Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm], PlotRange->All, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False]], "Output", CellChangeTimes->{3.41423145948454*^9}], Cell[TextData[{ "That is, we are able to capture a \"kink\" in the solution close to time ", StyleBox["\[Eta]", FontSize->26, FontWeight->"Bold"], " = 0.\n\nFor small ", StyleBox["\[Eta]", FontSize->26, FontWeight->"Bold"], ", this analytical approximation corresponds very well to numerical \ solutions," }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414199070843202*^9, 3.414199114919812*^9}, { 3.414199208262178*^9, 3.414199268037734*^9}, 3.414223333833889*^9}], Cell[CellGroupData[{ Cell["Solution for v", "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414223360605439*^9, 3.414223374159901*^9}}], Cell[BoxData[ RowBox[{"Show", "[", RowBox[{ RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"InnerExpSoln", "[", RowBox[{"[", "1", "]"}], "]"}], "/.", "ParamRule"}], "/.", RowBox[{"\[Epsilon]", "\[Rule]", "#1"}]}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "0.5"}], "}"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Hue", "[", RowBox[{ RowBox[{"5", "/", "20"}], "-", RowBox[{"#2", "/", "20"}]}], "]"}], ",", "Thick"}], "}"}]}]}], "]"}], "&"}], ",", "EpsilonList"}], "]"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", " ", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Style", "[", RowBox[{ RowBox[{"\"\<\[Epsilon] = \>\"", "<>", RowBox[{"ToString", "[", "EpsilonList", "]"}]}], ",", "Large", ",", "Red"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"Axes", "\[Rule]", " ", "None"}], ",", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", " ", "Large", ",", " ", "Brown"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", "Large", ",", " ", "Brown"}], "]"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"800", ",", "500"}], "}"}]}]}], "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414198690837059*^9, 3.414198696861361*^9}, { 3.414198758084427*^9, 3.414198770770408*^9}, {3.414198809987527*^9, 3.414198878166221*^9}, {3.414198930892914*^9, 3.414199015367352*^9}, 3.414223374160146*^9}] }, Open ]], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[ NCache[{ Rational[1, 5]}, {0.2}]], Thickness[Large], LineBox[CompressedData[" 1:eJwVx3k4FHgAh3FEsdoRuobUYtLBrl0pqW2/qB6tHOtq6UEnlp5KsZU2y1R0 qrYa2bAIbXJMjtRTuSfVxAyZHJljmyZzGz1rkgmzv/3jfd7nY7/7YEiskYGB QSDp//vFynpa5Jt/4FzO1On1GhhvtEkSUWko40rONE1rsKowN7+O6o7G8Hc7 06Y02NrVX1tA3YTNzeu1n3Ua/Lx3vPEqNQzjkpclk1oNBK5nNmZT96LFx2nS XKVB0bygrPPUFPSy0x/tGtCAblq37Bz1NG50LS4S12gQEVnMHP1wHRku54VT uzQw19OjfBcX4oE702GfrQZLg0dk7RdKYX0kKyhvcARHOZ7IHStHyJig90/G CBbUWwoNDZlQClaE6CJG0CDe2Mn9vha+T/lMc5sRtCUW2Eaq6pGywSC5TaiG 1mmDRdX+BzjxUyItuVwNo4mKObZLH0Ef1uLGOKTGGv3OhtDqJwhdIZRQoEbn aXdOx8pm3NtcQHtPUWPJFeVE+UgLrF5c2m7EV0E5LhK+/rYNHuLE6OoqFUoV j9mUS+0Yn0FtYpxQgWL3t0YiYSFyuU9sXIAKFxPuxxXROrDc/3f1KgcVPnpV SH5JfwY3duUBxzElUtxY9fPbn+NZ628zOC+UEFWzLvTYszFpmJFzLV+Jz4m8 vBXHX8KK3VPTkqSEs/es6bjHnVjyMHpR+BYlfG/Zx9cs4MC2xr1Qu0iJo3Y7 HN5GcWGhaa/pH1PARRVu3h/QjYi0JC6vSwFri1FTlq4b7/JOWfNKFDBuzmM6 5vfg/cOAtcMnFNjn/njQbOsrfEpyfDoeokDFj7uLmj6+wlmjkkyzlQpolTZz hnN6MW36lfdsYwXuh/rOuL6JB+ttXYdMh+RI35JZWD/MQ0NsWPhwvRz2Ar+B kszXEM0q/bXsshzrPE5fp7r1YRs3zGp7vBxRi7kThr198HY9d0TgLYeWnS1O ovdj/h83fcKpcuQax6SE0AbQED2gu/qvDNbC+7eMWAP40DrmU8yRwSSNHuZ5 aBCR9WW5xbdlMCiPYYqt3mDu6q2yKLoMh28ys63a3mDU5UOBWaQMjc5nTS0P DCGZe4qR8Z0Mln6HXU5S+LijZDDuzpaB/3V3b+oTPo7P67vGkkhx7y/QJDEC 8AIXzrzULEU0c42l3bQAWXPXptrkSZGRWUzn3xXCeChQx0iWokpml0fxF2F/ 0En6k0Apgi0pa5/pRPDQt/F6nKQ4b2JkyyeWMK5YdBGzJrRTo8RmPjF+z4nX iAXtNp9FePRmormJ2KauKugAceWXbhUVxOKwgPh5kyJcTr1NzyROyb2Ys2dK BM/4wm88iasuZqQeI/avPJjgTjyckRKVTdw506vUlTgiIcrhAfHCyX+oTsQb 1rlUfzEtAlvqaGJNPJP/8mkN8Z72qiHVUinQ3Xyng3j1jvT5MuJjrLoLQ8RJ c4KD3xErKvOCTfQiONSNdQwSc9L2CSKIEya+r+0gnnV4R8t+4jQvC3UrsVdc aMlJ4k/5b5c1EtcGrk+oJKblZBXUESt9XP1biV+5RQ5UE9M8HF37iIclztZ3 iWOcF1gpiXdVTgeUEd9YYq7VE3ud6zlbRPwfyCmJrA== "]]}}, {{}, {}, {Hue[ NCache[{ Rational[3, 20]}, {0.15}]], Thickness[Large], LineBox[CompressedData[" 1:eJwVzXk41HkAx3FXRpSrww5JjvKI1ApttvoUWiWR6BCpVGw6aXJ0OafkSIeV zZHk2bKOkTOEMuNY5WySME1rPXbuX6mpEPa7f3ye9/P662MccHrnUSUFBQUf sv/relTQ80y4eYMglTkxM0NBxUn/DJ9uhtSiqoHGaQqr72VkldNtsWKi8UHs FIVtHW/KsunOEKTWNmhPUthz5Gv9Lbo3lBOOtm3/QoG38qpTCv0IFumGum+S Ushd4HElkc6AwphyZNsQhQsddzi7axmYy+75t3uQwm7meyVT33OIrG1WGxyg MEceElWXFQYbuY3z534KEdy0CIlRJP6avYe39jUFz9sDwe7LLkPnxNW3Gp0U YtTKza/R42Fnbbc/7xmF5S43E8rOxCNkQs5jN1LoZZ4WDrbGg+NWeXW0gYKZ slWhdRgTFRHPN66sp9AylW/N7b2CuLzgJx015P9Tup1R8jWo05riHcopZPDO O1VOX4ejRotq1R8U9vrcZ334mIZv0q2zo1IpaMzE+LksvoffDProj4IoLPWU CdhJ+Zhkqn8IcaQQ3rkWGZ8L8Ca1aoytT0GvQuedoiIL/feF8WNyGaqGnV52 rStDdD5fxahThqbgbAMfSQUMAgKLNR7KIF+2Xqv4ZDVa7WqD78bKoDReqG2w tBZMx7jmhb4y2M8crPIqeQoDLduw1fYyvIy37WxZ3gg/Kndytq4MRjfE4wWy Zzizozy9QySF+Cv/3etVTUh4scjrxxYp8kV17ZrX2XC2ql8SmyOFpuFDamSE g87kmvLkcCmSj1UG5pq1oPnr8sA1XlJ82Vg48mtUK9QuuFl0WUrBsOFULGS3 QRLH1aDRpOCXcJJ6jNvBSlGbseRLMBnMzbQ4/wKLWg5Xqz+RwHITbTqw7iW2 tJumXrstgUuecdBjvU5s8E4Nlx+XINzwgMnffl3oyzoQpegigZVkl8ab7d0I H9nt1moiwTytD2qciW4Iisctzk+KodKYyTLN6kGIraJ5R58Yx23r3s7e1ouC dRW2c1liFG4NyG340oswp+s0WoIYcrG+9mj6K7jTOsZzD4tR6eWinObMRY9b 9XfzdWJEbWHeqxjlYr+HqpGHnhjGPNf+B8zXuLzjouqqTyI4rIlPo9v0wfVV 9vTUCxH8FneNK77qw5J5ZgtPPBRB3p4yfCbmDXK5uza0RomQoeLP2GnWDwsv CbNpnwjz3lXmKXH64dJdcCvcXoRZl2K814a8hXaXbildSwSFAn/WsO4A/kl8 L/EVCRF6l5Wi2zSAg20+DklNQtRbJqjpnBpEqMqEGyNTCB3XUKtYzSFcn5q+ PBUmxNCK7leRT4fgHcF6ftZDiNIcmI3482BayjFNXC7Efpa9juE0DwmjCtv2 qQoRzbwfM/TnO2TkCGL1+AIUCwwzNd34KJ1nN8CoFcBTR/On1gk+GOorHBtv CZA4S8lgiJidIY+tJeaMy6c+EM83b2BXEtsP89j6k3xUOHlsLiLWLy/2OEX8 +WLIlt+Jh723By34zsc5qtL9LDEjIzn98BQf4dwNvubExcnRkRHErQG0LBPi 0WiGXwqx3seuIUPivcf8TKqJq+ce8p9PvN7BqkR9mo9vv8QdUiRWHXrR/Jg4 sqY1aPCmAOhufNRC3OZy41EfcQSnPGmQ+Ie+vcIeYlFRpuesGT5qxoTBbcSd l47z9hJPWM45VUlMCz3w7CSxay23pJR4Y6DXg1jiu1uyqULiMvefjxUROxy1 DskjFjuudHtOnPjpy+NsYrM1piv7iAdjGscyiP0t9XTFxJbaCavTiO8Yachn iC/k7GCkEv8HBpzorw== "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 10]}, {0.1}]], Thickness[Large], LineBox[CompressedData[" 1:eJwVz3k41HkABnA5itod0ZZmpFGOzVHaiEr1KqpNh8TqMOkaypFSs9GJYpOj PLIiStFBYcjVpozMNHqQEnI0jLXKXOan1shV9rt/vM/7fP55n+edd+Dodl91 NTW1PST/t6uvpLFKum71x8To0YkJCprOjGNiuimyK8v213+nYJuZmlFMt8Ps UpvWom8UeueYRoaarwbPxjU0b5zCptetj2/SXRCySzH8ZIyCabzRvQnmRvzE ifuzeZTCuOvB6/vNt6L+Vd/g+AiFHeyvz5PonrB0cPIJGqYgcGaU8zO8MNV+ wr3wK4XFJqsKB5m7UOwU+nJ0iIJ2z4UsL3MfFBjlumaqKHTaXHJOoLPxLn7Q Ysa/FJIzZ1eZeftiSNXGPPmFgqvuw5WVGX7oblz3suMzhTJl/VKK6Y+hhkVG OQMUruTrL3A3D0bMM5p0i5LC7Zluf8TSOVC12mpzpRTOvL4u8HrKgdmgMXMO sVd0t7qJ9++wdZvlcVlC4QdVSHhFxkmE2QjV2H0UwpqTwxTMU6gUnjVkfKTg fq0jYKv5eZyYW8K/1E0hUrv458v0KGhlnrzObqWwc9cd7sDnZFTPsjAWcilM m4hkbZibibjgktc1sRTM3JUSftxdiGr8nC76UQhtWI7UwVy0Zwn4VqBgUKLX NWkSF10rLvlxGORfj3P9m5WPcdVTRX/4RYnqgJuGuxQlaA6KTUqrU0Jlvko3 /0g55q+NsrR4oIT6yKPphmZPMSfNouleuBL2E/vKPAqegZlvm169W4n6KLsG oSUPZTz2gjR7JZiJ8pFcZRWGPdYIWbpKyL+Ku1oWV8Pl3oWLVbJ+3JVV1NKu 8OEYdtRdj98PmtEDqrdXAOHGi72GGf2I9y/1u20qhHfbWIowtB9DTo96D4fX 4IaEudtnWz84SwQls/iv8E9pzsoUq36ICwRxjfNq0arZaVOh0Y+xgOZ0i9N1 2Lt9mSRNpIDVminf/Srq8Zk1zJv9RIENWfMOFRk0YJH0YE5UogKhRnvn/816 Q3btChMDFbBW/DatdctbuJ22Oue1QYEZugPagtG3aHZu2K1jrIAmL51rktEI dm3LDtaYHIF2Fe06m97h1rsY34wmOR5tPHC7cugdgtoPLEvJk0MlZ0z/lNIE l5t3LBfHyFHqsUEj2aUZNT1xC8v3yRH+a3RmyadmeHzscOtylGNep2tbdnQL OJ+2OfAM5FjhEJVMX/IeTv7HbRIGZGDNfTMyqek9ZuYOrx+rk0FVm9BzLLIV KQGWR73uypCq6cPZbtoGprSqzD1chhldpVnqgjas8jvPn+wtg9a5SM/lIe2Y 7NvXnWMrg1quD7dHvwPtxqVGcpoMx29wE/SrO+DlsyiQ0SfFc6sYbb3gDzh8 o+GcRpUUeq7HrS/QRIi61sSNT5dCtPBt06lnIrjSor6oc6QovAXTXp9OMNan edLdpNjDtdcz+t6J82dbzkgtpYiIvhMpetiFK3bPi+9rSJEvMUqnbRbjfq7O NE2xBO56tGU1o2IE3J50Ymu5BLFa6oYi4r8W1RZvJBaMqL4NEOs8Txp0Ibbv 6eQzxsR42G5y0pGYUZzvFkws119/agFxj+eWQzPHxQiKjg1XJ+akxqcc/CbG kYAZ8WVlEuTHR5wKI64c/lBfRPwpgsNKIKZduvtjPvFOf9b8cuKC7KVXs4lX rbAumPpdDKVoR1Ii8WRR3csi4mC3jNQAYrzl5QiJeZ3sdl/iMEFx3Adi3aCF jP3Esrx0d60JMbgxlek7iBvOBXbuJB540X3LhXjK8b1VR4idtuWKQezk55F9 gTixK8TYkfjxVkf/POLFY+pZvxDL19psfkEccbmux5rY1MHE5j1xo0GyyQJi HysDfTmx8X0W24T4OnOaaoI4xM7s3lzi/wAg2QZw "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 20]}, {0.05}]], Thickness[Large], LineBox[CompressedData[" 1:eJwVx384FHYAx3HkV1OERzo/H5x62il7JEq5T6JVJDlqKl1bya+KkqZflhNS utaWR5baKa3GxSVKqIhL+THHEeK4dTxyv3kWDbnbd3+8n/fzcjqQyDikp6Oj E0L6/4GHxjrrpZvozTczZ7RaNfT9bY6JKVT4/atrTiFexcm/VUHxRM/nt6tS NGqM2FFZKUvpUJRnOEjm1Aj6q/fxbUoAEnM+RocQfxf1+cWvlHAwbmT/bDir xqD7RX82JQpn81Y6npxSo9AqJOsyJRnn9rHpDKUaLOOKZZcoGUiTB6YuGFAj Yvcd3vhELjwvHTdJqFDDRMuK3OzAwfjwl2eJV9VwDVWNNebcw0ZfHo0Wr0ZK +1rkfyoGfclCXtdGNawrzYd0dXkIeCQItXNQ46nEv02w/jE+NfsaMKZUaIi/ bbtbUYm1EmGqn0CFyaW+ZqVHq5Bd1WbVWaKC3jR3ka1rDVimSS+DL6jgpf3+ aVjZc2Q4n8uKZ6rQluHZ3vR1HexWl1r6+ajgeE0+XayqB7P5Urm+pQryz+Kh d980oMSmNSFWpcQ9WW2L6dVGFCqr1lc3KWFq/0A9MsIHra5V0MhR4krck+hC ahPqgwPSE84qMbWBOxJ7/g20+2I3GYYrkezBr1zc+BZbaRPL6O5KiMv4OZ1O LVh/xtX2oJESs/HdBcvPtOL1m7Quv78VoPkZaaJr27BLuIFbX6vA5rtOMeXW 7bjOfHjdLVeBFPv9zh8iBeh/cK5gTaICboqdJr3BHahUn4jVBCpgaTZuzJ/p gE/14m/LXRTQryvgudzqRDMc/PW1chz2rH0/P0iIeVs6dwT0ysHdeqDw5ZQQ wu1cF/ojOSblNotG87pQYiGz6suR40nY5nm5Ad1YEdG9ZH+UHOe3ZHIqR7tR vcdlXRbkcBoM7CvKfIf+vb85x9jK4eOdkUvx6MH9oRqb1Z9kiHQQTOt29eCs g59HkUCGyRa25BirF7PipD2aBzLk6zOTGdQ+ZDLn351Ol8Fy6MldPX4figaa ysqYMhikssLXHn+PI/3ubTu8ZdApZvIkFv2g580ZX7eQIekmj23R0I/nXT/u apBJ8YKWbWyeMIB2M+s4bqMU5oFJbummIkiN7Qo8OVKIVnR0nX4uAu9C22BJ ihSPfgd1hDmI87Uf8IohxT6el7m9ZhDDE/Yxv6yUIi3zDktUMoR/ig04242k KB2zLzDdJsYCR8YUVzKGUHPTNW9mxBBYBTKnasZw2UDPVkTseM+CM0HMn56c GydO9BgQK4i9JIONNrNimIUc+WGY2KaiNCSBeEf21agOYkl4cIzVFzE6Z4Tx JcTJ+VfyDs6JIRTvTWESl15JO32K2CWB+mw38WhaciSb+MQXxb/hxBFxkc5V xJaUn84EEfv6uJV9pREjjFGYuobYUNT6upy4mz9ywYIYHXV/NhG7hpXyFxKf 4lfkDBCf/HDSYD6x7GFBqIFWDCuN4UVt9RjaUw8PRhDv9F5+WUFslLS//ijx /dcTLR+JN0SHFaUTT4XVmAwTP96+Lu4hcd6xIPZ7YvlG922viEc1lu3dxFRv F/ceYi+2yLSDmEmztpATZ9n+EdJKfMPRZFJL3FN89FoT8X/ElpcA "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, AxesOrigin->{0, 0.75}, Frame->True, FrameLabel->{ FormBox[ StyleBox["\"Time: \[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"Inner Solution\\nSubstrate:\\n u(\[Eta])\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm]}, ImageSize->{800, 500}, PlotLabel->FormBox[ StyleBox["\"\[Epsilon] = {1., 0.1, 0.01, 0.001}\"", Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm], PlotRange->All, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False]], "Output", CellChangeTimes->{3.414231508812187*^9}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Inner Solution Profile", "Section", CellChangeTimes->{{3.414200327363811*^9, 3.414200328810865*^9}}], Cell[CellGroupData[{ Cell["Comparison of Analytical Expansion with Numerical Solution", \ "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414223402719775*^9, 3.414223442774242*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"CompareSolutions", "[", "EpsRule_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ODESys", "=", RowBox[{ RowBox[{"Join", "[", RowBox[{"NewTwoDEnzymeODE", ",", " ", RowBox[{"ICRule", "/.", RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}], "]"}], "/.", "ParamRule"}]}], ",", RowBox[{"\[Eta]End", "=", "10"}]}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"NumericalSol", "=", " ", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"ODESys", "/.", "EpsRule"}], ",", RowBox[{"{", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], ",", RowBox[{"v", "[", "\[Eta]", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "\[Eta]End"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NumiercalSolPlot", "=", RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"v", "[", "\[Eta]", "]"}], "/.", "NumericalSol"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", RowBox[{"(", RowBox[{"EpsRule", "//", "Last"}], ")"}]}]}], "}"}], ",", RowBox[{"PlotLabel", "\[Rule]", " ", RowBox[{"Style", "[", RowBox[{ RowBox[{ "\"\\"", "<>", RowBox[{"ToString", "[", RowBox[{"EpsRule", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}]}], ",", "Bold", ",", "Blue", ",", " ", "Large"}], "]"}]}], ",", RowBox[{"TicksStyle", "\[Rule]", RowBox[{"Directive", "[", RowBox[{"Brown", ",", "14", ",", "Bold"}], "]"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\<\[Eta]\>\"", ",", "Large", ",", "Bold", ",", "Blue"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Large", ",", "Bold", ",", "Blue"}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotStyle", "\[Rule]", " ", "Thick"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"400", ",", "300"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ExpansionSolPlot", "=", RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"InnerExpSoln", "[", RowBox[{"[", "2", "]"}], "]"}], "/.", "ParamRule"}], "/.", "EpsRule"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", RowBox[{ RowBox[{"\[Eta]End", "/", "20"}], "*", "3", "*", RowBox[{"(", RowBox[{"EpsRule", "//", "Last"}], ")"}]}]}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", " ", "All"}], ",", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", "Red", ",", " ", "Dashed"}], "}"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"{", RowBox[{"NumiercalSolPlot", ",", " ", "ExpansionSolPlot"}], "}"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.413610742152112*^9, 3.413611218651717*^9}, { 3.413611253355247*^9, 3.413611273416408*^9}, {3.413611307366182*^9, 3.413611344232261*^9}, {3.413611462390807*^9, 3.413611481868609*^9}, 3.413611636829877*^9, {3.414199345952046*^9, 3.414199490804735*^9}, { 3.414199546646255*^9, 3.414199589062688*^9}, {3.414199647609153*^9, 3.414199713474342*^9}, {3.414199743980503*^9, 3.414199787201302*^9}, { 3.414199822356602*^9, 3.414199915536237*^9}, {3.414199973726532*^9, 3.414199989046771*^9}, {3.414200029225691*^9, 3.414200038447515*^9}, { 3.414200095223705*^9, 3.414200285423087*^9}, 3.414223442774507*^9}] }, Open ]], Cell[BoxData[ RowBox[{"GraphicsGrid", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"CompareSolutions", "[", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0.5"}], "]"}], ",", " ", RowBox[{"CompareSolutions", "[", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0.1"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"CompareSolutions", "[", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0.05"}], "]"}], ",", " ", RowBox[{"CompareSolutions", "[", RowBox[{"\[Epsilon]", "\[Rule]", " ", "0.01"}], "]"}]}], "}"}]}], "}"}], "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.413611224451738*^9, 3.413611293276521*^9}, { 3.413611373384556*^9, 3.413611449077072*^9}, 3.413611636830023*^9, { 3.414199927540831*^9, 3.414199927690895*^9}}], Cell[BoxData[ GraphicsBox[{{}, {{InsetBox[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwV1mk4lV0UBmBRiIpEGVMSotKgUuIhRWlAESIpkSmV+pRSJKnMQ5KhZIgM hXPeQ4bMZ0CGQokImVMhpQjf7td73de1f7x77b2ftVaeOnfYjpuLi2vXHC6u f9/f+10fGZ0z0lJOu9RmeM5Gy++0olK9wnroLe9WWi+ihdpvPU5BClr4/nxA uGj6IEbouoEuCofQ43vAaFfzcfgs/SFtpWAN0/GFW3D7LGrYBr1HFFwRcGbZ ndABT5x74l5lqHADpzRm3g4XBkCd+qzgs8wLU9SYyZRfILhOK+06NtcbxofW cE0YBaHqcmR84E9vXG0xdCjsCsax+HPHRt/7YLC6JcdwKhSe31Y1FMT5wVT2 juftiQiUBQYWHlQIRlaQenZvWDSKhz68FkwLhm3vskfF36JRtFexo0olBC0v +tsW7Y+BJfdJriTxUAjXZ9uLc8fCtHhKTnZ5GFRVfE70OsbBYOtGh2VrImAu J2GyaGU8NivEjfEhCj2hLfR9EonY1Lxryt47Cj7XO407kYgNvoM8rLIovPLP 7da0T8T67q1ivrsfoletdLUhLRFKj99s4zKIRjv/iGqjfhKkl/Jd/20SC23+ kYvPHJIxj9eNb9ApHvfX6Tx5eCsFA/u8hH6kxsN0wKXRLyEF1UGBy6Z74uH8 2ODm/pIUsP0bI+6qPkG1vZeCxWQKAkS+JcWlPUGpod/dANdUiMqtqqx8lIDX rzjqnobPoKATNFfMLwkRdYuX/x1Pw7LPEfwxyUlghZRuWrEoHfy3YxbIViRB P4JHbaViOoY4qaJruJLxJda2tMA8HVlG5fKaV5Px6JujjHFBOtRtJnbbuT7F Bvnv+RsvZ2Cf18nbjKOpsBOp4ptoycSmkDK9hEup2OvRmfr0ayak41fyB4Wn 4iHXbPk27ucYKe7yP12Xit83o/7yqjzHg5mToUv0nkGlesV102vP0XP9VOyF LWl4rTtAe7v0Bbw9bXPWiWZA5uDVjQY7suAUWOEmsSkDanPuNz/fnwWTuFVq 84wy0Fzbte+PVRYUiz7nfgzIwIzUbdm9Xlmom7ItCuDJxIJrrb2c8ixIXzvN HhzLhHOHrGC+XDbyPOzan755AQn+W1bSj7KRouX8XnLsBd5WGT7ifZqNBzwX 3oSIZEF0ILi2JzMb7kGeTI8jWdgrKKZ9vSgbWxMinh9szoJs8lL9FW3ZsOzp LL7qko3cj3EZmktz0CooFCJ3PgfK3W3ie31zcPjb4gXHvXNwdWzz0gb/HFQ3 iN6LCs1BdujHqYNhOSiIlLy1ICcHZerv8lUe5yBGVuHyr9EciN12un8+LwfH NmueqL5IA/f3CNu1Azn4cMxZ1e0yHQ7mB89U76LBv1vfJcqPDroTAur0adjh JJ9WFEkHR93PpOYADXEe7XJ8FB0rGQtmXxylweah4dK4ETr0B97XyDrR0N+8 eZrpSOHBdrFfWSE0/DT6Wy1hxUDDxbluVc00pLS08MGZAXexV67jH2g4asPY ffoqA6HTsxslOmh4ec61+MVDBor4NdYb9dHgGdyZo9vMgHin3PClXzTwvK58 ePZQLiy232h+IkbHYv0g+zLtPGzxWcWXZ0jH7rQiqBjn4Qvd/fPFI3RcERwW jzyZBz63kFBlMzo66w1qHHzycE1gkc9tazqyzfk3CFfmIeerAnPMhQ4jp1t/ rPVf4uqLrxTtLh2hQR6Bfw/mwynBN322kI7K78/s7K3zIb9+xVy+Ejp+G7do Nbjmo1Qud9P8cjpslm4bTQrJxxq5sHUzbDo2xI+b7n+Tj8CQXRcyGuloyD4n G2NSgLV3Z/slhugQbrKjbbMsREL7GZr7EgraX3WGTJwLMbfu/vY2MQrneZfL uV0rxL4DgVEa4hTeqL8Ly4wtRPq42/fv0hTCH+ldWPmxEFvn6lOKChTEzihu EDxehIfRBoUt2yhITg4877B+hfm/swIczCkYLGH2Trm+gl2Iw+/DxyhcXZsg I+H1Cv7vrQa3W1Fos7YIOhL/CsYREs7TJyjEVVS5cD69QrVDzUXLMxSWB6Wr 0GyKwS14qOryfxRWrXBJu32qBMZr4usPh1AI7FiZEHShBLwtOqNFoRR+xb1/ GOldgkyxknvy4RQ4Erp3nz4uQaNKp8rwfQouSyTPMFtL8GpPe+DxGAqWPKfD fdaUIlGH7VOTTCG0WyuYd2Mp9lSWByxKoVBZJuHvr16KX0HjmoapFNZ7198M 1y+Ff09YelUaBa7pHRcS7UpBW9H0N/EFhae/FhuVJ5Qitu+q3lAehdbm4f16 aaXgKfG3mp9PYRGDrV+dXYpbDcqHFAooXLl4HW9LSvFTd7rOoojUa2RgfXd7 KT4dXxacWkrh22DJQm7JMvRL/9Xs5FBQbz9boxNehtpSO92W9xRerHETc4gp w6Va7XvVLRTk3d1PBCeWoWQrJ73gAwVhIa8frbQyyBt2Bd1vozCoHSp1qbEM 2/psVFU/UYhJpjmniJZDItvlIXcfWT+ay3gtXY56XmWhJmI/zcLZMflyCFi+ D03qp+D2riICW8qhaBlWsnOQwn7+5sIW03LQj7iKmg9T+Os8ISgYVY7cH0pf 1MbI+pdTphvjy5GvTz84QDwwl+uJWWo50sSce6N/UGh6xK+WnFeO0zfGiifG KTyvl7DSbCnHHJkDpx9PULDevDPznEQFqgus2dF/yXov7V+RKytAq8l7uXGa 1Ov1bu2iNRVgUIf4OcTb7A428e+oQJ00u/r7DNlPlPXfhGMVyHv6QXztHAbK Jr0PNMVW4NYj7XyLeQw0Sbj9OpdUgfSmjnUNxH3qtk8EMyog5ixvsoeXgQWX 94zvKqjAOe7HRSp8DBz9MT8up6UCOuOi6wf5GRj6Ev4lWKwSBZmnJJQWMPBX wDdSWaYSZc0hHv7EQsr/gSVfia+he1K/EKs5mEVMb66Em4CuW/pCBrx6pDRc DleixnLlhIQQA6Ltyf77QiphIP1VuHwxAwp/I9V6H1Rim/FvfhERBrZL3enw flyJ2vqCPhtiawvHTS+fE8f9Np8iTmte16rwuhJDElZYJUpybXy5b3ljJf5A IdCJuG6J8HrrtkpYRdZWZROPG4/djByqxI9SPZkdYgxo1eWumTufCY2S/v3a Sxkw+praGC/MRDHPEz0vYtsF0dc1xJnQPm6p+Yr4rsG1N26KTCzZ5Sq/dRkD jSx4dO1hotZ9Ppe0OAMOJRxOsQ8TGzN2rM6XYODPdmE5NX8mxlv5YvuJ/Smz a2lhTMTknlgrJslARlrfuvtPmIj1Hk45S/wtYm6EYzET0V7TkqJSpF6LDgx3 MJnoYDYFaRAL34vYY1LLRMgbkdWniDfekPut9ZEJ7rH+ykziSw7ax0UnmRg+ PdG3TZqBeZ/v5N6bw8Kunnkx5sQPjtcLzfKzkBpT6XGFOO+wdfngMhac7C5X MIj31j6VOiHLwsZ311UbiVv0v15qUmDh/VaL19+JJ3d6KpZsYSHcmx6nIMNA QF6Ft5omC0Ks3W+1iaU3Cbam7WZhJ1W/8xixpmJM4P0jLFzWnaD8ib0Xvxx1 vMCCqkbwoW7ixYGzBp+usNDf+HXvL+JEXv1kE28WRv1CvecvZ6BiqvkoQlio G6/IWEds4i6TTT1gQWDBmQQt4p6R0/OVH7Pg/OtCyyFi3r4fhaLPWXCY/rzo LHGUjYaYP8XCOffjwteIldp8XGcLyX6v2ZrdJX5pWs2+VMFCyI7ZnvvE+xoW rxyqZkGke3vBE+JWA4urJ96yoPREuiWD2In5pLHpAwtzk8gMQRxYoOpXMsBC l+riEQ6xzJbLn9RGWDBYOrLjDfGLrGL19AkWDkwmN7YQaynzhsvOsrBSdXXh J+L65INf7vOycUVeY6yX2EY2crfAIja2tuV5fCEeif74yEuMjQxPl8MjxDdF 5SfGpdlYvUn5+jixSIizkZM8GySzJieIk+bT0z6psHHyxrzXk8RqvpPcppvZ KDvDHP1LzJzRsarewcYJgUaXGeKjHvcY2MVGQMis5ixx/4+GRYx9bESskLb/ 5yuu4g7Kxmww+/70/lvPP3iiLN6cjfOCTsXTxNG2qZJiNmx8ztMcmSJ22S9e vtaBjZs8evjzb7+b7znuPs+GRaLK65/EwlKTwlZX2DAq/hM1StzN7fzyojcb +28WJg0TU0NtJwLusqEq5jnSR3zn7QG+pFA2upP0vDqJjxW8elHwkI19ZgrG H4jXJq4/+vYJG3stFM78q/fMvfjpwWfkfxuNy/+dR8MF4adzcthIGaHblhAn Wtw8IJHPRv0HswMM4v90xn5sKGNDIX/v9XTivWtsY/dWsRH6MmziMbHk4qZd Nm9IfedoFYUTF3cywkK62Ngs+VXpCnEoR2F76iAbH3fyNjoSn8qO6iweZWOJ cVbNMWI+bw/Vb3M4KPzZnrnj3306M/RungAHEx88otYQZxpa3pAR4cDE7G3T MmIjWc3aA3IcCDB794+R9yDH9+LSaWUO1s7Pu9NB/PPbcmnPTRzMDb4gWU0c U8zlnLGLg7Nz6vfGE38+XskvYMvBlbiuXh3i3D1bslc6c1BZs/OnEvHddSlm 2y8SC4jZChGvnb6T4nCLg2Uv7xxvJe/bPW7/bnYSB15vfHoc/uWBb9GXjgwO er0aZwyIJV3WRfyic+Cste3GWuISDaHu1ZUcCA77ZH0l+cPf9tbLt4cDUUH1 Hw7EreW6inHDHHzTWH9Qjzgznaqjj5P9Xq8VWUVsfPWBzOe5Vfi58XBPK8m/ GIljhTqrq8B/+maeLvE6865fM3ZVUJnoeDdJ8jVOBDMBZ6tw8rnyzrfEArVx 8yT+q8KUcqFKGvGAjrnoZt8qaJuYZZoSJ6vUbzyTWAVLva16aSSvJWeLXOo7 qiDtscFJg+Q5b8rD7nizaryrCNwhtITcB5tfg2tPVOO99OyCD6S/9EiajObb V6OT6+W1ROKyECGupv+qoftZYoMasaeHnwz//WpUnbTjOUL619iBS+bnG6pR UGVafYP0t44fhnXa+2qwb4X69XBBBoKl3q86b1wDW3eDw/uJtXStPeItaqDY 9qqShzg+3EV+xrEG57v6bl0UIHmw8d7VQv8aeB6VunpoPjlf13KFra9r8Dno Q9EY6dcDg2peKoavsTOI//Bv0u/HPklsWGpai3O+ry4sIfPECtsJNdnjtXDf 5qaX/4uCYV/TdiW7Wiz8femDNXHmcIjujv9qsWzVpEbaTwr2f+aZWUfWIv+Z xMwOMp+0ioxdT2muxYm60brDoxTK9lTXbD1aB5oHne/oFzI/Zlw9Y2ZWD5P2 Bu2iDgoKQvwHr8Q2IOO8TasTk0Luee+M4Pg3+BE4Wj1F5smm1RF8xuFvsS0m yHpnAJnfbjUqHY9uRHJ9+3YlZwrbjT6pxcc2YZ3QFaWF+ym0n7+tFRTYjM/5 3hPlaynQtlssZIa9w8TcZxtzBSksPcr+8Oz2e0g1JM+UD9OBbq6w8kstGBuq +GNfR0f0UoeFClc+4O6UR6r3czp8Hjve2eLUiss/62c7gul4VPeQFXy+Dbzn FHezz9Jx3TViRMbtI7Lyc/86HaTjy0klcYtT7cjV9MuyUqUjYHpobod9B/Jv pdGHFtFRMKz/fdGxT6iukI1mjdDwbrV69w75TtBqnSKsG2lwWGOrGvG0E3zz vqvG02koO2p5TWd5F9YpFrooPqBhs/lQmmhCF7gy7mTZuNPgckvvvaZUN/4U ctu3m9Nw155/ck5EN0RaT90Q3UnDK5mTs0Oin8Ez1mbCK0ND/owfj3LwZ7yJ 4UncxEVDHV13KGhxD7yjDpus7MoBc4U9KzC8B7Q9W1FbngPfPNOELoFeKFsJ LEtPyYGV3Edry6BefBX1jD18NwdTuapSKnx9COtWFFd0yYEnz+DryBt9iLJ0 6n9hlIOl8ttPrubqx7bGjD2Cm3Nw2fXouIBHP0xbtfb4L8vBaKCAk9jfftin OUr2/smGtK+O6GpiL+3msC5i/WtXitWItTx05ncQP3LsEzEhTq+X+v2OeJ9e eWE4sYZwSzOHOGHWY6HwdD82d7qGZRIbuw1mC8z0Y6ZAbP4lYk/HFZaSxA/8 Ir3PE6famM1TJn7zQ+y3C/H0IabFPuINdPF+O+I0lQTuu8QBzNVMM+I5veYm 82b78ULd+qYG8dqPITOixM7LB35vIzZrZD2TJ65+6nZejfh5mdq0LrFL9L0T 64gtHgun+BDripZoyhL7RuobhRMv4DvEkCLOCrwxmUDsHtu+Vpx43rXhQ2XE 69NmpBYTb3Bb9aeB+JpcaMRCYkvHY0mdxI6acoICxH42YQdHiP/8oXx4iXPM OBOzxErmeye5if8HusrYRg== "]]}}, {{}, {}, {RGBColor[1, 0, 0], Thickness[Large], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwV13k8VO8XB3CpJBSKolBJSkqKihafFhGlKEtSQpQtSSghEiV7JGVJ9oSY mTtlyT6bvUJJyi7UT1laviS/p7/m9X7NM899zrl3zjl3lc3FY3b8fHx8mrP4 +P59/j7kkmR40VDr2JdeZ8OLVlq3bNeua1JUgYjFVKPzIi00jPQ5hitqwW/u mjsfpg3wnbE/zFnxCB5Xfcwxaj2NgCXjMqcULVFudyHiQNAF1HH1+48ruqDr wJ3HkYM+uPjYs+ao4nXU293v+VgSCg2qVzFgqR9spZiDw7fCwGe7bt/JOf44 Ncf/a59hOGquxCaH/fCH5amzaRndETiZfPHk6LsA7LFi5e+ZioLPyOpXxYm3 ENAXrOn8KwaVYWElBooRWBrSYJt79yHKht/XC2dHQFp9Z2TAyEO8PLj2U41y JJRVfk436cfDgt+aL00qCkLxR0uaZyXApGxKfoXcXTjp6fyJcUiE/rbN9kuV YiC/0Ubz0cpkqCkmjs1DHFpGs4u/SKViS+u+qXP+cWjKMr7rh1SoBg7N5lTG Yeh5p3G7XSpUerZJBmo/wPHNz4f7aalY9+j1dj79h/A4Za1qqZsGmSXzfH8b J0D6/L1HUvbpmCvgNm/IMRlmvqFdNQGZGNTzEx3PSoZovNNXxuNM1IaHLZ3u S0Zxte9597JMcEOaY4I3PUbMO5UQr/8yEbpoJC0x+zFeBciGxF/IgoT8ahYr KQUDBhrsc0eeQHFv+BzJW2nY+TVD/N54Npb2xgjGp6ehcSL5KV3kKQSD4kVW VKfBlndS/tmapxjmZUko8aWD6WDhuMvsKfINqxR2X0vHtiKae0nhU2hY/dK2 c8mAg85yeyePHOj5WQcxTbOg9mvPSs7bXGyJrNRJcc9C22tuxYUvuZBJXiUY Hp2FTg/Rt79ncvG9rDvEtjELPlbVE0Xr8nD/r3XUYp0nKHyiKP71ah76fG0S Lm3Nxvrb8vGbJJ7B3+csbaNEDrYLXPy2bns+HMOq3aS35MC9fdPuwIP5ME5c rT7XMAfJz9eacM3zsfZl7/OO0BxkB3Nt5vrko3Hq7MvQ2blICpywtS3Ph4y3 LXdoLBebP/T59a0swAsvu48Zr58ha3HGir/xBcjUcnq3bOwZyk0GlHtTC3B/ 9qXXkYvyobfglMLLpwXwDPdhex3Px74vMXL6xQXYlhKTZ9BKrlOTubitrQAW fV1l15wLsPuAUnjtYhrahUUj5V1pGMwwPut1g4ZjI+Iip/1puPg+xXfqNg21 ryTuxEXRkL7jhO/lCBqKY5fdFKHRcIl74dyBBBriVyhe+TlKw3WxKmc3ioaT arvP1F6m41vgNffpPhren3Ta5HaFAfb6/2rVQUdIj65z3C0Gfp1a27JFm44d jgrZL2MZ0FKg+Snp0ZHo9VF+HsXAxNhAH99xOqweHF2S+J2Bz0NuP0+co+Nz q9o024HC3uhp/+ehdPww/FMrfYoJ/WPz55x/TUdmW9s8ODHh/j7ELLSVDlMr prbtNSaY2064ZL+no/CiS9mzB0yo1fQLNHfT4RPRRdvfyoSS3htexygds+tZ Dy4ceQ4BC96912IMiOuGn6vc8wI6JYaGnvoMaGe/hLLRC2j4P7NWPsLAVeGv UrHWL/C/CSbajRjoatKvsw94gbKl5kFrzBkoOCGoKsZ6gbY03Y2XzzNg6Hjz P0vdQoQon/EaC2AgKtwr7I9BEexXUM3FTAZY357YnbMsws/MnsaiQgZ+G7Vp vXIpAuOkSSKjhAGrJdtH0yKL0BRYWhdXyYBq8oTJoddF0NuxR391AwOvCi6u iDcuhubV32IGvQyItdjRt1uU4LyBupCMCIU9/9s7bOxUgr+aO6uvLKTgKiAn 7+ZdgqE17wybxCi81nh7NzehBAkeB2e5SVKITtK5tKqjBOzmBPNbchQkz69V FT79EtFmpd3fNlFYNjmY98myFEpZAgFfj1LQX8zun3IphXOO7f0GIwrXNqTI SvuV4qrylg05xyl8sDQPP55cCqk2zjcLMwqJ1TXOvM5SmGjwn7lnSUEu/Kky 3aoMPyReC9o5U1i90jk7yKYcjVGP7mQEUQj7tCol/FI5LCPj/ARuU/iZ+O5B rH85Iqifg7bBFHjS+4MzHpHvw/VWLwul4Lx42Xl2ezkOOU1Gn4uiYDHbNjpA qQItIorbQuIpRPVoRQhsroCA0bwv1QkUWJXSISEaFTg60qszlUhBxb/pRrRu BXL/656xSabAN73jUqpdBcnPsfol6RQyfoobVqVUQDJ09oVFeRTaW78e0smu gFqy0NTaZxQWMrm6tQUVGA0JO7Mzn8LVy754U16B+b3mLyxoJF/fB1V6PlZA ZFnR9wAmhZGh8gX8yyphs9Fn/EIpBY2PF+r2Rlfi08N7HF4dhWdKbpL28ZXw f296pKCegoKn55mI1EqUb9F5FttAQUzUb7ydXok/oSP8J5soDO2JWu7eXAln v33GNW8oxKfTnTIlqmCr2bLpwHuyfvQ5s16mCnmy+inC7RRu7S6ZGVOogqC0 4LJXxG5vq2OwtQoHD0VvON5B4ZBga0mbSRV2uF5bva+Twh+nX8LCcVXQYiUU svvI+sIpk83JVaiNZA1c6KcwOIfvsVlWFTqgpysxQKElSVA9/UUVOjszsy0+ U8hrkj61u60K9kdydrQOUbBU25V7UboaFpqdRR4jZL3fnp+xq6rBd2pQk/8b yVe99p6XStV4dpK+OJx4u51Bi+COaoitHPqY9J3EE2f5J+VkNTjtvAW5YxQq J/0PtyRUY3ZG0zufn2Q/abefF9Oqwbsu5zRIPKBx9rFwTjV2TjPyjv2iIHLl wMS+4mr4Tufprv5NwXR8fiKtrRpeC3fMUP9RGP4S/SVCkoUk6eW/E/6Q+IUC Y9fLslD8OujwOLHoeg9wFFjQPyvjpDdNQd3eLGZajQXD9ZoLxoj9+pbvdD7G wmDpM/GtMxQkPqaH6EWyIOMed/XmLCYU/8Sq999nYSJXbAOPWHP57U/+j1ho lXCvEuZnwtLcYUthHgvvZvUkRRJnt25sV6xnweTxQY2Q2Uy8nJALrGpmoTFU dAOHuHGxmIrlBxZkVc4snDWHiQmjsRuxwyw8stuffplYq/G50pz5bFJ/bHYd nsuE4f+ympPF2Bh4WFbnR3xW5KHvTik2TLt5xnTiYH3v125r2TjraGouIcBE Mwde3QfYmI6ZNqonHuhXXe1rwIamm2/LL+Lfc+QbpEzYCCqysJCfx4Tc/jmr DG3ZYOk6ersT25fzeGUBbHjPH1m3QJCJ/zTF5NVD2PAUytyjShxCmXln3yXr 71m6HiPOyR7YeO8xGxIFt2XuEe9SULk9/wkbU8lHExjE9Y88uq7nk/O0c7a9 IR6JmRPjUMaGuYY1T2Q+E34LD3/9xGZjVUJTxTpisTsxB4wb2GhsuNm+n3jz dfnfWh1s5FTt97xC7G6/57TEJBsxgddcWojn9t5+fmcWB56XrkUNEd8/3SQ6 I8iBpEdmxzTxi2OWVUNLOVANav+1WoiJgw0Zy8+s4JC5T6hmK3Gb7v/cWxQ5 +ChTyNMhntzls7Z8KwcRm2vNzhGHvqj2V9/NQfS+w0PuxDJbhNuztTnI8Q/K CyDOzT2mtuIwBwckbmREEu9eGx927zgH12sOvkkgbkzp7p9vwcGYeL96FrGl jBL8bMhNEjjdSCP+dt/1wYQDByP2z5NLiP3FC0cdLnEwmvEjm0UsHjaj33mV g6S3siP1xKkCuunG/hwcrFK90EK85UbEdM1tDtClsu4DcfVUqykiObhivnRl N7Gxp2wBdZ+cT2jQZIC477vt/PWPOBAPTKodJvZwyrVJzuBAQFTNb4RYYGC8 RCKPg+KcVPdR4jirnZIhFAf9Ev0548TrPgS4zJRwwF85uuYHcaFJLde9moNf vWW9/6z3SnzVcC3Jr+vegX9u1ze/duYN2X/5BZV/dmQ/bm55z0HrCfXSf/tN YXCDfjcHa2yDY/5dL6x4063yQQ5u7DKn/zuP7NYrnerfOUh9ErvsC/Gz/DKN p7/IfhrKDf/i0VovEL1ihoNAbYG6f/E2pRt8uSfARd+4uGQHsdWKWG2hhVy4 amrkthJ/f9iR5CfJRdA767uNxDckFH5NyHCxwtqTzSFeFOlk6KjAhe3OU3pl xGnzGdmdylxsT/4tyyRWD5zkN1HjgorfpJ1DbOp1h4l9XPiwfgXHEn8ef7WQ qcfFkM6h7DvEV12k7NcbcaEtUibnS/zwbNYySSsutl3zErEhdj4kVbXBngvR Zvq+Y//iUbvjoO3KhffoAGMvcQ+/U+Flfy7yZO4fkiOmhj+cCQ3moi5Nw12Y +Pabw/PSori4MaTQ8Ys87xtSVUzfPOaCb1LKpZH4753k6aEnXFxdvyu+kPjV JbGMWTQuFIY656cSe+wdG1et5KI4oumFG3FZF/NuZDcXTnLCTsLEUTxFzawh kk/e76Zv5P9rUxDXVTbKReCeCP9m4nn+XptGZvGQJJzNe0BsuGJ3w2F5Hnr5 lostJ+49zRIUOstDeZ3p8RlSf54f2FqwyomHmJ1zPrcRB2/MNNO8zENebGIr jXjD9O1M+5s8dB9T5VoTeyYe0uam8VBsKSJZTOqd4Ic3foF9PMz8LF5pQOpl e9X+tYlfeVCQ8muQIc59SjUyJnjgiiv2fiH11ujafdneOTW4MnPxcDBxvPTJ kr1ranDVZHJjManXG090//xrVwPPNrNuflLfExfhb+iFGtRbS5s38DEh1JA4 V9qjBjJfz5yIIx7ce0JCLbAGFTd+fFMiTldu2nw+tQYL0s7f0yP9Y9nMS+em TzVIH/2mcZn0F4HMBz3JZrWYG7vxz2XSrzysfg5tOFOLt/XhwarEfcuMR4vO 1cImmPXsK+lvlZGifC0etXCMbKw9S+zjdUtW8F4tLrp8PGpA+uHYYfcTrq9q 0TV3bGbBDwqfxo827tGrQ8ilbjs90m8jlr9b7WpUh7fzJbzGST/W2m/plWxe h2Kl24pJxMnRzgp/HeogZOd27Bvp51ab71wrCakDx3ve34j/Ueh1qVLcVl+H xLohuZfDZF4YUvdTPlqPfm+7ra/JPDHWKa26xKQBIw2zG2a1kXkt59p5M7Mm TKX15lSXUFAUFTS4mvAKubt7e9IeUXju6p8TkfwavqPXS/p9SL9fEzPPKPoN 1DIzzH9YkHnpZvO60w+b4arT5rd2OwVNw0715IQW8tys19NcROGja5BWeFgr +L+NRmh/Y4Cuab6Affct9POink7yGFhiyn3/JOgdSqtFdv5OZwA9fHer3Ntw OOzQuus3GHi4xH6B4tX30FnqnPvxJAMBjxxub3Vsh2XR5pdF2xhIanzAiXD9 AJtBI663KAO+LjHfZd06oHF5sPvzIB1frNdJmdt8RNSJ0t+9LDpCp4fnfDr3 CRq2/B8bk+go/qr7beHJTlLH5rce8aLj7RqNnh0KXUgNcf9004QOe6Wzm2Iy ujCWvqjqqQodlaYW3nvlukF5im53FKJD7cRwtkRKN1ge/qYyvTQ439R5t3t5 D07kfpo+X0ZD8DnByVkxPWjwUDzoFE9Dqaz1zLBEL8LfdLyyvkxD0d9bs9dH 9OJInkXI2BEaGhn7h8PF+zDp+TLbcy0N7JXnOGHRffAsufCOzkdD4AuTlG6h fnRFqLrf6SjAKfkOS4vwfhSrLI05zizA1PNNy5XnDaBA2ntzYVQBfGYP1cde H0DiZMasVvKeukRB03oN32cUfqo/3X+gAFdcTCeEvD5j6W2WdtSqAoyGCTlK /vkMfpEi99MT5P05cK/EGuIBXRshY2Jd76tl6sTPbwo/1idOchhYZEwsNnW6 bjuxnk5VSTQxZ5BffhFxyozXArHpz5CuONzEGc+HkdtQgdDfz7C37FJSJfZx WGmxjDg67k65InGWldnc9cS5r7aYyBJPH2Gb6xHf2xfkL0ScrZzCH/zv92vW v+sby8es/hPGc2c+Y3LgcuBD4g0dkX8liGvlZJdFEZs1c54oEN8y5eTfIs6r VJ/eT1zMlvpwmdj8kVhmAPHKtNLNR4gDY3UNo4m1289xtYnzw65PphAbioud 3kk81/vrkUriDX42weuIVd1W//eK+DdTWG4FsYXDybQu4vyvFEOS+JbVXYPv xEarLfVEiGlmvF8zxJ/M53XyE/8fKqyiig== "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesLabel->{ FormBox[ StyleBox["\"\[Eta]\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"v(\[Eta])\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm]}, AxesOrigin->{0, 0}, ImageSize->{400, 300}, PlotLabel->FormBox[ StyleBox[ "\"Numerical and expansion solutions\\n\[Epsilon] = 0.5\"", Bold, RGBColor[0, 0, 1], Large, StripOnInput -> False], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, TicksStyle->Directive[ RGBColor[0.6, 0.4, 0.2], 14, Bold]], {213.33333333333334`, -160.}, ImageScaled[{0.5, 0.5}], {400, 300}], InsetBox[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwd13c81e0bB3DSlChUqJARSSUipfpYT1o8JUpGiZQ9Unb2Snay9zrDiMP5 RsmItkTTKCHZlSJPqfS7z++v83q/vq9z39d1z+teb+ViaDOPi4vrAjcXF+d3 +v2qrdWHFPam26oM/OtiuTc7REKST2IxsOyp2wfBvXCVvRn5RlwElLJZqOxf fZycmbfnjrg8tIc3v13eaYG2XvnVFeLqePdSRuFJlBMWv9AIZYjvB9ed/EXn pvwgq39vV7G4CcwNjdzS2q/Csvlfw4z3Joh4dSZsODMa6Tu77eJzT+KA8Uvx TbYx4N/wJdVHygznWX8sUn/FYmZO5D+DDadw36u3e/XSBFibUF2/Vllhw5dM udvLkrCdlze5UNwWQ41JF/NupiE1sr9gd4Qt4u+JrSxemY7fC2srX36xRfHp daWy7ulo4bF9Or/JDu2QLUpVzIDxn3vzbawdoCAlJmKVlgmPySB3WbozxD0+ T0qb5cB83E/+ReoFmO1+7sivnY9Ypu1WiacXsG8q66yjXT4a7YzUHLjdsdwh OT0xPh8yI5t0eezdUavS/F29Nx8Tg92nVTQuwm8fT/d3jwL49aqnXHt3CXGr /LrdswuR1TG9wEjKG5c7Ws8FPihGeJ5yl/wxb3zze/R8/1AxnN1cS/+EeMNt eGvEyHwa9q6YMKR99Ia+kWR6uRYNvUc+5MzSfTBX+v2naS0Nku0dO/O2+mHP 9SdbzuTRUdhW7vR5dwBylHt+hRgzEZ09odnsFIC4+9LrUlyYuOisIJyaHYDA xIaSiCtMSC069k6SKxBPTYIect9hYqq4LeTxmUB8PLR+wWmpEiQN3WtfJxuE WyMuE4NDJXhlU23fUhKMCtegKR2TMsx0pqtXNwfjxxK245hTGUQOBy0s7AnG 3vzZxoshZTBVNsgPWRqCEnGRENXyMvTNDXdpO4TA0kVK3mFeOcZT1hxoUggF g1X0qKWoHNyPg+XqGWEQn+JZLNl1A1J77L6XNYUha6v7h5DxG9Ct+Lc5qysM H7jz2p79uYHw5LWnLy8Jh+3KZ9LLV1SAz5pK3m0Xjs9uU5debK/A6t+jC27L R6Dv39l1yj4V2Lzl6OBNWiQ+L+u8VP27ApLKdYI3miIxNjOlrbigEsJqclrF PZE49UJ4VeqySszu+ZOVJHAFmvN7+A6LV+K+PuOEm+cVfE2q+LoBlbB04n6i oBeFdWO7tCn/SiSWVlZmDV2FStZ/uvTvlQirWNuXxBUN1csuixp+V8KrOoI/ Wiwaq949vfWEh4VTdRYOPgbR8B/ZsfHBChY2tS6RPUFFQ/Tu9RS9zSy0jJ9J XR4eA1GpdUd9rFiYURAMCJGNw/nPB1p57rOgu6NYqGFPHLyfl8nHPGEhUWcX fdY4DpcL38gLdLCwxdyqwy08Dh0Fv9X/9LBwPoYlbTkchwdLlqQGf2VhwnPj 2WyjeMzoCOnvWlOFU92PFvuuSkC9Xq9Zll0VwvqEXqRKJaDcgGo97FyF0iGL LGpLAl7eu/Ln+4UqzH77uu3bvgTc0llVr+pXhZSlYmZ2ngm4reZ4zSG2Cu27 7ctOdCZAoFHL6GZlFbRyeA23pyfCNObZ/gXT5Pun5FZjWiJCuJNMjvyoguVu aT3P6kQ8czq0+frvKgR2aey+1ZaIXdo/9vEtqEajkNMGTZ5rsLFaJlu5shqa kc9mDzleg2ijVvdbVWK3pALrvUl4stM8dMatGu0NkuJhh5LwXmPf4ahL1bDk L0stNknCmxV/e0S8qxFYci9m9EIS+pWCnDcEkvY/zni60JKQ8ld7/fxY0p7p ycO+y69jMXfGo2d0Yh3x74kD18GfGxPa2V2Ncyfa1nt+uY6p/AtPW95VI8bB 38Ds93Xs3hI6UNpXje5rvTTpVck4rSAR7jpUjUuD2abVB5IxVLtF7/7XajDD JBpfVSQjYE/okYpFbAg/lLwqEpACTaEr/gVKbOx6237z99UUDEvpRwqpsHFm MnCwLzUFC2YPLgpUZaNcpH8Pg5WCAvZqH4NdbBywy5vcOZSCB6af7zfpsOHP K3XcTD8Vq7tXqCw8zsboYen12WvSIFDX7CDjxcbej8OBhXJpePH02D9LfNhI vFzax1RJwxtRtfBxX9J/uWruzUNp2GTddogewEaUwH6JDt80NLWa6PFEsKH4 3HHd/LdpuHNl82Lt62w4n6BE7TPTcbf5utDPG2zc/eLj7UpPxxuvIKWESjZW RaLLozodHTNSInJVbNTXPEwNaU2HhuBtw8MUGwJiPauzfqfDVZ7Z7FfHRsXb vyvbzTMQ1ft6kddDNqbOHBBUW5eJ7XFHssd7yXftI1KaCplY3xuy/3Qf6V/6 hPLBHZnk/F7S0N7PxsjgWcNTRzNx0Pn62rJBNt6eD0wMD8sEsoLHDo2x0eJ0 U/DNp0w0tMuZyHxnI8lbVsirPgurO03LjZZQOGqqKB38JAsS9ft8Ingp8Guo qER3ZmG2od25ZimFyN+ax3K/ZYFahx5hfgp+AebXHm7IRlNQ+bwaQQpnw64J icZl48CGncmMNRRUE7iFb53OgRprkfRBRQqSM2tPDDnkIOPJ22eqmynwmqmn C3rl4O+2DinJLRT6ZFwkHeJz4PWi/O7kVgpRNW8V1zblQGTUQiJYhcKXLz1S WJGLoRTj7nO7KOiuvqmRdyEXGyKN1HX0KNQ+0rW46ZWLwU3N4wv3U9ji99z/ qX8uliXyeT8iFu3/1PQzinwfOip36CCFz0yZ/YYFuTDxTf6jqU8hdW+iEc/L XPBeDxv5z5DCJxsnJxvVPFTbas5mWpD2fvGNmGvkweVSborGKQrO8aVWRlp5 iLqs+E8X8eSt8RM6+nl4HWr9aoUlhW8C9trrbfLgmxg15mlFYab23Op3SXm4 1VA0KnKeAhe/ZZPRdB7eCZw8SLlQ0Cz4q3F4Ng+JXwzkd7pSCFLPoXS48vGT 2q9xm3iedW+JMl8+dvopzb/jRmFBjXnycpl82G2c2nXTnYyn1UmH1mP5iC+U WBThSUGYMlypW5UPkbZR13R/CldchGzv1OaDZ8Xfh/wBFObkX95SayT3uIi9 UTDxSIax5canpL/p/iXnAynUBZmU8A/no+FgnYBcMAUb/VNaXWIFGHmuFhUc RoEatHNyDi5A4PpPBeVXKWzKVmgcjiyAnNNk0NJoCrknxgXPxBXA8tzS6vPE UY8da45lFuBP3iYR8RgKpypceHZSBeDljv4ZHEthkd+lNJ6xAtzzDJ7YnEDB RCjoXurRQpiXtH3mT6YwyN+6reBEIcJ6g5WOEbvyrs4usyB1hvLP6WTiCO4y j7t2hcjnC1i8LoXE96VTbiKoEKbbVOylUymsbFWKAqsQ3JGm6aLpJL4HvjMH agrhuOyj/nFixeb7Vkb1hZj+4heTSKx7y1zD7nEhbDLkqpZkULhIj5xIHCiE pGop/Rvx89A+gyHBIoTVx9XfyCL5BG66PSlSBNGThV4ficd8PeR+iRfhR/SK h2LZZP7c+biWbypCftz+jaHE286oV+7UKcIcw3GBYQ6F+D3xQjHuRTDkGi3o zqWgP4NOlZdFGBnT6s4vIPtxVenaxu4ivFQxrHlG3KYqcuZwfxFWHa/d9JvY 4NLk6NnPRfjF3ffyWCGFI9O5v64vLsbITJfmHLHhN26JH7uLoWfYya1ZTEFQ 0Nk6VKcYTz5u9D1H/HxbN235wWJIN66/Fk18zI2ltPFEMVgyJnlviI0mrbRN 3YoxXqqgZ0ejcPxzs01dUTEUmi4p+dIprOJXYu4vLcaxowmvMohfb878/JJV jLueYevriE84XfT81FCMZb+f3PhFbDIhc0W8uxgtgnksDwYF07Gw0kB+Gvp+ Dd40Z1IQ4/02ybeSBsUMF24v4u6Np1TT1tCAApmficRmdmr1lfI0nLIamH5A bD4y9GxAm4aBVl+FLSVkPob0pnQ9adj2Omd6nHhs5F486zINsuPXv3CXUrg0 rrNFMpSG1461+auJoydh9yuehjdfdFS0iW/P7nhfyaSh64DF4iTifX/YfhKV NAxLdDyjET//qyIWc5MGgzYHw9vEY/OVjG1baLijeyGqn1hEQP6JeC8NRtGH nimUUShcUWwbPUiDsai/927ircIyC2fHSL458f36xPtEJbVe/UfiVWBNuBBf lBa5eXUFHUNyLj8qiDt2LC74oUvHRrvlynLlJN9d4ZrnDtHxMHDNh+3EI7vn 9744Ssfxl14ntIm5tLlEb5yio6ch/Ko58ZbDP2JtvOhgZXoqxBLfMvBQfOFP x++IzL9pxP8cnX6kGUaHXXtrehGn/eOT89cm0qG5pFSmjjjKcsTneQkdogKf 4oaIV1mfE9Fk0XHZdTp7kjjPZpBdVkNHixLbY5a4xr5vMvIeHfbr3IOW3aAw fLHzHN7T8avFeOk24guex+eXfaRDWDPz/E7iOe+XeWITdDg63onVIl4V0P72 +w8S37XcvUeJda88NCwVZCBk92lFZ+Khp+1LSkQYcPK/dPEi8RXBrkaGOANh r+XjfYjbMka30BQYKJunqxNO7Nr39WOREgNu7mI9V4kFZWczC9UYaFNx0Esg PlHOuzRfm4E7b02yM4hnvwnezd3PwHyrs1dyiTN3rPHOMWDgX9cHB4qI+xo3 DWeaMnDijNuhcmL7F4ebUy4wsFbujEk9MZ+IsU+yFwNnw1Wnm4hvmFtsu+5P 4u9fc/4e8fRHp5zEKAYqW349f0KcrOBxPCGeAY9R69Y2YnUX/2XxyQz46dzO 6iC+/CPWNyafgZp24UeviSX3pChH0xkoyA2T7iK+G5QzGlXOwM73d4/3EJ+9 T8u9Us3A624e63fEC5dWnIi8xcDL/oD974np/9bwRzQyEKPtvKif+FBS472w +wxYHFqYO0D8ufOhX2grA1kHAwQHiePXdaiEPGeAHrv89EdiZauusaBOBrps voYNEb8q7s8L7CXjxTKKGCb2Gh81CRhkYGW7tfUIsZjSNwH/MQbGHxwQGyWu uzh732+SAdHSbaUcn6qd5+87w4BK3D7RMWKuOV5Vn98MPA6pOsNxgbbQhNc8 8q7LLAjjeF/EmgLPxUzcHdf6v0eeSJt68DOxP7TWkuOo5YorLgkzkeqlKsKx ovH2h+5iTOj19JVw+mtL2x1wQZKJ4fqhNRy79eqquW1gglftgi0nXmFp/U8u ikz8c6w8gZMPdd640FmZiU0b76dw8jUptTBzUmfC4PGgD2c8ZidtBB33MqF1 QFWDM16Zqs6P7HVJ/zUDnZzxhI9HoN1BJoYURIw44z1Q77/D9ggT9SyuMs58 hPJEfD53nAmW1YMPnPl6GJ1iftaKCYRljHPm174jR8jalok/a//WvSFetor+ +IwzE7JynxxfERvm1Kif9iHf3wrbtXPW14fGLxaBTLwsK2Q/5awv+UfF5uFM WGo49D8m7qnsEjZNJPm/3v+mhZglxlPYncpE4KdaU856jQxRVDHLYeKZvW3N HWI144Cj5qVMhDme5KE4/dfT+96ymDjfveRrJfHghucuFrVMfA96UVtGnPhD JvbUfSYWH419V0hsd8Zg3ftWJpZYfVLn7CfNx56lp18wwQzQcuXst08Zjx9b 9jFxr6rQnbMf98N1kfUsEytaTr7wJZagpyV/4CpB25y1sAfxzPJm2bOLSvCj YbWKK2d9DKzUtREugVScNO9ZznkSdjvw/JYSNMd6Sx8krm5dOOtgVQInhQT5 5cRXVZWuTNiWwJmtZLKY2Cr7pIiTSwlctWRtuYgFXEvVnP1KkBZVs5FzvtkL Gbq7JpfAQUZNvY14vWnWxMXHJdgX85cWSvzj7n3f7+0lQPzcpA9x26ZJXo83 JWg4/HetG7HfH+2NnoMlcJOsFLcg7swdsfGeK0H4pdCnKsSxwyrvLyuXQjv5 +FwPOe/9Eocj4tRL4WEf8m8Hsd2eDKW8vaUYyGBeuU+se21ecMvBUtR5G9Vy 7ofZvR0yS61L0dfJtySU+Hyys33qtVKo9t0L2kCs+Q/jO2u6FPGfFiabkftp y6R5dstsKRIj/u4yIF6TsVzvNVcZ4tKMWzWJZyY9U3/ylaE9Mrxalrg0c5+G pmwZ3h76lvWZ3Kei0x8CnxqXQW8BbcKP+Fu+ON8IVQZ1NlMmmtzHwhemon3v lIH7g80OX2I1rYfLBFrI/78nqNkT+7x3E1DrKIOoMn1Wj3je2nuCoeNl+P2m LnMeseB1B1FJyXJkui+wvEjqA+WImg0mV8rhlvQn+yCpHy44GGo9NLuBKm+G 1oMiCtbuARYBfhVwtFPi1yT108eprCd79lRCpUKEL47Uc99n+/bs4GdB9qHA 65/XKPTqOvYf62DhwFN93lhSj24bUaFlxFehKVWsQyiCUx9JuolbVuP4nUcT w6Q+bvU3cmxZT96ty8T0xb05+ZU5FE2x4Tfq2lBB6vH79doxlU0UDlZvO37S nrynDCT7+oJuIvzC6lEva7J+zkrtOGRYg7iw/uQ5M1K/3HFs6BSuxbXmBZlc xhRuukzZJbyohdrTDxYyBuQ+pWeLhOXfgqIBa65yH8lPJvFHhvVttAdvsmkA haoNzLefttfhWOLA8A51Cm8deL9Z/ajDXEnXvG3bKLjw0jby1NyB0SBfqIEC Ob+32tr0RtRDq75GtVOKnI8pbs/fHmjAq0fW7QPkvcbb/Gz9Uv5GBP1ylDAV pjB/ONRhz6VGPD0y5jjDR+JX7NUPetWIMzfmfIUWUljNPsAa2NOEQQXdZ1lz bCidPnnDOKcJUzuC6+j/sTGnGrGnd64JV29Fn+qcZEPoyAP90HN3saV55val UTauXy2Z0XhwF3tXrjO6NsDGKd789SuUmlHxXziPRA8b+jxtjHXEi3PCJcSJ d//+uU2BuF8/XGMdsdjno9o6xCvvhrmvIX7TwW19iTh4ftiH1cRH0s4UdhF7 fw1tXk6sI79eLn9bMzocokLmESuv179RTqzBczWHm1hKzHvHbeIN+VdvcxFz 8XXovSS+PBM9NdfNRt2XQNuFys1Q+Rln/YtY7WYfw5649lyKzjSxbAWfsiex okfq6SliYYb6rRBiyZg032/E39LjH2cSX+nIqJokvuGvOd5GbFWdK/2JONvT 0b2HuPtvHiaIY11Tfw0TPzcsMBsndrSaXMqt0ox/BIqvjRKbma1NWkbc4EW7 MUJ80Gj/WjHi2lH6k2HinfoXCzcQb7diDg8Ry+/LVVQhVhoo4eH4f4WBWeY= "]]}}, {{}, {}, {RGBColor[1, 0, 0], Thickness[Large], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwV13k4VlsUB2AkV5JkiCRjJBpEhgo/oUK4ESFDhhSVISWRMbOQzFNmvgHh 4ztUKpIS6tKISioXRVLJLanu9td53uecZ+3x7L2WrJuvlQcXBweHHycHx8Jz 5vXKzY17lfVe/Uz32efrolcYJS3DL82L7d2REnLCevBTaIp/LiUO5lkP/l1/ zGE/y6V7Q0oJofGSITL9Tng4pCRWJ6WNx8qteY8SvcH7eEc0Q8oYKVP93F5f Q6Bg3rG9UsoOg58Nm3J7L8Cl/W+r/Nd2SBbJ7xwrSELetkGv1GJ7nI79Yani mQwBxU85wXIOyNulp5HzMwWzv8X/s1B0hpeCu4PY0ktwt6MGfq50g21suOu1 ZRnYyseXVS7liQLr4wJFTbnIiX9TphPnCfVxdmSZaB7mea7WP/nkidDtYp/k TuXhziLPB9xtXjBLbi3P3JAPm18d3B7ux8GnkXXNObcAZ6YjTynQfZCuX6Ul 5VAEx4kQpcc5/uCZr9HlMyhFCtNzs/QDf4j6Fy3x9CpFq5e15nHOUwhkX1mZ klqKteMqRouOnQJronvj1qFSTI4MHlLfcRrha3y6p8+UIWRIOzv9VQD+46Xp +BSW43LfzGJruSC0HRrdffZeJWJL1AaU9gdB9qlDqv5oJXxO+lX/igqCsYbj qmFuGvRWTFrR/g3CH1Wx1oqdNAzte1c0Rw+G1bseFcurNMj09m0r2RwCkVDr GZsSOsofXvGe0gnHW6dOqwAbJpIKJ/XbvcPRpR+uF+/LxGkfZZGcwnA0n+7L O5vAhNxf+1/JcETAdbD34JcWJr5WPozqco1AlMfsGwu5KmSMdvSuUYiEE09x 3qPRKjz1aDx2p+o8xv8rOL/Rrgaz/Xnaje3noWfslfXYuwbiZpE85S/O43pe ZqhTVA0OqlmURi2NwpdUWds1V2ow/HtswOB4FAbhsNaS6womslebtClHQybw zE9axRVwdp1fd5MRg88PBKU5Bmohp+v1raYtBvefel90n6iFUd3f7ZcHYuC/ ZZin9lctYrMkD4UuiUWQirbhH8E68LtTWTpesTAWabvYtrUOYvPvF19XioOk SXuQVHAdNm6yHGmixSPjrWFu4XwdZNRahGrb4nG9fp3yysX1ENFct7PyRTwy q+RaIpfVY0731+WM5QmYKrdW1JCqx11zhu3JwAREJZi9E0A9XLw5u5X3JKLs zrktBWH1SKuur788egG24nbyF77VI6ZOcjiDIwmifpKXS+brcbYxTiBJIgkS us6LryxiwbnF6XiwRRJokUkD9BUsqPQsUbClkuArWy2qtJGFOxOuOYKxySjp rbhr58bCrLJQeJTCRWz5JZcw1MGCkVal8C3diyg90ZJ7tJuFNMPt9Dmbiziz y8b8fS8Lmxzd+k7GXoR00Zv2Zy9YOJrMkncZu4i+5i3fD35mYTJw/eFC61Ts r3pWJri6Ac6D93nPrbwEU53ATl+vBsQMCz/OkbsES68776V8GlA96nSZ2nQJ mSMGXff8GzD35fOWL7svoYx95D1PSAOyl0o4eAVeglvKr8gdKQ3o1TlWY9t/ CZ+Wvfgrpr4BO4v4rLbmpeFrm0rdw6/k/cesHhtaGnyfh3qs+t4AFx35PYGN abiq2T/kNN+AiIEdOtcepiHiwWP9J9yNaBX2VtRflI5lH/zZgaKN0I//Z27v iXRo/el+WqxBfDKjzF0vA6bReRvZJxvRe0tGKmZvBj5w+iYZBzTCRaAmp9Iu AycCjFnPzjYioqoj+b1/BgY5zvu9Cyfx/50N9KVlINt6RdStZBLvoL3ZOcFM ZHHtRDyd2FDqW9rbTFgkcHInDTbiiO1D2cBPmRj77+nnwFeNSD4eZuEwn4ky uT+0Q8ONGEwfosmvzIK3U3W03GgjAkYKDzaaZCF8r1bJmc+NYMZItz6ty8Kd sM0OTn+xIdIpc0E8PBvqpnPDpqpsbH/Z2zR/IRsWalzZ19TYcJ2OGBnOyQZX cGGbogYbV8Tf6DJY2YjX14yf2caGiVfJ9LbRbDy/+NTtiCEbYXxyBxzMcxDc dyGQZsPGezN52cLVudj2QFviViAbev+ORZSvy0WzTXJeWRAbaaHVw0z1XGRy 80fFnCPtX9EobtqbC1+jqdyd4WwkLjeW7juXi41nZXXyY9nY8OjEGu6XuZDc q6zyPIMNH1tq1bGCPPRWtJfG1bJx+1NwkB89D5nUjwPS9WysjMfAmcY83Fta 96yRxcbN5s6cqJ48yHtwGQ2w2Vgu8ULs8nwerB3VFHhb2Kh7+Ue01zEfd1Li vTk62fjqaiKkuaYAayxCWryHyHuDfXL6ygUoGXoyNfyatC9vq2aqVYCv+XOT lm/YGB85bOVsWYC/Shfbbxxh4+XRiLTYmAKUp6Xu6nrPxh3vJqHnHwuQbmsi UDTDRkaQgvDZm5dBM7kd0MlLwfLgBvnz3ZfhV9HyYG4JBYEd6upJ/Zexfpe/ mcpSCvHz+vuLv1zG7WdenbHLKISEO6Z3KhbC6/Q2LiUhCodj0oVXXSzE0VaV WtHVFDQucYpcO1SE+JmMzisqFGRmJW1Hjxfh6mQBb94GCnwO2nlCZ4tQuyN2 KmojheG1vjLHU4uQ8EKgYf9mConNLzdIthVhdnrm73dqFD59eiGHFcV4eDjB /s42CkZiTTtK/IvxdU5MJ3c3hav3jZyazhaj5+bzYMc9FDaFPAp7EFaMGL9n 6VLGFFa9+dj2I7EYLozUg0UmFKaYa42tyophvPnC4XQzCjl6adaLnhQjLu5V 3W4rCh89vL09NEpg+Wzrz3eOJN5P/nHHHSVQPrZZ8rwTBZ/UajfrnSX48S7B XNqZwvS1CVtD8xJojimPHjhE4cvyYwayHiW49dhJ8LorhdmrR8ReZZTgvVuO ud0RChwCLm3WMyVQyBLaM+VDQb/szw6zuRI0VH5j+vlSiNQuogw5SuGm2Gvw hZjLfahKjb8UnGaRQl/9KCxudswSXFuKjjl5iwl/Mp9u9sd79pfCqKBepOkM BRHKStSooRTZz5sv3g6lkOAr7Hnjaimadze4aIZR+K305JpmaynkCvQ8GMTj +TYu6x+Uwiz67LLkcAotkXZVAmOluPdO84dpJAUPc+edAxJleKz2ZFNpNAVq xMvb53wZHraeM+9IpKBSqNw6Fl+G9yc58mUvUCi2nRByvViG067/6IQSJ3ad aN5fUAaxeJ5ItSQKznW+i7ZRZdDyrFLITKbwV0hA7qIPZRiSVWXuSKVgJxzZ kWNZDtuCWpZwJoURgZ4tZbblmPzx3suW2I9PrLDGqRzFN2PL8ojjOGvO3PYq R7f6qWLpLNK/T/3rJiPLsZ1x/ZF8NgXRHtVEsMrBeBFRJppL+nfv3KxJczmG /7nUbUm8of2um/XNcqw1exaeTGx0zXGHV1c5XhRZXVyUR+E0PX4y7W057KId Dn4gfhQ9bDEqVIFKHUuZsgIyngiV69PiFdDgP72vn/jDuTPrfkpVoH/pc9Fl l8n6neLnEFSpgPrROLcA4i2u2vXbDCsg+ylFaGchhVTdVOHkUxUQ7X9j0FFE wXwW/epPKiCo+8gnupT8jyurJVsHK7CtZ3NdHfFDDXFXszcVGGdxxr0ktgiY fn94qgKR/vb/qZVR2DdT/DOTtxK39Jd+HSS2+sIp/V2nEp8jjj4Vq6AgJOTj Hm1YiTSzZJYu8aMtgzRB00oIfVfY5E68/yRLdb1tJQJ3P+GqIbaedjM4eLIS /0n+UNWppHBgqt2jpaISxTN5IiY0CisFVJnG1ZUo8qSLeRE/21gw9YRVif7H h9viiW29Twd+vFWJ+txhvnvEdpNrE6QGK/GcERgFOoWDH2KqIwRoiHuQGCDD oCDB92WaX5SG1MPfJHcQD6531shdTcMWnlx/G2IHL82b9Uo0WArYKicQO46P /vPWgAans5L9k8TOo3u+GgXSsCJZK6WCSdZjvCOVFUqDSW75+DXigAnDTTLR NIjFjM79Q5w0Da+fqTR81go0/kF8fU7rdT2ThszmS2nGVRR2/2KHSNfTsFrP l3IgfvRHXSK5iYbsPaqZPsQfuFVtPO/QkG8wGJ1OLL5cqVtqiAYWQ0prkLh8 RaVn0ggNKh0ndCaIN4us5Zn7QMPRoQt/fi7EXyWz8+l/NMjrMlslq8l+kxdv urCCjvZ0Y20H4j4t3rLvRnRU0UJNe4gdt8fqH9lLx99PKg8MEI/rcA89tqRj 5SIpxVFiDgOOVbXOdLhY7BL8Q7zJ7HuKx1k63K/FSmyqoXDN4syGx2F0GJqq mW4j3mU5c18/ho6MJTdhROx4YJpbMo2OgR4q1J440WU8+FEVHT16g+aRxCvd j4jrs+j4o67FTiQu8Rhh1zTTIVn6YSSduPnY8HR8Bx1OvPGFFcRjp/uP4DUd rGsT5+8S+wce4K75l464tRYaD4l/Bz0pkZikIz3fjfV0IX5478tv3+ngfXBv 2QixUUKnVbUQA8qvAi1/E48+6F1SJc5AasXRuUVXyPkmNNDKkGKgd//HM0uI H+a/30RTZmDoZ+GEMLHf8Od/K1QZqEjUGREnFlKYKyjXZGBu/f76NcS2V/iW lhowUFjafV+ReO6L0O1iYwZudReIqhAXaK0OKrJg4J+KDs3NxMOtKmMFBxlo n/vxQ5P4/OKthfkuDExf8C/YTqxgqmOTd4QBu5+SonrExx6btWf7MxBRNJRg RMwvbhOcdZaBwy0usXuIax2dtmSGMRAe/8HelNiqxGM8PZqBXT113ObEM/96 F6UlMrCGfzz2b+Is5TMHLqUycD/+zrAlsbZv2LLULAaYCBayJg79nnIuuZSB z1z6v22JZXSz1ZLoDPi1UM32xLcji94nXmFgydInex2ID9+lFSc0MnCquKvJ kZhnaZ1t/DUGVnzsmXcipv/dLBDXysAemWWrDxHvzWjtiLnLQLfSDSEX4qn+ zpDoHgZmGgVGFpy6pk896hEDq9TVL7oSq7kNfIjsZ+BJn4OIG/HTyjclEUMM eERcPbXgsxPv7cJHGPg2FVKzYAnVL8vDPjDwKeVZ24JbTs/dDZlmwDJ9tm7B zle5ws7NMvBjmv/cgjl+82kEzzPwn7OJzILLDIQnz3IxMXTgRfFC+7vjVpcF 8jIhKPplfqF/493yB88IMCGU27J1wYmCG1YEiDDxuMLLeGF8G2y2dp6SYILz 9jpt54X9lKsT7i/DhJW2AvfCfJwcMtI8qchEv1hq9cL8icibf/TdwITh1qwt B4mpozblPmpMaCt6pNsR21U7OXhrM5G1V/nRgYX9Ne0hdEKPia57QlML64Xg MxFepkzc3Mx5cx/x25thWp77mKjQd/G3II5eFDd15AAT275mcJsRdyZlOx52 Y+KS0Ob23Qv7q69I2N2TicMvJz4ZEi9bSe9y9WEinWvjT/2F/VTUrH0omIkC 9njNwv58UT8gcjCNiZX9n+I3ELMkFpUP5jDB53nBXok4PmqDukMRE1eTDnCv Jda0Cbd0rGaCN9PivQRx2ve1Kc53SfvZwbM8xF6uFmte9zDR+cCkkJNYvyuw +tBjJvy2jMnOk//1Y35Xl8sw+T7wwI1pYmP4/eU+x4SZU6hpP7E0PTfrHUcV YKn5rI94VrBd4fBfVVhhbIpu4rK3okYeIlWoTDZi3lg4L2KuRxzdVIWrH1vG i4kbe3jmjrtVIfxBk6or8QUN1YRJzyroPtKj2xG7FdqLe/tW4ZcuL8c+4uV+ 1Zo+IVVwPSxsqUd8TNjqlF9WFdzXPQ1dRSx78PLk6S4Sr/bSui5yfn6/fffc t94qJJmcb7pF/FBlmu/M8yp02Dsrs4lDfhmsDxypguKac1eLiPuLxz2Cfleh M5cZeYo4ZUz9dahaNX41734puvB92ljcRe1qHO2XDOMj9tLNVy3Rq0bpvWu8 f8h9YJTOdf6OaTVqee/1jxHP6fWtXepejZtyR482Ex/N8jmWk16NN2aBdjbE +rsY31gz1fhBZ/8dTu6vTdOOhXfmqjE4b2Zwknh1vuCeZxw1kNu6QdadeHY6 MOcHfw26uNaX7yauLti9Q1+hBhoP3rXxE6+aeRfxwKYGwp2b/TPJffqlVIp/ nKpBEc96i1xyX4v4f006d6MGCuyJvDhizZ2dy5bfqcFMP8+TAOLg1yeXa/bV 4Jg7e6kVMZdkh1D0RA1sVb+mLyEWyjy+SkbmCkYtTkoHkHxALa5Z0S7hCm5u fflMj+QX/setdnY61KLhxO/vJSR/cT8V7hQeUodbd6s3j5H86d+vl7t1deuh zlOzlTuHwre5YV0tARaquFc81bxEYcjoxJv9fSzkm/c2ZZD8dMu4Oi0/tQFe 964EvYtayH9kTkq5NEIrXHoqKIRCT5j1iTuypC7TiJ48HbAwvprjFV/ZWKY4 8ueON4W7Nw2S69sovBvYfFiZ5O+WFjLDw5FNeL8xJWgJyfePHZbT2mvVjLGt FTp7bEl+cuPErX6Rqzg0f9+Qex+FJt+vXpceX8VlwbGKt6QeKaEXiseUXkP4 aY1l8jvJ+Namfc93v47a+8oXR0l906DIfPlxawvaBpN/8pP65+Vxvi9u31ug LsFMa1Km4MtHW7+o+QbUXaTsY+XJebvZ02Mo7ib2jfjUNJP6KzH75KOXJrdQ EbJlzFeE1Aft/8guFWiFXmrIYCI/Be6x6OO6Aa2Q6v5xqoub9H/DkHnk01aM L36pdfEXG2JsE9Zb3TY4K2Q+afrGhuoh+1qbojZMDwzVeEyx8VsjTnfodxvO i+Vaa4+xIbzvnnn0kdu4LLDitQ+pTzMvVM3uuHcb8ZYFLOV+Npz5SmVXqLbj i0bfCdNeNswXPWSsIb7td/+cCbHO/I8tysSxVW2JxsQSU5YGhsQfZFj03cTP +zjdA4jll6aPGBDvy3UtHyC2f2XtuIPYUEl2XemWdjw92793A7GarHntFWIl Vu9BFWI5iSCt68S+E51eysQc/H17nhAPOF2NUyJu+RThyaPWDmmDvPa1xJpN w4xjxH68jjvWECvU8asFEi/eaW0qSSzC0L4WRZwSZGa/mvhLXmpXAXHIB53A VcS1YfoTD4m7u9c0iBIXBp449YKYk3vlbRHiFL+cn2PEKjoCfcLEJ9yml3Kq t8Ox+vfUCmIHB8mMZcTuI7O/BIlNrY0lJYidJD/xL3ib+elyRWJz67HVy4mV dhdvUCdWTXqtLED8P6/5HkA= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesLabel->{ FormBox[ StyleBox["\"\[Eta]\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"v(\[Eta])\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm]}, AxesOrigin->{0, 0}, ImageSize->{400, 300}, PlotLabel->FormBox[ StyleBox[ "\"Numerical and expansion solutions\\n\[Epsilon] = 0.1\"", Bold, RGBColor[0, 0, 1], Large, StripOnInput -> False], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, TicksStyle->Directive[ RGBColor[0.6, 0.4, 0.2], 14, Bold]], {640., -160.}, ImageScaled[{0.5, 0.5}], {400, 300}]}, {InsetBox[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c8V18YB3DRlChUSEihVCiFQh+i4VcqEjKSVfbKKkqy957fYVP2vCpp qlQaMqJklKLMhITqd75/fV/v1/fec899znPOfZ4NFs661uxsbGxBC9jYWL+T PWtkq48I7ZNWX/75uPPZfcwAUTEu0Zl9e56dWDfLuw8uErWh70SWQmPgXLXu P22cnmZXrRcRgNLaf1V2HaZ41b15bbnIZsi9ffbAN8IRS1uUA2+IKCEiv03g waQvJLQf780XOYzrcT7uci0ROPvouC6t5zAsZxiM/IxIpO95bxubqYVoTbnT fPZR4JYcS70kfgQbPub+a/sbjem/Ar+OSR6DqUSCMu+KOFgaUp1za3Rxluku FbgyEbs4OZNzRQwRrmXNfeZOGlJD+3JUQgzheLXeMlQoHfOLb1W0jhlijcp+ SRnvdDRw2Lxc+OA0NL0CWkd30HDqz+OF1pbGaLvQsOB0Bh2e4/4XJK6fQcTA YJyLRQZMhnw3t6Ra4LuV8HnZQ9mILrSRFX1pgYotPGH5Ttm4b6unYL/AEqIV HPxfk7KxaXCrJoedJYr4tqXc+5yN4f73ZvLKVnh1cWVlv28OfLuVUhI+WmMu hmfX3rxcMJonF+mJ2+KOjdVfnjf5CM7a2bn5pC30byVwT47mw8nVpfhPgC1+ FST5la0owL5Vw7oFX2zxl6FoXPJfAbpPfM6YvW6HoPTj154/LIDYm+Y9WbIO uLS74S5VdB25r0odR1WcMYIPB2rMCxHJHFZ75OiMmtsez776FMLdSZo/lekM c12BpqmkQogvOflRjM0FnMo+C0ueFeJn/quA5+Yu0M/9qBwkW4TEr4/frJdw xeKsgZULp4rQZl1t11Dkhvrz871mNiWY7khXqn7khkHT9UMSV0ogcNR/ce4H N1zo+vvxdUIJjHYeyw5YfgHaOpKL3twtQe/fgc799heQLzfHGcRXiqGUdVoP pN1hcsk0sKe2FAueX5O6e8MDzdd+F+4fKYO4qu1UyQMPVDzkx9N/ZdAsP/6I 0emBCJhPCy4rR3CysNnlZZ7Q7YvisFxXDi5LKlnF1hNN/R1bbVCOtfPfFtVt 9oLuvgH5I0Hl2C6j019b4I3qt86iHUsrILbzDm/ZA2/Q3E+ssFhVAX4FKfX8 D97gD1Ba1CtYgVnVP4xEnouwcpo7cVO6Ak+0bxi4el2E7d7RpV1HKnDWccEL 6UOXIBGS5PcnogLxxRUVjK8++C/sZhn/wkoElQv3JrL5Yi+32QvV5ZXwrg7h jhTyhcvag+9NeCtx5o6p/aVjvjj1U2HxZbFKbG1aJmFA+aLp4tFFh1Qq0TBk nroy+DKslkSuXuFWiWlpXr8ACT9Ixz8Tq2+vhKZiPt89VT+4xncXGXRVIl5j 7/XZU37Y9ajsw/e+SsiYWDS7BvuhpyFJe264EuejKjeeHfDDm7JOz8fsVRj2 2mLF1LuKKePIh4u3V+HM+2dLfdb4o/OazSlf3yoE9fK1pIr7Qz3236CKfxWK v5oyKBl/OPOPqfwKqsLsxI8dEwf9kbjCWvN0TBVSlgsZ23r5QzA9oqAlqwpv VOxKDDr8MdZ6y/H64yqoZ3Dq7kq/hvUS/c5LllXjzUhy06mCayjqvPnTakU1 zqpsPORVfQ1lEY4qd1ZV42qnssrtV9cwc/y8qqFQNe7zOUqqcQQgXk62/+DW aqiFvp494hCAbZwFvxcdJXZNzLHcFwiGt9SgZhgZ/56YSNCRQHy8sPHX90gy PndJar5hIE5k572MiCXjFz2O+uYWiLlgn+H6FDL+l2kv54JApE9IlPfnkfGM Th/1WRkEpsOeA/sfEGuITMV/CkLyTR89x8lqnDN4tcFrLAgm2/fq2/+qRpT9 lWPG80G44dKwwXq2Gu8Tugs2rgmGn+cj2aNsNfDoZxpVawVjlH/u/uDyGhQG id5vKw/G9TSjg2fFa8DfKBYh4BeC4y9/HHc8WoO9XW9q5yNCoPL15JfRYzUw H7/a35saAuXf+iMOOjUoFehTvVEZghQhfrsz+jXQss0a3/M1BFP5CtfXnq3B FU5xfWPtUNA/fM0dcKvBt6MbNzDXheFG9lpZ4eQa7PsycDVXKgyDlxt3r0qt Qfzl4t5C+TCITvFkc6ST55fuzqw9EoamtmW3ehk1COc5LNrsEwaHXcpqvnk1 2PbWYf3CrjAoLdtYrlxdAycDStCOHg622y4Lfr6uwcOxSxddrodjbjRViNZc gzWh6PSsJv+37P+j1lKDuzcbUwOawvEqQFw6uL0GPEIf1jLmwyEYru483VWD 8q5/q9+YRGCLwpWVrt9q8NNci1dhfSRmt3yc6WOjUL7/hLiadCR+sPM/OMdO wWmjwc7/FCNR3lui942DwmC/le4ZnUhsUj73bWAxha7zV+ODgyKx+qydwAsu Cg2OtbzvRiLRsbxx6TYBCokXJfi870ahbmY1n8N2CjpG2zZeexEFH48ljWUy FLiV5eUjO6LQ5qOU80OWQui82snMiSj8rKl+57yTgq+fSUKjZDSinfsD9BUp WAUl8AnGRIM7hGfilRqF3XEL+G+bxWDH2Vc7fXUpiE0LG3y1j0HlH96rXicp cBorpfN6x0D05BtXVz0KvZucxexjY6BRt/U/c30K4Te7tgk/iIFHSg77DiMK Y2MfxLEqFnnrG+XizSlorq1VznKLRc+4UtM5Zwq3nmma1nrHojXPe3aPCwUZ 37dXXl6JheeY0QIuVwqCfSMPfofHojqOO6PYjcJo4abDujmxKDlsrdnrQSF1 X7weR2ssTu62C+X1pTBi7ehovTsOVmrZBiUhZLw5rkET5TgcMpibNwol8Y8t ttBTj8OvjtqKJWEUxm8PGWhox2HUsE/7TDiFCR67/Rus4xA8nuXCFkVh+ta5 tR8T49B4XcFUMJ4CG/fZB3qTceiPTanPo1FQy/mnfHQ2Dr6bLa8q0in4K2VQ GmzxMONq8GwkZrfsLtrJFY8dUy/YBxkUFt00SV65KR5zlzlq12eSeFqctm86 GY9Rob0WVrkU+Cnd1ZpV8eDenPrHqphCmDOfTf2teMjF6ll+I/67ufW2wv14 yIppzDmUkPyhnTq75WU8+N6oP3EtpXDH37CIeyAeKYIJg67lFKy1z6h3CiXg Xe6EiXY1Barf1tHpWgKqUqNKvOsobGVK3x8ITcD2tPUXvxBnGgzxmsckoPPX nxSdO2Q9nzvcPElPwI8W9Rapegpnyp059lAJ2LGp1bDpLoUlvh5pHN8TELiC 32b6AQVDPv/HqTqJ+HIotL31KYV+7qYdOQaJ2Li1+Z1UIwUXzrXMEtNEuG50 ML5EHLKgxPOhbSKc93YMrX9G5jfWITXsn4iVlZfVzZ5TWN0kF45Kcv3hHLxo ovA2sPfYV94kHFoTFHi0mczn6ta6cYEkfJY6/z2W+LuPp9ScSBJ+zLb2txKz X+BiW7k1CfsdaGnGbynsMFeq2KORhKatjbxWLRRiVWP5oi4kYUXGwUfmbRS0 p9Eh35oEO4user5Osp/WFAvff5+ET6/tHE8Qv9otYH60LwnSx75WRBIf8xj/ ZjVK3KA8x/GewonJzLmkpcm4F2yUMUKsO7FAdEYlGYIjCiUlXRT0Rx9Z38lL xpWPnB/7eyis4ZYrPFycjPurhFRX91Jo304fba1MRu3baI0DxAaO7l4j98j9 69wP5BIbDm8KE3mfjJmCui1n+igYfQ8qvsqdApuGko4Hn0g8vh76qemVAof0 5J9HvpB4DD6OrbycAv5gHW1XYo8hDRmxwBTECQecSSaOHIftXGwKnpfNX+8h rptV7KkoTMFpRenvTl8pCPBsfiHSnYLkqRceVwco5K7Kt4nsT8HGfZ2eWcSy /JsWz35PQf6g6e6HxAcFxdTbfpH734kPsw9ScN8oUBuxKhXzB35o+RM3Ky7N mdFMRcIdnVVu3yiY7A1WO3ckFfupjlUxxIMqC7tbdFKxqm9bWxEx2342wbIz qfioGp/XTyxzdCba2jsV1L4Cz5PfSX6eHbz0tigV9yuKNkkOkfMlrFG3mDcN 8fftp7OGKXx9+WZZkUAa9E8/9KKIw3g7798QScOLcsum58SvaN9kCqTTMHTA bHyC2KCUc3n2/jT8KJPcoj5Cwa7l6KMUN1LH3zaOaiPmEjh1Kdk7DRdkHpoM EJeZmO5IupKG0GXt7L+JJ784ZsSHpyEoo7tl3SiFyzPRPlHZaaB+mMWYEceu b5YPeJuGi+dCaT3EOy06v/t3pIFj35axUeK2/L6sq91pOCHxXvgvsZDcBM+V 72kwfKm5RHiMQs5+vmFv9nTcZ6wR0Semzp/KddqZjtI/u3weERsWmxo7KqXj zlBA8Bvi2XFrXod96VhrddfpIzEueV61/S8dlZXM9mnixsgUEyuLdISyFS7d PE7hQ0Unv1F8Otil2oQCiSuFOHLfp6bjWMb7nzHEoQHb5I0z0nH33618GrHC KT8dk+J0nHvyMb2SOH5mU/SZJ+lAKP1hN/FhuCyxnE1HxjMeyP2gIHo9Lfkz Gw35raOv9hBPr3wkYbWEBoU/C1U0iHM+rda05qfh6GRJ6Sniv0F1V8/L0KAp WzfnTVzdtHjW3oKGhMO1xreII3bLhQ3b0DA55NF2n9iCeVrA0ZmGm2vUZBuJ eVyKFZx8aThTwgxoJ7bj073gkkwDFSFU/YNY3deH/QedhldrXuycIRb4khvn mkPDdr/2+L/ET6hfZW7lNFTE5/3inKCwwYgx7P6chvOutw3FiWcePvGZekPD sYR3X6WIX20d5/R8R4PZINNgO7Hvn/1bvPppGGtv6VMk7sgctL74lwZzNwfG EeKyZbxTvxfSIfve5cAJ4mA35cBLy+lY9sKpWY9YXjM620eAjtaJv0mmxNED 8j2Xd9JhtmRxuyNr/PiBkBglOo6d97ZwJbZVpcll7aODQzr7nTuxZgL7tYb/ 6HCSyfX1Id65j5JuP0HHwHB98RVi0W+2LQP6dBzYwPXEn3h2X/Om5ZZ0/GIr rw4hHvwW+FLYlo7GB3vDw4nbEpU8ZZzpgLCVVhRx+feMpzo+dAg+mw+MJz6f 7GSXmkCHi+z2SRqxnro4X2EaHae/JwgyifcPt9XVkb72U6Ljlkxikf2qK3qK 6Gj5/HlpLjHXyHjNeAUdtxg1HXnEv1Nyz7DfpEPFzSqhgLh1ZHm5RAMdQsmP nhUSP0y9Z6j4nI6fs9cPFLPiqXFhgdYbOs7ntRWXENNHJQuN2unYLWb1r5Q4 PO29rkMXHSLTTqrlxN6a0XOXP9HRU7HyfAWx9Zh6bswgHXu7LX0ridUO3Jiq nKSDqgq1qyaWGTdhNszSoe8Wo1FDvI628lA7GwNRTRVLKeKlBxvGBhYzIKjN eZvl6XGv1N9cDNRdqTKoJe6nbVVfzseA3PDTPpabD/Z8ExZkYI+YheFN4rs/ 4uNlRBlIyqPXsVxMP6isJsHAwiXxy28Rpx+a/ayzlYEDr00OsxwyURJpuYOB NWFr3Vh2Z5jv9lBkQOleVyjLFodXdwerMmA//ySS5RM/G4NTNRhweDF+meV9 TF/ZQi0G5il3E5a3acl11B1n4L2W42aWBSc/X315ioEn3FN9rPkszkjZ0mPM gF+sZBjLk1pH3o6bM/DotLAIy58m/15it2Hg5NR4Juv93mRUbuR3YmBs5O4q lu/+d65Jwp0BvVeZLqz4FE0JeiheYmCLZFk9K56pmS/Xa11l4Mq7PzOseAcf 8X9iFMzAdHCWOMvu07ucHSIZaO8t3VtFbJ41uPZKPANmcXvVWeul8uu4bRaT AZ8CUSHW+kpnc/BW5TKQYJ09zFr/tdq1txsKGTi7dbqElR8T2SJcgxQDUn6W f1j5xO/2M9KnnoHzCvP2N4gV1BtX8DQw8Jz/xRNW/l3qceVRaGbAzcddnZWv 9NKDsc/eMTDBCDDPZr3f5XWrTLsZ4BLe6cTKb3bhx7yBQwwEmLVr04k3DaUl rJ1gYN09tg3pxAdvO/EXzTDQUCrfl8LKT0OBNW8XMXHbTXhLAjFvkr2gmBgT 3vOdnaHEu6zU0qskmXh+ZItAMLG+/Op1h7YzIZB4UjOAlR/Nd4Wd9jIhopl9 7jKxODev2B09JpbHLW13Ye3/kJuShmFMqBnOe7LOFz39qIKhGCYkTY9nsM4f TwmLzX7JTPRuE689Snz70XLp/BwmhHpKazRZ+5fNbPtkPROxi++NyxPrXly0 K3aCCbOUTBce1vocfl+98Td5/pE1NNZ5mby2bHftPyY+LDelFhG/rzFU7ObK gF5W2b051nk9UbR3m1QGrFPyRQeI3ex11RuNM7Ai7KlkHbHZ+j3rVC0ycCny 9bUa4qOvRacqbDJQZeHSXEYsJT9yneaRgXKe5wdzibtmQ1Y6x2Tg96b5hEji Q+H1PasfZWB6kc4zI+JoPf57O1ZnYnCDnfAo+T4FlizZ5iCQierVvaNfiX0W z6Xmr8uE/QI+qofY5maf2zrxTDiJD4s3E2sIl0kuks1EjSKvdxXxzGet6I7D mbi2xnK9J7HlBT9TP99MPN3+uP4n+b6eG1E0uOaXiZyhb+1DxDbnx08EXcvE i0ufBj4TOxiba0aEZkJiifuPFmJ3DY2tKYmZUC5bl1tFHMi35HdpcSaipxNi XIlzq6ITu7sy0SDTfW+A1AdffjJeqKpm4cY6/Yh7pP6Ymu1VVeTOxpRVWscY qY+6NR36TjZn43CGh8MSUn/tGJQvoMXmgHkhXPRPP8kvXjFXkbO5WLxy5GcY qSebrug5NGzIg/0q3fuK3az9UGKf9zMP3xNEDoWTevbJ3f1RFQ/yoRUTWd/T TvrPY2K9vf4F4Ml0cLQn9bSdlbjiEd3raL7Ck5/3moJxvcO9Dv4boEsuLFlH 6vda55+2cS03YCUnX5FJ6v+s60yBoOxC8h47br9rIPHbFD9DsyyC1Jd5o2Ok n6iSLOwa2VWM4KbOP16k/+iy55ywmCnGis8jSp9uUXDmLNjCcbMEOrsUNM5Q pL6StbHuDimFjmIeX3Ql2U8prm+7tMqg6ftB9B/pjzgfvd6wnLscw5OU/KYi CgsHAu1VPcqRXXQvxbiAzH9bt7Z/WzmK+qssWnPIeVGjVflJtQLHizLcFpB+ Tc7sdNmpjAo8OGU07Ez6u7+7Q1S7/1Zg6sav++OpFPhOPNUOPFeJI8w8Nskk CkkRRdPKTyvReH4RjR5H6nPO7A2r5KogH/n81lPSX2pzvLqxnni8MlaTZZX5 3zukicM/6L9+Qiw0qrNfg1h/5+f+x8TvmhdYehBrT8/xNBCfSDPP7SSufbf9 3H1ijc0bpLJ3VOEyWwLvLeKdG7TLSok/WZxm3CQWF7qoWEcs8VR0M8tsXM2H WonVk4pVa4nvjF21WbyzCp2HntjUECvU9t6wIw5aPHu3gliinGunF/Hd4Pta LPPfULodQNy2NKS1nHgiPfY5nTidl/97GXHZFbWhV8TXVGRWlxIzvRwufCDO ezGZUUIc7ZI6N0Ccb1InzbKDxfjyBfJVQOBhtWJiY2PhxBXE74R4XhQR/6d3 WFiI+GhV2ymW92i750oSZ2jTewuJNx/M3CZP/PqbhT3L/wNRlRAE "]]}}, {{}, {}, {RGBColor[1, 0, 0], Thickness[Large], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwV13c41e8bB3AJFVKhrEJChYQGMt7EL1uRlVEhZWQkIWSUnb0559hlbz4N be2kkEJ9pVIpM1nR+D3nr3O9rnOd+zyf+36e53PfG528zV1YWVhYYpewsDA/ p9+v295sJKw58eeJ1wHvo5r5F8TEucXmNbVyp9pU+DThI3Ul9o3ocqyOea7u +88Eh2ZZNW6KCgKOklZBvQ7oGNgiUC+6Bf4XDNUjL3piebdaZIWoCko/OSne nw6BlMmDPZdF9WFX0qeo2H0RR9v2m9Pe64P3VfaxsoIE5Kn2u6UUGuAKVS7K 75EIHumJnCAJI9wrPhvz+m8SZv8KzplKm4Ln72sF3pWpcLah+hbXmSPVNlQ6 cnUGdnJyZpWK2mB0ZYGzw41c5MR+KFGPscEVTfbCGOE8/Oa41vBqwgbL7NVM tgXm4f5S1+dsdw+hpWr8w5giDZZ/HrC5ONshVOkor00BHf6TEaelyg9jibOf spdTAexHQrZ05zjB5BwPj7xeMZIqXbeLPXeCw7NywUtexbjjZrHbY4kz9DOH k4YyiyE5LKu71N0Zf4vlZ29+KsboUP+RHWrHUNTyQvRTSAlCBlSy0/9zwQ4H t0mVS6VgdE6zW0i4YdWNBj6el5cRXaTUt+WgGyLf9UlOjV+G1ymf6j8X3BC0 NCe5ZmUZNNeMmpd9dsM29Vf7qgzLMHDgU8FCuTucXrCyPL5XBvGXnapF20/i F6tKf1NVOUo7aj3H1b0hUD0a1OBYiYT8Ua02T28YyCxOfgyuhJ+XDH9Ovjd0 DAe//cishMSyg/+Js/ggIPa9YMWTSvy83HHhqaMPVi7m74/YXoWMLw9ebpA6 Bbv8yfB/01XocWl2v1/li38Bw162rjWY7c1TaW7zBVfABjPx0BoIGkdwlL71 hfWRaN6n6TWwVTItvsB1GizWnm1PbtVg8O/Xvr0ep3G76+7Dc3y1GMkWMbgr 4wfRmcJlb67UYsnT85tvVZzBNw52drWxOkhouM3U3D2DHZktZ2//q4Nu/f42 Rt8ZHC+8+HftinpEZ60/cm6FPxyu+vYcFqkHtzOVpe7mj9hxt2Bn1EPg9zf2 1i0B6F/37+r/ouqxTd5s6EpZIE7dCCjvWt4AcaUbvHV3A6H230Sc/ZoG8O/e rH35bSCOhIl49ws1YEHjDyNj1VlI3jCOaZRpwEOTCutTAWdxVlv7Zo9RA456 LnkmoxeEFH6O47MXG5BW3dDA+BKMS9E2divZGhFVv34wgyUE3+9xOe7makRg cwxPgnAIXP8ctrLkbcThGw4eQaYhGLeZ1Dsj3gjZ9hVS1lQIkpyfPNVUb8T9 Ecec1dHnILBnRIHNtxGzMrxhF6TCEKY8fKfpdSN0lS/z3dYIQw6Pt5Lpu0ak 6ewpX7AMA+PJCr0PHxohb+/UeSo6DJem74T9GG3EicTGTUe/hqE2zU2llbUJ owFbj+VbhMO/Q3F4Ua4Jh/ufLA9eF4H4X2wffEKaEDXI150jEQFjGpe9YkQT qr84MCj5CJjtuZM5EtWEhakfilP7IqDYTbmYJDchm0vYzi0gAivmJA49KmrC S3X3Gute8vtjGv60B03QLuA035l3Ho8lNt/4tbwZL8ey2i3LzsPq3pyU9cpm HFXfpBfQfB4/Q2+Y165pRnifmvr1jvNQkdQRNBRuxh0+T2mtpRfQbR64T0W2 GVqxLxaMTl5Ade6holkj4lMZJc6akfhy4E3gzjgS/7a4aJRRJPQTxY/1J5D4 PDU5l20i0dbLsTY4hcSvepD4zTcS9inCn6uzSfzPswHeZZEYDJDl7L5E4tke Mg5eHYUPfJyXtt8l1hGdSfsYhWcKakttp5tx3LpjY8BEFEr3V8xZzzUj0SPU 1O53FNQkhhrNFprRnz5QtmldNFz7BTNVWFpwZijfttkgGv7XZSpfcbWgMkrs Tk99NCrbHDiNJFrA/1j8omBYDDJu9VZbGbdgz7uXV35fjIHsp7XKvaYtcJwM HxrMicGrpcY7rcxaUCv4QaOiMQZZ23RpelYtMHArmlT9EoPHC/tLWI62IJRT wsrOJBacW50fvPBtwTfjTRvzReLwiN/YmDWrBZqfv4aXbo5DJM+oxlx2C9LO VQ9W7ohDVq1p1rdc8v+1uwqvGMXB7O292IeMFsSv0hfrDI7D00P7Oh0vtUCu 6+QGtndx+Nz19Il4cwu8rCkhd3o8tlQEG7x+0YJ7E0FnfcrjEZEbsDe0swXr YtHn3xyPD8EZ7JLdLbh19XHOhfZ4nDiTPeP6ugWrhN8KMH7HgxF591nvuxbU v/u39qX9RfwQfnrD/FsLfjoa8O7ekIBLuqp291go1O89IKElk4D/FQyx6rFS 8NpkrWSonADhrZ1+T5ZSGB46Zn7YLAFPIh+3PeKg8O5EeFp0VAK4LK87V3JT uO95hffNWAIOLQoYcgpSyDgrxRd4KxEWwiee62+jYGYrt+n8s0RIldPcE+Qp 8Kjt2JHQm4guF4FtHdspxP7WOlg4lYiCXXvljJUohITZpz+WTsJWVVk7JWUK x6LS+YSSk2Bg1lNToUVhV+oS/utHkhGYX8NhaU5BfHa99RePZARcN1Y/cJAC p51KHm9gMs5dKFxnaEFhUNJb3CMlGYZzQXdUrSjEX30nt/5uMv5nwi28wpbC xMRbCaxJwU75Ky5ujhR0Ba6oFfmmoIMrdlrNm8K1J7oOVwJTsKyonm2VDwX5 kK7Q56EpWGxlHR8kFvowdvdXfArMQqXNI3wpjFdK6puXpGBzBF988xkKOZpp FktfpeDi9Ml/n4MpjLl4errsSsVo3bme0BgSb5F72F4tFeJZhdZysST/KdVO FtqpeG+y/Vsv8eT1EWsdk1QImx7B9ngKU6vc9250SYXsCYe+lwkUZq8dF/gv IxXNoiFPhlMpsPAcvWsxnQq5nVTQaRoFrZJ/asYLqaAKUyTY6RQiVAooHZY0 fOGN/JNJzOo8UKXEnYaD8R0HWhgU2K/aZ62WTEOZpEXc9wKST6dDHu0H06BR /ltcoZQCP2W+VrcpDTpt4oXy1RTivPlcb15LwzbL00ONxH+3vLq++04aAlLd 7HbXkP1Dszy69XkatDqbP++ppXAjwqaK52saWIry4vfUU3AxOazdJ5yOo5Ym y9Y2U6CG3Dy9zqfD58gdbs1WCrL5Mne+xqajeT6soZK40HqE1zE5HWPXWyrW 3SD1fHry6kF6Om6ZaueMEh+u916qSqXjuMHtmJRbFJaFnMld+j0dex4dDr52 l4INX8SDHLMMdGf0t2c+ojDE065YYp2BSW626mFiH06B/BoH4pwRbrXHFGKW 1Pjfc8vAyu/nrQaIqYnezaMRGfi3NVpY7CmFte0K8WjMwLf5rsm4dgpdkYOm X3gzQWvoYVvRSdYTLts6KZiJja98DEyIvwf7b14UzYSe/TWJVGLW09wsq2Uz IXc+NFOgi4Kio0qDqk4mlMU+x4t1U0jRSOFLPJ0Juy7Iru+hYDKL3h2vMhFh NfniWS85T+uq19/pz0S0Lp/18j4KHbsEHY0/ZIKHbc1pXWLTM5Pfjo1nQsFi 1qOV+MB04WLm8iwcvlZ1qrSfgvnUErF59SzQlZWNnd9RsBpvc7lxKQtXSyJW 57ynsI5HoVK/Ogt6Ww30HhO/3kYff9WYhcxrKpLzxNaefgFjt7OwXTm2y2qQ 5HdUMk60Pwt8Vy/yrP5AwfZ7VHU4TzZ+JbF5+34k+fii91M3IBuzbIc5FoZI PoYfpDSey8YeBwlVsc8UzozoyItHZuNJqcEmXeKESbgtpmTDTcRMLJG4dUH5 fUNlNhwM1t0V+UJBcNWWZ6ID2Sg5e5BF7iuF0jWXXROGshE/uvqNMfF2fkmO he/Z+Nqw08OTeJ+QuHbPXDb4ZESf1xD7bRK8cnFNDiLnXCJkhyl0Ki8vmdfN gQhF+yX8jYL9nmit40Y5yEy++VKZeFidbaDbLAf2+U/cLYhZ9rII1R3OgdDY 5HACsbzxfJJLYA5m/2StWySOPzoc1FVFvo8qCm3/Tu6XuMfm1by5OHBM5vL/ Ril8ef5yRZVgLi6/p/4eIo7j7btTIZoLH6dEGS/iDto3+TKZXKQY/f2dSWxd y8lVvDcX/HJb0j8Ru3cbt2X75uK2jW+L/xgFbkHLoKzAXHxumbWPJa6zd1DM DM0Fe5ra21zi6c+eBWnxuTj0qN/+BvG5+aTgxOJctBjKBf0jTtnQueNCVy5+ n9lqGDpOQcmp73tEby4mOln9E4l7Ln8oCh/IRd7ZjmA6sbDC1KrQ77kw0GJZ d524ZC/faCBrHpxYheJ/ElMnLEu9lPKg0ViXd2SC7I9qBztPlTy8nREMOUm8 MOnCe1IzD+t+Hd9zlhhB/uFuhnkwqnYxTSN+nJBtf8wpD2IbX/beI37b0Mdv m5aHYx4NjA2TFBqFl5b25+TBxb/dYCtx7AW5HXYFeTDf0PViJ/FuyzAz++o8 zPmfcjciTpuXTDr8MA+ad2++9yd2czTd8L49D/+JjR2NINZ6GlB9pDsPlULl Ny8Sj9GePj06mId7rAmchcT68FnmvJAH993xcw+Jxcpzsz6x0CA2mWX7knh2 dZvUsWU0xHreyusjLvm4VteFn4ZmafGmEeK/Ua3hJ+RpMJ7yMeD5QaG5nWPB w4kGtvURu0yIL+5SiBt1pWEi8Wy4BbFT/iFBT28aUjMDq+yIV/lU7/YKocEi Vb3Yjdidz/y0TxYN+wdrBCKJtUOCWX/QabjmUHsinljwc2nqqRIa3GP5clOI H1Jzdb71NDw/RRXSiTfaMkb9ntKwy29Rr4l4/t7D4JmXNHwcvF12lbhDdpLT /w0NwYIq328Sh/zZuzVgiIbxLV8FHhP3Fg67nP1LQ6FMpfBb4roVvDO/2Ojo /S8w4z1xtK9aZBAXHfc2qU99It6hm1QcLEiHQ7W67Shx0tcd788p0THWcGRw kRk/7WtMsgodbw1UtP8Ru2nQFIo06chKqYpnnSLnJ531/H1DOiIH375ZTqyk Scm8PkBHq2PPWy5isW9u3V+t6FA6//ExD/GCZqcklzMdjA+1h/mJh79FPl/v Rsf0kYplAsQ9GSr+8t50NPzelidEXP+94JFZMB2pboYhosQnsrzcc9LpeFX3 S3kzsYW2BF9lLh1Fz70VthLvHe1pbSVzcOIXSz5ZYtG9GivfV5H4uz7myBNz j022TDbQsW/zHTUF4l/ZpYdZr9LxNO7cE0XiV2Nc9VL36SiIZ7u8k/hezm0b 5ad00s+yzewirtM5vcTgJR2NJWbblYnp49KVtq/pCBXjsFQhjs/tNz/5jo5r yzWOqxIH6iYtnvtIx0aeNc57iF0mtEuTh+mob6UbqRGb580YF43T0Rm0IKZO rPW/ipnGaTqi03QHmZaftM+/v0DyvTkzQYNYhLZa7zULA3fVOaQ0iZfvuz/x lYOBwcaGCqZnJwNyfnEzsN6gQRjEQzRZbS4+BngZooFMd+57/229EAPssnz3 mL71Iy1NXowBDtPyeaar6fvUtKQYENOaE9EiztNb+GQmy0C4sJAc0zFTNQnO igyU90hvZdqP4bjrjDIDyQaqfEw76a8diNZgoGeb23dmvAM/H0fn6DDwWehF LdOa+SHbKw0Y2Bx14SjTcgYKva37GZB4lP+PuX6h6U/hzy0ZqBBQTWCaoyB7 63s7sr5kdw6mpw2MuiYdGdgobeTFzMfH6b9BrK5kPdRUGzNfLwsaN/F7MaC+ GLiM6VuGx9ul/BhIS55RYea7akbojHIQA8WTYTbMekQbRTy0jSb58BNxYtbP b3an98kEBqbmbI2Z9XUsGhYITWNgAze71G5i9bn9bkX5DOQ6TBftIJYpXsrb VMpAK/eJfUrEAiZXrt+vZGC5QkEfc39NFYtyD1MMVPtea99GzO/7MyH4Jnke Ce0VcsS7tR+vXHWfAY3FeUUZ4qD3p1bt7mQgtsNVX5q5v2r3pTx5Q+qrbLNb kvk850TWOAwwwF35ZbUEMev6B7yRIwwYvDVJ2EAsOZKbLjDFgFW3/TYR4n3X vfir5hnI3xfQKsjcnzaC67rY87HGS7WAj5g300NIXDwfb3a9jmGe353HtPKa pPOxJFYqg53YasdaEb1t+QiSMU9inve8zlvrvfbkYzSlwvg3uQ8keHjFb1jk Y9yBf3qcWCnmqrRNXD7YV51f2klsYZVYNpKcD9c2q1/txP5STlvCsvKxSE8d YN5X19u4ZC6X5OOYYXbAHeK9LEe2Td/Mx8IW9y+1xOZn2XemTOWj8x3Ls1hi P/3+5k2/8jHENnL3AnGWQN2uK//yETxcXBFK3N9iozzAXQC7851Gfsz7eqpq j9zmApQ9D/rvMLGvh7n2Y7sChChu0lckPrJBVUTDqQDU6YRTssTGL8RmGlwL oHwnIVGKePOOsXLamQI4lNMZQsTvFmJWeycXIN1rUWwJsV78zfdr2woQJ+hz 8zl5nyRZ8N9WXFuIFhm+Vw7EkTXL5E4KFmK1cJCvFXEwx2LOZZFCTG6ise8n dr36wVdEohBhQwacWsQ66+uk2bcXYtuPFckbiec/GST16hfiO8Mk/SN53zqf DnMICylEP9+5UXvi42PK1ufDChFNKbyyIHY9MXkg6nwh9iuUNhkTn7Rz1L0Y W4jLWjOH1In9dHRkszMKUTx//H8ixJF8y37VVhfCoDSz8A3pD0qbkjIG3hVi wqW3xpD480/GMw2NIgi5Hdu6nvQjMwuDGso8xche5WirSfqnAd2THw52FuPN LVc9fdK/KQ7vKKOllKBd/u0mBdJP8vKKnxI9Wopdo5b+NaQfbQ+1OHl/4yVE RSaZG//HPA81Hpd+XsI9z1npJNIPP7y1N7Hh7mVcfRjY3EX6azNT8cHBiDJk 6JdvNSX9uPsxCWUj83L8ScrV9++gYHfz5O1e/gqM8BX/6Cf9/xXvn26p3RWw d+wJNSXzQ1F5vmBUcSV8OnLX+baR/EmmzdOcq8CzU1749W0KTdKV78Z2VuNo zPbVI2SeeefBOeU0X42JGJ0o7asUvDnLti69WoNwB43WCjIPpWx3dRmIqUWc 9JK4NjIvxWef6npnUIfk3e1pYmS+4mx7sZGLpx7H0zOObqugwPY10kPjTD34 TC6eMLlE1i83YBLRU48nfmaTdUXkvmgxaPyo0QClofv298m8p3DkUJ1lQQPm zTwcRPJIf7IrRmPgbwNEg+duRWZR4DvwyCTyeCPyMlRXFaZRyLxYNav2qBFv DK1Z/iaRfp6zeOMahSb8eCb2aeVFMp8s7ajYQGwfRHdnWv33L0UZ4tYtQlPc xMLjZnt1iK2ieJcw/aZzifMZ4kUNdjFO4gO5jqV9xKw13205iHW2bNxcrNgE zvMtXX/J/Ku00aSulnhaXsmWaQnhs8qtxN1vaz/8IWbh7tR7Reyxq3zyN/GN iXBXDqUmrBzO41kk3n1lsMKdeJVRuOEcsVQ9t1IAserc785ZYv4KlesXiG1K zh5ieiov5Smd2GfR13WGuC5Ua6SDmK/KJfoncX7AydNvif+z+riS6SSfnMWv xHTWI5lTxCedJrmW7GjCzCGb0h/EdnbrM1YSp7D3yDJtaKG/XphYtMGsaZJY 1cSvVJq4yL5jD9Nb9hXK7SAWWm50b4L4/ysu3/g= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesLabel->{ FormBox[ StyleBox["\"\[Eta]\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"v(\[Eta])\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm]}, AxesOrigin->{0, 0}, ImageSize->{400, 300}, PlotLabel->FormBox[ StyleBox[ "\"Numerical and expansion solutions\\n\[Epsilon] = 0.05\"", Bold, RGBColor[0, 0, 1], Large, StripOnInput -> False], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, TicksStyle->Directive[ RGBColor[0.6, 0.4, 0.2], 14, Bold]], {213.33333333333334`, -480.}, ImageScaled[{0.5, 0.5}], {400, 300}], InsetBox[ GraphicsBox[{{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c8lW8UAHBJEbJJCVmRFZLIOFbDKitkFLL3Xne4pGVc2TJSItnz3mtH oVIiicKviJadUSL5Pe9f9/P9vPfzPu9zzjPOEXH2N3elp6Oja9lBR4f9StVH LNvvWdNMXaBNnfd31DLyNK7fY/xWa7d9lgYrtxbYxqXe+2Q0paX5mn8sbNsE JlOOZ/UarWjt5/gvve69AxTz3+DqMNoJSiqU98yJvsA4fnSg2YgbrAQf9w+v 4aFRk+Foo5EYPF/Q5td7lwD19MFjvF/FYJn9jfWH+4lQ9WzyRjBJHAKKQ3e4 +yZBsdnjCXmKBMTa9ez225EMqa5RqcVCUqDvH55UwpYCPklLa6k/ZeFR3rfZ dq50uO3n95FqdAxGM9fXpDruwMTuc9QrBcdggZwUHSiUAwoFcmSOlWNQGHXn 3XF8Dgz0z2l65SjDMTOhLmWVXOBQ9M4X/HEc6P7wUIWL8iBlxd0+7roqlLvE cBp4FEBqhNOoWacmeEqGiBoZFcJnDp26fzxawDGgEDAcVAhKpYfiyz20wP+m r4F0TiG8/fBJbRcHwGvKw9ey3wshXrDa2P6oNvhMDoUWxzyAXqJcBTtRB3aI ineVlBWBoY60d5iAPhAWO/Xmhh/CiRgpnhu6+lAuX0r6uvYQxDsPt2V56sOa 2jfFRp4S+Kctxt5E04cE75WXn81KoE77YP2mxSlIelvmZdtbAvu12TZJiaeh NmS/ynb9I/iutRyfsHUW9vRqX8V5l8E74tKxPHEDaHoh7NV9rQyetC+MVxgZ wMbhkI9zBWWQpzUr//qOAXRbnBF/97YMTLWmBzlUDCHqhzAfx8lyoGkOH8j0 M4JR+m+dVnQVcF2juezeJxM4djXmiFFoJSxIXpKc33UOqn9BonRCJVhz0xep yZ4Dj0u/P8/fqwSpGYP8wYhz4NgYuXzoVSW8zPqQzMB1HoSsf+hriFTBzUj8 SWVRU4g9Zcvh2lMFr4ZyhbMtzSCKu57Ja6saSL3zDu3uZpB3kiuYgakGlDsg bzrKDF4/als+w1kD+eVT/Ir3zcCb7OJQLlYDfrEyXL3zZuAn2+Xz5UwNcCq0 MPy9bg4rojajSuQasEoY/XG5yQLaQrQkMrlqIZqc+UjitQWcKC99KC9QC49S zN1nP1sAuVJUuUWsFjayeqfDWC1hU7m1oUa5FvKLmj8lXbaEhLDGP2xWtTDd lvOuZdcFUPoZt1GcWQvBS7ad+8yt4O+Rbzyl7HWQt8JH+s/NCjhWccsTfHXQ 9WtQ6wHOCozO+XWzCdUB35Zhq3yxFQSon402lq2D5j3qtFPrVnAkVKTK7Gwd 0IsJVAbftYYWo3lzMrEObl8Yy+6fsQE9eq5EmWn0/lShMKV/NvDey2X27Y86 KOl3ssjgvAjA6L0UslgH7Qbf99qpXoTK+wbs9zfqYFZzLfbrtYsg8lwzp5Cj Hk4fZvfdOmQLJ5STGszV6+HvL10dGWs74LrKGl6cUA9MyteFyF52cM1beyT4 dj1wB77YXCLYAWet0bp6Rj1Iz56nUovs4JOKeG7T3Xqw/mQvo7tsBydcSSe8 a+uh7lkY78Uke5Bn3XavelcP7tllP64/dYA4wtTtH/sb4Otn6zO30Lmy85fQ ygWhBnCT21WcMO8AWYveB1pFkZ9cdry97xJ8yel5HyqDPMczcsf7EtQlxawX aCBrR3dVcF+Glg6x6XcODXBstfT8D0VHeMbY6LsjrwGC75CIXhqOkDT3W5Va 0AD1WtaVs6cdQbWs46XrA/T/WwwsC3aOUBo46kwpQxa63LN8zRFGoqq59zUh n+XR/PvBEfDdk1dmhpDziNLssU7Q1BD5cZuJAuYVWucuJzqBhIS/IisrBQJa /wVWZzrBv0udRjzsFKgaJzadL3cChdzfi/t4KSAtGH329pATfNLXeTB/iAKi d6PdOCWdYVFg9uLICQpw3CMVcr9yhlZ8PvNzZwocrdHuuTLsDA+v0fqsXSlw roNupn7CGSoM03ZMu1MgcYKkaLnmDOcOiA/89KEAo0hMR7rQFag/S8ueCqPA v/sxH3kDr4CPTKepeDwF5h7EHuDnc4Ei49ZmtSoK/DW93kcVdgHCx40h9RoK sP67RbpwxAXOLGZZqNdRQNYm5WuqhgvUuXkmKFEp4Mt6r27vFRfgzHulR99O gYWQNsOdNS5wOqe890gfBZZOrUctGLjCLl1ug5ofFKBb2ZRLsnAF5qZ9511n sfltT8g4uMKt4/2C/PMUUNjYfcYzwBVIbCcPhS9RILCKl3s60xVk5pV2Cfym wDLfsfIPU65wuOtc7d+dVFj75jvWRXADA7YDBScPUqEj9+G5YzfdIJo+C/oE qRB//lPn/VQ3SOb/UuYgTAUhmukjYokbuG2KzYeLUuHs9WOhqm/cwD3tvl+q FBXyxP+wVYi7g9lzvQ9OylTQdYrTTXvpDr2izjMEQyqw8rZRdgy7w96b6eb9 RlQYeb4mFTDhDvlm2p+ETKjgo+DObrLmDlkX1QIbz1Mhc9tgfLewB2QxcPa8 s6TCj3z2sKggDzicePNKyyUq3B7NKXXa7wnvZtrMdQOpYCyzr0JIzBPWLyga GgZRgQmfVjUm6wmL1fPTpsFUiBZMrL+g7QkDQ/kstqFU8HMktBm4e8JTJxcz +0gqGH29/EaR4gnC/7psRWOosHtZ/M8OMy8IG9cS60imwhPd+5vttl4QrCDx seA2FQhpgv9wLl7Qwz4UQEyhwqoy385f4V4QIkUQU02jwlQ4496Zu17A05v9 LT8TxXfrx6HBOS9IZB8+oZxPBdye6rOFN72hsa7HPLOUCnzdPNryqd6Qmpch ZVpGhRpS1InmXG/YvqS3d085Fb7+PnV4sMobHHfUMkZUUMH06/hO+nfe0NbD MmFYTQXxp8yPnUR8YMejcP7uBir04d2OizT7wF3X2VDux1TwUH0lW/nUB0p/ 3zStRaZfVRRX6/OBDLo6h3MdVFD13uIym/CBceaDPNc7qVB4MX2JtNsXilhu cMw9pUKYypPyCXNfeN4cr5T2nArCS4Ki92Z9wc+c55LlGyqE1DV+2Fzzha4T x/q+ID8PsUixpvMDckqjb9ggFYL+3KRj5/UD28yAMxlvqdBDv/qRoOUHQ8mz +BfvUP55e3PtUvxAJ6d5hnWUCs0nw3j3nfCHp0OUW4yfqcC+xdEXpOMPyTee nopBdnlcHvfayB+YD+ZbbiCz6U+uXHP0h15hVb+ZKSo4mRgPrt7yB1/m8tIn X9B6cBRNHhz3hxDZgN2WP6hQruvOcEYnAHYVvyPSLVHhXNCw5MHTAaAqbEK4 jLx8/5TRT8MAOL7Tc6sNWXWHeGquZQCcsvW8FvmTCl2PJ4SX3AOgnDOgZ2aZ CuMatup3yAEQV1kST12jwt4TJkGzYwGQurx/z+8NlE+31oyOiQCQVTC5dGaT CpaZMk0ZXwJAnUI4k4Wcs7aHTnsxAGq4ed8f/0uFww09Sen0gdCaNrjDb4sK WorapZpHAuG+vPJa7zYV/GWOTSSHBUKfzB0hdQYaBHxsnXqFCwTJgeHKOMwp p7/tiQmEi0MX3/Rh/n1x4WpCIGxv+Y1c2oX8lPQ3/F4gJHwmL+J20yDI7jW/ Y28gmJj79hUy0SAswdNMQSgICj98kythRdZasfQVC4IusLSfxvwTb1MmFQRj FpMKIntpEG59+7L4sSD4+Ung9R3kCDGaL//ZIFiW8PlynY0GkS0M8XRBQfDc 9vSMKQcN8LMFTwa6g2Bq5eyVEm4azFnc1V7rDQITPTW9D8j2rXnt+weCQPqe 6CgzDw3Uk+40O48GAW4kQd4XeUM+rW51IQhUUtwJ8rxo/KDrhfz8wXAkfZ69 iA/N549PrKNXMJhJ8Vxz2E+Dz07edNf8g4FnKYvuBrJZryexNCQYKh6kaNUg K+S6RS0Tg8EuRWUn/QEaLGo4BsWlBcP9sZDGQmQfkoXzo9ZgkH57/OAHARq4 M57UXWILgfZroRwHhWio3htlbOUOAS95dRkNZNXQqL4b/CEweGT/fntkpqlm G2HREFARXPHLRS5rV/c/dzwE3vMsM/ELo/mHauZV2IXAD3WK+J5DKD/T2r88 HoVACit/wCsRGtgITLYoV4YAvTTfhW/I2uYxMXR1IXCgbYibXpQGnB2drNkt IZB/1kP4BHJdrq7Ys9chqP5rDSlAXjXXN5VYC4ETFSynPMVQPjrPlE3qhMJw RWnZZ3EatOPoTXnPhMLOcA+mTWQGlba1s8ah0B70BLglaEAuU9KpsQoF+SoB DT3kojTB90TvUBCnkwu8jzzgurLrYEYozHvu37Q6TANJ5gInq++h4HUo6l+J JIpf10XG+PlQcC5lWmtBriPyVLYth0Lr8/CX/cgaK7fWxbdCQfNhHv9vZPPx kOQVzjBY/C9WVV+KBsQqw7bb6mEga/ym7j3yO/Nf/C/JYVAS96t29ggN0sfM dz9MC4PDjb8+bSCbu1SvkLLDoMY29NceaRq8DvV4rVIYBrUbwf9JIvdkj14t pITBwm6RLGdk6sf2hcjxMDCvX3j7FjnT60aXlHQ4WPZvyjyUoYHlylTtzqPh 4JM+db8OmQuvXfDxWDisWD/e+RiZnPQnMl0zHAq1WhJGkK/XeB+lMwuHqbMF 1YyyaH3+Op8zEh4OX/QWHFyQbWL5A653h0OkLT0zhxwNgsnJmi96w4E81MAk gEzO2c3COhAOGuKEFQnk7rrV4pTRcEinUpPUkZWmBsbyFsMhp+f+iCsyi/6t M/X7I2CNvD5CRT5sSsf7SygCCF2SRR3Iuvbhn1XFI1DdyHypFzkixJXQLh8B aUnmuf8hTxfp1L/Qi4DyV4+1dsqj9bBrQ2jCNwI+ZNeAEfIHzsA50eAIcOFT W7FAXhX83uQaEQH7N7ky7ZFlVIYtZ2MjQNVHtMwXOdutLv5XVgQ4D8ayJSMH PfP6xfokAp5abI29Rpa4NdanxhcJJT/M9+kdpUGN4TNeF4FIoFc60WGAfJK1 3oF8KBIuGqbZmSKbJsfPf5aOhBrJbU8H5KgMtb2JEAkDmi3fwpAH7mcZf/SI hCihoPASZNsrV9OZ/CLB+uoT00rkL+L+40rBkbBS1iJYj7xRctrnBiESDkSv prYjS1StJSikRkJLYNjcEPb+ZouXsS2RUOu/4bGNzIAH7sqOSMg2vh3HoECD ZE0Zu5HuSBDI603fg1zUQT8rMxAJOcvuadzI/T21zO+mI2H8wBdmSWTxt+yG kmxRUKT3ddEIez778vlLxyh4dH72TxLyIO6iTb4r8tLwtRTkYZZv3/y8ouDW XfyeDORxGXpGrpAoyFaTXM9FnvFWPWVzIwqG0dVbiswwV9Q5XRkF06SMxSfI jHglM2pdFOSO/d3sRmZm7Zi4QYsCyoNmuhfInLJj29KdUaA/5LDyGlnIh1Mr cCgKdA/pEEeRVecIzVsbUaBW7ae0hKyOZzHs344CbZXo58vIWqx3PtxjwAEu Idx6DfmUbMO6HhsOutb1HDeQzX1mVOJFcMB+1lCIQRHt/zmrer6zOGDZRWfJ h+yPn9b9boyDuO5+PD9yEGvQYJMZDhgo/AUHkCNlk37a2+HAJPLkgBDydZ+n Rx/44SCYrvXLYeR7c0crjmbgIMmy7MtxZDq69wKeOTjIFJYcOIHsxE1KKCzA gfnXgno1ZNGTA168ZTgY2i521UQuuhFwZLMdB5Oiq2H6yAy5/HeUu3BgUKMh fRrZtaqDye8FDmxku4fPIB9+x/F94i0OXBQaBYyQS0RrH/Z8xwGXFJ+VGTKT ykU+ugUcJMyYDJkjexjsuK62goNCAWZjS2SpADPXii0c3NujJGWNXNb2UyyV Cw9Pho6m2yNX2Sjdd9DAQ/phJ103ZDafUY4sHTy6j6fs3bF4RceSBk7jIXku KNADWeHh4GU9MzxUVYzf9EKuXQkSOuKGBzmB3kA/ZC5GAbKzNx54cCUO/lh8 Dzzdyg3AA/7FsF4AspIO939sODw8CzTZDkRuINfnribjQbEm/lgoMk+hHYt8 Bh429L4tYw6l7MS55+BB/fRoRRiyyriF7WgRHgSHizkikDMXN19wl+Gh9Wpy M+bf9EVqJtV46PukeDkSufHIKn9HEx50p55kRyHza+bd/NOOhwdlT+RwWL5N 9deVuvCQt5DbhvlkePpI8Wv0/PtMHx65pUs5M2EKD7MppbVE5PSHRBOf73g4 KbV7XzSy383nDCbzKD6KbBGYDxnbB7P9xsMH6eNyJOQ/cg+lFzdRfJ0uxWAe ZF+a7KcjwGT2mTeY495eNU1hJsDjTD+XGGQHSh9jEDsB9hVRSzCrZO17bM5D gER4+xUze6RT2LH9BIhLfCESi/zdtlyOR4gAjlV3bTB3aqxNr4oS4Opz6wTM OUKQ906SAGb//jRhDqa7ZUGVJYBccPw0ZuPPg8xZigSIMmRjuYos0XXwSbgK AXJK4uUw/yt2i7RRJ8DPSgZjzCM3ahTUtAnwmRTjhrnGc+Pb/lME6NfbTcB8 y0i/YMOAAAcPZCdjdpYjW42dI4CspMZdzOrs7/e2WhDAmfz7EWaenyLdeTYE OBTcX425p4Fy7JIzAZ7q/qjFHBFhUCjsg763tq4Is5lt2kW6QAK4HHTLxiyt 8R/HZCgBwj5Y3sS8U0jyeWcUAXpY4kIwj28HRBdGE4A2vG6PmTLZrHI1jgDl Do06mMlPGRau3CLA7q5nopjdi88V65PR98rJ0mHWvpFtL5FGAGLrzAcsXvs9 P3PvzkbxzmCqwbxsKPvyax4BlMfiYzEXsXWoPXpIAD31NwcxE5b2/LxZTgDd vIJpLH9WgxaPPGsI0Pn76yPMTJnf+GSaCfBMZu0w5slwxdcsjwnAY9Qzga2P 5ou4a3NPCeCzLJ6F2UeQfbWyjwC9bgV/sPV2atumnDxIgIyo7mLMQpOFzv4j BFh/kHQO80CRyhuFSQLs7ebPxNavsuylqvpVAnCPZG9h63sv2yPX9D8E4OQy Tsb8dfHnwdB/BFg+2ymIObv+WoIKExEUqukUsf2xdbLSo0mACFbRGorY/jo9 6J0Tc4gImqcFKrD9R/aUfmUgQYTRg3/EMAtnlxwdlSfCvHAHcziyztr9Xxs6 RLid+LEhBDk+0VHq6WkinJjg58c8KCZsm2BEBKYUv4hg5CvmeW0CF4gwoRCl EIR8rTozTsODCLERoUTsfHl9+gKVwZcIiV3zvdj5w/eR+/urQCIot+TzYC5h TTFywBGBv7+uwAf5hWcCF5FMBP17PBme2PzFSfceNxBhxrF/2xnLT4vW4I0m IhROeIlgvmu+tdO0HY1fHKbthHw0Jsp94hkRyiTnwy5j6/FjiPyOMTT+vqZu O+SMbM9W3R3RoC3yZd4CWXCvxftuk2iIs+WL1kV+Iik7s2YeDZMBjeo62Hmt u+uvhE00UO++WAPsPAynCV93jgZy4mln7L4w/Czgfjo8GnyeMgqqYvuBNr3W cy8aYhRvH5TD4uUUxv18JRpmy7dsebHn+PMS6+vR8NZ15SU3Nn6W1Ampf9Hg m/HkJBeWfzdfOX0GEsTe3+BkRyblCpsVsZEgP1q+hAmL3+64bBcxElRzkvw3 0X2qN2Ys+cWYBDtrG259wuqF88xDpudJQK6+PPofsnPXM1KrGQlSmMKOjCOT KnVH06xI0ESZe/IeuTVaNUnXkQTZfmpTb5CPi4uvFASTYGiGZewpsqTvZrtt Dgn0kgMpD5FZtkutBr6RgFLoTvRAjiBb36Ilx4DZhYG+QVQPDb3MZSYrx8L0 nqsbCsh67/eTTF7HwjxnQMZtVN9Zm35fZwq9Cj0uX8+PofoyOmvJtZIjDloj PsnKIWcmJovolMYBTsxANhrVw+bzxImBc9dg87BWDVZPiwg+SjP4cQ0cfHW0 WJAzGkUM229fR/XBG93TqD4XFHu3KiB3AxLOKnkmoXo/TV14waPnBvDGZKSM oP6g6nHTTK3PTSh5LzLMifwfF3lsivEW3A1N/m2D+ovaN3X9nDW3wPHByJXb qF8J1vLjOnohHjbtV01eon7GIOqKwfHFeBBy8rDD+p8ukdKrJzITYKRp660R 6o/Ms6XqRJUSwTpXlpSC+qn+Vq2jW72JqC5gHhhF/dZP4+LqtwFJQLbPz+RB lqw4JZ7GQoZn06r5dqh/2xGukneungwCCmNCaajf+3rXoNQZuf3h1G7MvT32 1DBkX8G5hVTkdL6rA3eRvzNvtWOWovYzLCJf/ip0GbPpmodvcgMZ9AucC1KQ 7wXnag1QyLDGPyN8G/labpXRNPLM7WVGzF5PO23WkX8wbS4mIytzfw86RCUD 4x+WDszP65RLApA7Psg5Yl762cfOSSODXH7gPTLyu/2TByWQe3mjbmJu1lk9 ooYcSI4NwByXckDfCXkiOk0bM7+ie0QtsvoVykQS8pZN1LVu7H3jbc8xfyYl pX5AlrrQU4O5YqC+YkcjGeDMCAlzynpPEy+yXccnD8xhh0Z7jiCT1L6bYrY9 O/9WE7m2bkkVMwTQTZohz8n8OYT5f9LozHQ= "]]}}, {{}, {}, {RGBColor[1, 0, 0], Thickness[Large], Dashing[{Small, Small}], LineBox[CompressedData[" 1:eJwV13k4VG0UAPCptEl24pNdskZIi+WgImuGsiv7vo6dmTElhBKyhWypZN9m JmtIhJSUypJsFaHIVoq+9/41z++597l33nPO+95zhB18TZy343C4J9twOOxX ojb0p83eVbVuhVUfY187dX13g9q9Bm/UQ4t4P+txqIPVtZT8T/pT6kdkYh3T /xnCRPKxjB79ZfUhzY7j7R9s4T5PLHur/g6QzhA0Z7/hDbtH5fob9DngIHPu 96FVIjxWY5B7rC8KSU74jdODCVC7PWCE64so6Ho/1xkuuAEVXROxARQxqD+d verqfRPu45+MH6EeAs4GrW6fbbcgxTk85b6ABNwecyl+yJwMXjcXV1OWZOCp B0nqCXsqJPn4jNH0FUG28M+wROsdGN9lRHPMU4R64zG8v0AWyOfJJrIuK8J4 cELmMWIW9L+aV/PIUoI9HdphSsrZwHrU8y7/7DEYSX+ZIFiUA8nLrjbXYk6A OM9kv45bHqSE2g/j29Tg24H2Oj39Qphk1azZ4lSHXnbS0iChEBQeCcWXuqlD c8VUo2RWIbwZ+nRyJytAwbED8jIzhRDPX2lgI6cBi8/5/xRduQc9ZNkyFrIm OHrnfnlYUgR6mlKewXxngPekMH7+3QM4fkWCM1brDORy3c/+svoAxNrEmzPc z4B3ceqFx5wPYUtDlKWefgboY68/T+IfQo3Gwdo/pmdh8JD9aaueh8CrwfyH ckMbdAtif23VFsOM+s/4hM1zwIy/pxThWQKD5EXFHDFdIOpf4n0WXQLtLd9H y/R1Ybot+tZ8XgnkqM8deXlHF4TDBabfvikBY/XpAVZlPSgnPNnPeqoU6Grv /kv30QdzckaeGa4MYlQbSvI/GYJm6ZK0flA5fD986fDCTiOY3M5JkUooB3OO 7UUnZYzgePp400J+OUh80707EGoE0B5MEXpRDr0ZQ7cY2M+D1rlwLhXhCrge RjylJGIMB2/asDl2VsCLt9mCmRfwoL3NQdRjsxIoPQu2La54SCatUxj2VIFS K+RMh+Mh7kHBhg5bFdwtneI5WoDut/HRKxWtAp+r0uw9C3gw7W9m+KxTBWzy jQx/Y0yA8WLa3NHEKjBLGJ69XG8KTR5vv6axV0NkYnrxoZemUHBH0u8IXzUU J5u4zk2aQubqua0G0WrYyOiZDma6AFezw3yqlKrhblHDp5uXLwChINeT2awa ppuzBht3XoSvDYFrRenVELBo1XbAxAymxiwai1lqIGeZm/LRxQz+vHbKGOeu gY61AfV7EWYwJP/bkVmgBrg39ZqO3DeD1twHuwxkaqBhrwr97C8z2Kegs2p8 rga2i/KVB+Sag6Z1k8lNcg0kXRzJfPXNAhYV6oWkp9HzUwSCFbYsYNXGKezN bA08fGVvmsZmCT9eKAYF/qiBFt2Z/dYnLCE4L4CYv1EDc2qrV79EW0LysNxA AWstaIuzeG8KWcElevhjvEot/F3T0pQ2t4bFpEcrRQm1sEcpRiDRwxombdjw AUm1wOHf/WeRZA1XeFo8VdJqQWruPI1WZA2qeNu/j3NrwfyTjbTWT2to03vo 6VFdCzVdwVyWN23A4dEht/LBWnDNLJmNeWoL+9UWf83w1sGXSXOdOHSuaJJv WF4UqAMX2Z33ExZsYWEOiI0iyO2X7ZIOXILenO3SQdLI85zv73heAqb9U0J5 qsgakR1lHJeBcbLn41vbOlBceXR+9qgdpK/spuJy6iDgDoXsoWoHXX85Q6h5 dVCrbl4+p20HqhJ5m0730P1xDPu+W9vB05zUoLoSZIHLnT+j7cCo68EoVz3y OU61v0N2IHD9zNOZt8g5ZCmWq/bgYOz+amsPFUzK1I0u37CHwbRouX1MVPBr 2vKvTLeHuu9KFzlYqFAxSq4/X2oPm+8L9xzgooIUf+S5pLf2sHvctHpeiAoi uZEubIcdYFN29u/gcSqw5lMKOV44wISRWFSnAxXkqjQ6Hd85QJDaE2MzZyoY teK+1Y47QMU+xqRJVyrcGKccvbDqAAX48yGLXlTYLXylNVXAEZpoZL/JYCps FVwZ4/J3hGmVUWXReCrM37v6Hw+3E/T/t7r/RAUV/hrH9NEEncCykOHwqSoq MG3FUS5KOkG6Mv3+yRoqyFgkf0lRdYLcBa8JeRoVvJnya/Y7OkF54GYFroUK 3wOb9XZUOYHA0HSERB8VFs/+Cv+u6wxvSkdeVsxSAbf8R/amqTO853vU6ziH re/fuLStM0j6kpO5F6ggv7FLx93PGZTPF0cFLVLBv4KLYzrdGRg/4PC861T4 ya1YOjTlDNotR/9u7KDB6lfvkQ6SC7Cr3dU4eZAGrdkPjBSvu4DcrpZPvfw0 iD//qa0gxQVyFad0bARpIEA3LiY/dIGM/IzIYBEanItRDDrx2gU6RLUmkyRo kCP2m7lMzBXWD8Rz2CnRQMv+mtbtXlc420bXJurRgImrmbrtnSucL/la16dP g/fPVyX8xl3hBu8xHX5DGnjJu7IYrrrC7Nfrk7TzNEj/pzu6S9ANbO7Nq7y9 QIPZuyzB4QQ36Ln0tKz+Eg2ShrMe2fO6g5d4oqeGPw0MpA+UCYi6w6j0A+dz BBrsId6uGJFxhzizqzvOB9Agkv9G7UUNd6jWyD1qEUQDHztSs66rO8w5Rl+3 CqOB/pfLr49S3UEwp7hQ6AoNdv0U+70N7wFVkRXCLbdo0K5V8KfFygP6RS4N 3U2iAek2/1aEkwe0XrJ0JybTYEWJe8daiAeErh7nUb5Ng6mQ3fu/5XoA2BiO ZKej+G7OCg3Me0Aij7a6wl0aROytPFd43RNeSs0Zpz6iAfczTo0jKZ4QOd8l ZFRCgypK+PGGbE84qmr4b1cpDb6snxUfqPCEu29EFoLKaGD8ZXTH9kFPOM9q W36ukgZiTxmf2At7QbyRQmd7HQ36iC7HhBu8wCkyT43tCQ3cTryQKX/qBY/d hvgqkbevHBU72ecFVPdwGYNWGpzw3GTHj3tB10Wm2ag2GhRapi5SdnnDKvvE 3OxTGgQrt5eOm3jDcZ689aTnNBBc5BfJn/MGxS8B4/jXNAiseTz0Z9UbxLqG DKeQnweaJpvjfOD79UMLAQM0IPy+jmPh8oF+5s/PUt7QoHP7yhhJ3QdSPb9t dQ6i/HP1ZFsn+4DHe50rjMM0aDgVzHXguC/8DJFi2jlJA5ZN1j6Cpi80Z0Q+ JSM7PSm99lLfF+qOFfStIzOfmViOtvOFkoW9Y1+naGBvaDCwEucLlj1ue1s/ o3qwE7k1MOoLdPK3i/hZGpRquTLoaPrBjvbuic0fNDAivDt8UNsPWqmfx20W afCz4Kz+kp4fZOio2jcin9gmlpJ9wQ8CuSRngpdo0PFkXHDR1Q+Od7QJzfyk waiqlcqdRD/g/6jzvHaVBvuPGxLmRvwgOYhJZGUD5dOlKa113A9ChneHnPlD gwvp0vVpn/3gpLKKXSpy1upenMYPP7jpFLKk8JcG4nWdN1O3+0PlWVsBz00a qB/VeKQm6Q+dfeY8z//RwFdacfxWsD8EMRTyn2Cgg99Y09SLCH9Ye+/w6Arm ZO2ve6/4g11pVHcP5nXL71EJ/mBWqNFtvRP5KeVvSL4/PPry613oLjoQrF/y 2PX4Q0v36dK8PXQITnDHywsQoEfu1P4iJmT15QveogTok5Q/NYF5iWhRIkEA GfVJJoH9dAgxT7ospkiAI9TA++nIoaJ0b55zBPgoub06ipkOYY0M8TgCAYST /uUYstKBOJfX3v+MAONO3LgiDjrMm+ZqrPYQwM5u4dMgsk1TTgtvPwESxF4E 7+akg8rNOw0OwwSQz1XodUfeOHK7ZuU7AXrNKLzSXOj9hJhCHp4AcI7RK8jn Ruv57XXVziMA9kv8N2/JS4dJe09ctG8AvEjIcY5Cxve4kx8FBkCXYX1BGbJ8 tkv4T3IAhA1wOG4h/1C1I1y7HQB5fX4cef/RwYti6lDcFABNooGEQT46uO4+ pbXIHAje/SbGPAJ01O8N727iCIT54VtuJ5BPBIX3xfIEwo9Tw6YWyHumGiwE RQIhpoVUlIFc0qLia3QsEAJwoMQpiNYfpJZTZh0IlqZU9Z1CKD/TGmtuxYFQ M3Yh7LkwHSz4JhqVygPhdW6j7RSyhsmVK7iaQPil8YlvC5mttY0pszEQ1rOE xRVF6FCTrSXa9TIQ/i1NhWQjr5icMT60GggPrgucchZF+WjTKZnQDAIfTt6I MTE6tERsN+bSCYIKo753a8gMys2r5wyCwGVdiYnlEB0SSxQ0q8yCwPjZMgMg F93m/0D2DIIjxGXFu8j9zss7D6ah6weOUE3E6XCYMc/ebCYIVNoa8+4dRvHr sNwdvxAE1c0jt+nINWTO8uaf6HrQgGsvsupy3C+xzSCo4luv/IlsMhp4a5kt GO4PrzwDCTqQK/Sak1SC4XcI7chb5EGTNZ7exGAoZx/m/ipJh9QRk10Pbgej vrLu9BqyiVPlMiUzGJZ7dlrulKLDyyC3l8qFwdAtHqMmityZORxVSA2GqHKj JVtk2ljL97DRYEjP/MP/CjndI7ZDQioEJP/7ZlogTYcLy1PVO+RCIJV7+/Ny ZHaiRt6YYggEsPJJNCAn3vwdlqoWAk+/0ssGkGOqPOVw+BAoPubds10G1efa +az3ISEgLDbsfRnZ4iqPX8yzEJhL69xilKVDQOItte6eEGhgF/zDhZyYtWsf U38IsJNip4SQn9Ws3E8eDgFv81+hysgKU/0jOT9C4L28Y70d8r4zcTq1vKGQ /l28uBpZ3BjHtSYQCo7rFwiNyFo2IZMnxEJB101L6hlyaKAzqeVIKFzSanf8 gDxdpFnbfToUKpX4cVvILTs3BMa9Q+F+866Vs0foMMTmPy8SEAp3hebvGyGv 8M/UO4eGgsw8n445srTyuwtzV0PBtu+xuRtypktN/FpGKNCWCHVxyIQujzWm 9lBQP/zBtxv5UNxI30nuMJh9GRCrJkeHKr0uLie+MPjA4HbkDPIpplrbRKEw iNcf7dJDNr4VvzApFQaHH90aMEcOTzu5/waEgYS5uK4/cn9BhsGYWxi0in3p KUC2coxK3eMTBs/tnAsfIn8W8x1VCAiDqcYo73LkjYfaXrGkMEg6NTn2GPlQ xWqCfEoYOAvh5F9hz28w7b3aGAbyzZpZv5EZiMBR3or+j3Fs7RbyLTVp6/fP wkDmZEDbDnm0H1q3z0n3h8HdTmLjfuRXndWMg9NhoKK+V0oYWewNi95h5nBw 07+4dRa7Ptf7vNcuHJqvLc7GIg9EWFrcdQ6HF9zbAhOQ3+37+tXHIxyode2r icij0tt3sweGg+/3qPE05G+eJ85axIYDg9HhC/eQGeaL2qbLwyFvmqm5CXk3 UQFPq0Hvyz7Q9QSZkal1PJYeDjoPQ7vbkdlkRv5JtYWj76Yz/TmygBebuv/b cEglbJx4i3xintSwuREOsgXhI7PIKsR9eq/+hcN3C4LvPLI6052hfIYIePzO 4u935LMydb9OM0fAdAb3thVkE69vyvHCEdD4HE/fRPaaN6vlPhcBGn3RYyxH 6eBLnNaaMYiA9qCMnezIBCbCQD0+Aq4SxcQ5kcNkbi7ZWEcA6+kBUx7kGK+n cvd8IkCv1NlBCDl/Xq5MLi0Cjj9OMpVDxuE+8LlnRQC5YUzlKLI9ByWhMC8C dhMO8isii5zq9+AqiYAKUmKPMnJRrJ/kn5YIkPO5NKCGzJDNc0epIwIcp1Si ANm5onWPT3cEzN4zk9VEFh9knRl/EwHrr929zyA/FKl+0DmD1nuTKVcPeY+y JTfuewRIug7zGiC76W6LObkcAel9crcMkSX88M5lmxHQ453mYoxc0rwkmsJO BCVv7e6LyBUWCgW2qkS4bvzN+TIys9cwa4YmEVTtL5DtsHhFXqX0axPhGffr JHtk+QcDl0/jiVCcIlrkiFy9TBCQdCGCz3H2aFdk9t18iQ6eRLgvte7jhsX3 v6eb2X5E2PtRztQdWUGT4yNzBBEajzUxeiLXJdZmr9wiwo1zB4/7IHMWWu87 kkaELK6IFcxB1B0RrllE4FzyLPNFVh41tRouIoKZrAiTP3L6jz/dHCVEyM5f q8W8vr3opGElEZx1IswIyI8lV3ha64nAPFGTEIDMo5Zz/XcLERpSAgUCsXwb n/ml0EGEotUdZZhPhaS+v/+SCB9HiulByFnxqjqf3hDhvxcvjgUjb9ydpvEM ESFJZ6QCc2OHUnrCFBFi9d8mhyCnPiAbes0QQfb9/Apmn+vPGQwXiHCBvdI0 FFnIwCaAeZ0IfSo6DGHIv2UfSP34Q4Q/7hJmmAdYFide4UgQ1NV9D/O1N1HG yYwkQBWiEI5sS+3bTWAhQdxllwDMyhkHnphwkmC1Hqows4TZByvykiDhycoM 5hmrUllOARLghuP5I5DbVFenV0RIsOK52whzlgDkDB4mwd9+33DMAbg4U5oM CSptuwsxG0wOMGYcJUHJZd4uzIc6DraHKJPgLr/zV8xb913CLFRIYPq+egcR +X1slfxJDRI0PGM4iLnKfeMr71kS/PjPUR5znP6ZvA1dEmhuH9DA7CCbaDZi RALINzPErMLyYX+TKQna2dcuYuZcEn6WY0GCJT+qFeaFAU8iyZYEur13rDF3 1lEVLzmg/ytdbIE5L/3fN3VXEnilfcZjDg3VLRT0IoHWTnMdzHir25Y4fxK4 +m87iVlK9SPrRBBaT/esOOYdAoeft4WTQHadkw3z6D+/yMJIFK/R2HVsvdSJ BuWoayTwN9cZxpz4lOG7YxwJulQt6jG73je6fyaRBB02T1Ixa8Rm2hy6jdZP ueKFmdd9kmNXJgluet3TwPxTT6b3Sw4Jikcl2TAXMbeeLH5AghTBkIdY/kiL e5eul5KgyFDHG7PZgGmxexWKDy1RDvOe9K/c0g0kqCpPe4TVy0TI0Zf7npDg uMsle8wNlhHR809JoFNZxYXZi59lpbyPBIO7GAKxejz7z6I0cQDVFyuzAGaB iUIH3/ckYCyo7cDqt79I+bX8BAnmmKZ2Y1aSuVRRu4Ly1WXogu2P/czFzqm/ SZA7U7GK7Z8vP5YOBm2henJ9eQVzZm10gvIeMrynWCZh+2/zVLlbPR8ZTn3h isX2q/aAZ9YVITLk+uf+88Pi6S71QvcQGX68OxSEWTDzodzwETKcS9Iwx/a/ 5mrB2oYmGWLxrL+8kONv2Ek81SbDtMOGBeYBUUGrBH0yyCZvo2Pni6NJTjPf RTLEMQZ7eCBHV6ZfU3UjQ9aAbSV2Xr3Uvkhj8CYD7nzGbxdk7jGOmRf+ZIja YNTE/JApWd82ggzMrJVdTsjd7gns5EQySCQZ1GHn4X4xSv6TOjJ0803st8by 06g+EFtPhjXGS7JWyLkmmzuMW8hQ8k1fzxJZ7kq463gXen9qLNEcq8exwCPb RsggYj7UboqclunepLUtEhZUKof0kfn3m354ZhgJ540yz55Cbj8s823VJBJi 14v/ncDOe62dfw9ZRII5XpJ+HDtPQ+iCMQ6RsIKPFTiGrDfJ56odEgm9bHyv sO9VKH16tTM/EnhwDxrEsHjZB3M8X46E07EhA0zYdeL5Q79+RcJljr2a+7D3 Z0gcl9iKhLcnA8r3Yvl38ZY9w0CBNL2PkbuQKdmC+CJmCjidtd6Hw+K361qm kygF2jNjn/xE39/TIwaHPxtQQJGVr+od1m+cZ3xrfJ4Cgg7WW9j33qGji9KE p8A3oT36b5Ap5VrDt80ooMVa+ekVclPkiZtadhQ4Zuy5hvULx8TElvMCKMBU aDnSgHzY+0+LVRYFhIY8k+4i7/v3yKz/KwUOdKQzXkYOTTSPo9+6AkIPc8ue o/7pbW82Y6LSVfhr/OWwOPLpD7wUw5dX4Zvt4sFo1B+aG8/82hMUBSP31gRe oX40MmPRuZz1GrSJX9XF+uH0G7eENR9dg0SVrhR/1E+bLJDH+42ioZdojK9G /bcwf/Ft3dlosGraFPmL+vm0x8J6LUkxEM42baqMzC86uMInGwsC2i3lRDQv 3FYR/O7WGQvxiU17O9F8UfGk/lu113WgJY56/kPzyEf2xJGp3XHw2amCeha5 +nXNK7aqOGhw0FQgonknQN2HXe5iPPjzuUjR0DykG+6oe+xHPBxwrTTeRPNU h/CjqOPpCXB6it6thGySKVEjonADMvWDosLQPPaqSV1us+cG5GSMjreheW3J 4H7lG7+bkPlCPGcDzXeHy86K3d6XCFyf5os0kLeFKOcY1SZC3Mdk5hA0L37J 1X3kgMx4NXQtGLmn04YWjEwRvzyGOZU7qj8XWdtXpgKzBO0Vww9kTVyXIWbj VTfvW3WJsCj490YQcn5Atno/NRGUzFz2BSJHZ1foTyMf/W2wHIDs8bTN4hey SI7iCGYljhmCEC0RxidwpZif1yg99EPu9crWw7y41MfCRk8EK0p/HAF5kHfi 4CHkdBG6P+YGzRXJk8jPOu5aYr6W/N8Ze2TcXk9JzDxHXUOrkT8n7ez2R960 CI9+htyqMF+FeZJyM2UI+dbbgUzMZf21ZdseJ8Jennw3zMm/Ouu5kOvqY4wx BwsNd0oim1h7n8BsdW7hjRry57+mQpjBDzeBR/bKPbUH8/9gMOs1 "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesLabel->{ FormBox[ StyleBox["\"\[Eta]\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"v(\[Eta])\"", Large, Bold, RGBColor[0, 0, 1], StripOnInput -> False], TraditionalForm]}, AxesOrigin->{0, 0}, ImageSize->{400, 300}, PlotLabel->FormBox[ StyleBox[ "\"Numerical and expansion solutions\\n\[Epsilon] = 0.01\"", Bold, RGBColor[0, 0, 1], Large, StripOnInput -> False], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, TicksStyle->Directive[ RGBColor[0.6, 0.4, 0.2], 14, Bold]], {640., -480.}, ImageScaled[{0.5, 0.5}], {400, 300}]}}, {}}, ContentSelectable->True, ImageSize->{865.3333333333334, 652.}, PlotRangePadding->{6, 5}]], "Output", CellChangeTimes->{3.41423153933678*^9}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJztfQd4FUX39zWd0FuQXkWKgFSld5CiCCJVQEAURHoTkN5BBBSR3iSogPTe ayAhkEZ6J5BCr6Hz+3bOtltm9+4N4X15/x/3eXKzd2ZOnTNnzpmZ3f2098j+ /Qb1Hjmgb+8SLYf3Htp/QN8RJVoMGS4UOb9jMjnNMZneSSthYtcwmeQv9TOP fZmXZGJBHfbPxbTs2+omZyphV+zPSamgcmd2ld1+Y6sKF4Ng6lUO+41dFIay ZTJm9coAz1TuxK5GO4KZpyF3RxCo4rs5AqZeeWQMzACTqqk4RE0Fy6ByVASq csqaGbiJSiB9TKpgVhVOSoWTYjEOwaocimWcdlkdR+pijlThLrvDiJxfATbT mNBAlM1hRGo/jc4sJgx0n2tm0VI7wz3T2OcXZwZ+F0uNuzmMUoV11mriOJ/W SF3Nm8gimF4Fr6ty9T5Vm2orBVbErcrUq+yOQFhxYxTWRbnKZh/Cg11lfR2Y razEKA2eRYxwmBpPf+6OYPGw7HADELxRkUFYA3QNXBnggNe/jmuNd+XGrqRp 9/UNE56xGDBNx43Z2bLWKA29+e0NHj08LA7Zs5W6XmUs/C+OI15c4DgWzRnp tc8+PD9g1AKtImYjg8Qq0HJogFllAQaldHeEBk8b+di3M0vNu9vH4mIfn0Mz jabWHBorpAOH5kRNjWfQtl95nPEiT8fHvCiQi6JKSbQ8ShfT1escbxmfJlSD cghCddKODzT6n9Og3Rho91rGmIZGHRogVppyfCLydBjivz91aSZkGYwmnblD ibcQo2kHvGnFIVgHliv+Q4hUq8oAE5YjMVdmScFbdHGIE168kk9EL/T8V5nF pwMLGxnCr/ZNpqF8jSwbWIsxOrAcWov5ryJVPUtesczKs7goHtQqJcmhVeuS sVp15s2uBeuqVcvbSuHBeont5GlQkz/1ykO3ncqzu247lT99fOqVJj5nBZ8+ fw61U2fIvIqGcotGUFoyIbOtM9NzpZGTctXSYDtDaKXJ0C5atZ0O2hdKI2cF sIXBdrnsoLUSThOtVTsJbSmxOeK89xJIetpN00uOcOZoQ6cvtUKrtpPQFmP/ 3Fhr6tx0duXOEa6RwXY5LbmN+v0v4iR61VYTz8Hwyniu62074+3eJF7etlN3 q6RxTocL6JeEQTxsQH/NlaYmRJSoZgFujlIzAf8vlL1JvLzp/L1JvHhIZQbM 0sqpJx/zIwsNGT1PnD+sMPPKihps9yqwBdm3ziyblLvYK9PIbDl4PFvN+E/u PST2z/X56Y1S93dmqo3P8eaptqqoRvN4bOEvp+kXNWhrVtGw/jI8ffpcrPCy BdzX9Fs+4O536yH1YoQmYHz+MnxAdhAsdu0OTcAbWfJoA4ZOXqwFyFRAf9aA lhUciikeeXE7PsWW4jWPPDjz5VBNQKa86KgbtoBdOm3EzBnHtLVaoA5CVu+2 Bdxcty8OfNxNE5DpIGjQNFvASxUbISV7QU3AF+84IaDdt7aAAc2/whMnV03A m1lyI7hGa3NAF6oI/GYcsXM7MpHq8tvChhSrjjNV2tjChv28Fome7yJ2zxkN WF5vuphX4MTxOC26+/rMwKkCtrC4d+MeDnp9BJ9hP9vCik0CvhpBYj24kkZN 2pjVsU+6iwcCG3XWAr808VcCv7L/NBf8Sq6iCC1XTws8zns3gUcsXM8FjyhZ Awn5SmuBXw+MRLxnQfhOXsYFP9e0B/wKVNUCf/78BZo0WoEVy/3MwF0V8D/X X7R0GPlscbDPvnJtcKxBDy6Os3M34FzuD5B6PkwLh9LFMYUqWONQ6siNrNup y0dIlea4ljU/l4+rh30JR8jYXzg41HYBbfriuTB4nj9+Iha0tmrw+PY9QhTQ aZAuoovjf0VgzveQcimej4g4zlcBhzqM0Ofo4lXqhQsXrmojGtB/G0YM22OB KIMnaJ2s0KdFXIZ/rvLwH/erWFAjc/Cyz/5WA+FfuIYt29YpiIrA6Dqxh0U7 majQrdS9rJsVWV6dmIs1MQkcAa1749k7znjx9JnIQF6xhUMbadzcy1KRadm8 EFK5qVhQ/ZWRu1kgDxo4lUz++oWwjMjAXaJVZVCshNXHvlvOMRm0kbvZIGcy RC/fkhEZXCR+zciICMz6+lSLvjhYojH9otpqmYj8mqB7Ngp95npnyJD0NiOs ult2+48fP3NIDAdIyDPPyhV+5sJk2o4Zj+aFBX8hOmtRXDks0qz+Oomxz5li deBb+wsbAfVXxK0QxXnvJbsN/3mNyrVDGNgnstiHiCtQ1pyV0pymd6KTiFhg n7H0u5UGuqCPP8Nt95z20LFPurO7Ej+J6Nxt2gR0HkxkH924I1bk0cd5vGwz 7Gj5gz7O+RtwJH9NJPhGGMI57sf96N1rszVO1XcIn4jwazQwTp9O0MJp0f5U +8FIylpQl887iakUwl38diIHJ0eubsNIVw+Tr4kVn1BDy+V12WmQ8ht3oV9U Y7EjYIs8bPYKQh6/6YB95Il5SyKiVE3DyK8cPGsZgekhl/Ibw8if3n+Iw161 sP/H5faRH/96IjYXbc68EAc5H6ZTR2/MmH5UZYi3CSM33r8vkgwlKemOYQK+ 5ZsisnBlYwRidp/GbdfsCJ+z0jABNmjvuOfgErAM4YTGgnlRZwV0HapFwAZG aCuaZsp1bQmk+Ro3PYQ8s3orlRudXSWZAG3zCOWJ/x62TyC6SGXEFizvEIGk EwH4t1BjnFl7yD6B/Z3HYXnFrxwi8OyZOO+t/sPHPoFN/wSjSb0/cPd2ul0C itT5yiK0fAOVKd7um9w49Pd/KDhV8ioDBMLeqy0ktcWMEUg9HUAdFjxslmEC AS174pmTixox6xEQGlHjgE96GSYQPGI2MZVy8oI2ASkGwNWcRRD6fl1V3Jw2 BJRxoPTB7jNYWaId/HeetyGgpkRS4x1NvsOWCu31CNhIcO/2Q2Fuq4Gt7cfY l+BA9S+pk++m3bFLQIa56ZYTZ8uaRbLNdRr7jpgvThpbjxgmEFm8KuK8yhoj kHzcX7SiEbMNEwhs2IlmP8WK9AgwK3rKrKhlTwsCBhJo9aSIkw6BgPG/4kKu crgcECtWVnlVzNJGB6a3noFpg/9RFZnDjHWH8lo1opdTKp4k0VE3aGY7dtRc kkwkJAu2ePB6/PbxQBvBjN5ypNcdTx49xfncFeDbdbhYWfkVkMoMB3wxEC9N 76hBrHGGnTm1lktjZmmJEBa9i0sVzFx8pcymEDZjmTii/9nvqCjcJRJ7fc0c 7NWchR2SKEOEUn2CYLGk7qBgVoeItCyh3be0/v7o5l3HxDGG/uWLl3jg6onA uu3tDnmjp0T16IUs8sZRYbaJOnnJbLRkIiFpsxjTei3HD9/S8oxYmd1MMM2D cbr9nXKfvNWOHWFmrDuESmbOe5w3Vpf5Qp1QJOZ4k5AME5y3PALqdlAFaqrX eOQcss3ko36GCUQVrWw5jeoRuLz7JBEIGbfAMIHAJl3x2NlNlVqPAFtbpWm0 +VeGCYSMmitKfczPhoDimtxlCfKURGDZ+qq42WwIKDAygcRDfhTSn1p/TFsC mcDvsw+jVcvVePHipRYBGwmEtmjedCVWLDphn8DJ1YewuXBTXDkVaJeADBNa uArCS9ZQpW6i0/jKAR+xk3+cb5gASwzvuWZljsU+AdbJj53cENi0m2ECwUNn WnYyj4B0TAPxXu+RXSviZrVPQJZayTP0CAQ07oLQXGXU7N8AAeZz17//BdaM XG+fwNEjMeR1IiOu2yUgw/w4cjfGtlugSt1YbazYtNz4etIN2tb0GzRLi4AN zMVOgyg8UdaNGnO4ySI1vuaZj1ZgFG487UsQtXQT9UHEL+vsEwip1MRy498A ASGwErduPvvGPgFawRTKbwSE2yUgwyTlLo7w0rVUphrpNE7cfQoBOcvi7PLd hgn81W8BBtefhpcvDRBgS+Qtm6/C4t98DBM4uDMEwysNRYJPqDYBT6nxoZqd EFXAbIEki30CtAMkLhDbJxDQUYyI78VftUtAhmH7WBb5dkO1sWLTcmN59/zS pN+0CNjABNdsg3tu2fDi2XMbAjbcsMSQhVqChzQsQcjoecTU5T2ntAlklTus SV/89pFZluNhn8D12BR0qjUTmzeH2CewfVsoWtb5FZeD4u0SkGFmNxyLPfV7 q0w10Gkct1OKKj5obJgAO59GqZIcIJdjX0YfEsSL0qR7i/BISPktJg/RgRvJ 5PUJyKwHdh5E4kYu/suMdcc2kPV2kfhiBVdrSTO0EoaZi/W6iMsip1+7JYZ1 8hrb+5ZgvHRG42kZPNlCJy8mjcas2W4hm+PPMNCjwozicp4S9ItqymYQvU3S bK6mtSXbYf20zJFDk9DBiWswoOqPuHUr3bAo7lp2LVkQRg/fhSktpqr6cTPM vSZuWfexMTcw4MMxOP3LJsd078ZBKjMc2H8SLNIl4wzbxZ2WNT/C3vtYVUZZ qbHxjNeBcSZTvRkURV5R2XKRJMrkTXENdTb8ksL6x7fvmYmseUcZr7ul+2bp vJrFxourmRwOYZSZk0PL0KlLxMp6OuTl1Ze78ckW5HkTkkzg6YNHuOuWHX61 PrdPIOF0CHpUn4Kd8qKCDgEZZumUnRTMPX4sOfC6nMY5pcaTW8/Czjq9VAW6 2CcQeCKC0tyQ+X/aEFCciExAXqq8fj5Ui4ACIxNgoRDbPRTSAvsSCIhFU/5i oF0JZJjA+l/QUoOye1iH01i6GRnRRSohOUchVUXO9gnIJymUJFGPQNCQ6XRY JMYnwi4BGSaw4IdY23yEylRtncZ376SjRbNVWDT/pGEC3hsC0Kz+ElwJS9Im kFtqvKP9GKR45seTuw/ESif7BG6n3UWqR152ZsA+AXlUKutJOgRkmEsfNKbo W3EzH+s0FkJ0pGZ7lx1cMUyAjnexTv5hqg0BxabzyB0mJYnsVkNq/I42ARmG nXqQTuSKlR/pNGYxwaWcZXC6eD0tAjZMnfh2Op1QPzF5lTaBvFLjQ5XbUU4s 5GVipT7zd5Jv4o5rNgSV/Mg+bjYfsb1VYWrQwy03D/hiAI35KwfPipW1OI3z SY2Dq7ag7bnbkYnizZ36uO/GXqHZKbjaJ/ZxCxEBfnuvK/5YdFIPt9z8cO8p 6FFrGuLjb4mVNTmN80uN5884jAXleuJGQIR4s6k+7rt3H2PYxxOwr3l/+7iv XwynOJsJqYNbbn6hvajvBHnbtQansZfcOS17ip2z/7R4p7A+bma3bJhGF6ls g1sxWBG3C+5fTqHG7PT2yxcvn9mgt4IQnOt3E2CRt1fn8FJAaiy4a+wrUBu7 /7lgssVtJSkdG8CFEh9hWoOxePDgCVVW00TvwtZiMGzoboyrPZZZ41NtCjJD ISGpaFtnAfZ2l05s8dC/KzVO9I+kWS20fAOTDm65+fkWX1M/Rf4mnfKsymlc UO5U6SgYm9Ce2MPtwiYCOrlxyyMXblwMpUqaQV8lLy5opnZ2rwNjPnbdjsci O6+cdsuisr2Ll++8gxtZ8ppUxo1mvgbyxEKSHNEr/6XTEpdzF2fLE4/M5Mh0 as4IL/MR9WBgr9Fi5buWYBlMegtLwoTPWUmhMFvKFUZmuihM5iTWssLYyji7 wYXRkc+oFsggBZuUt7Ckp8Duw3HNPTc2zN5tekUpbGjIggi9TRP7plJtEBV1 nQTxsk/Eah9atG4tc5bu3sOiyXvwae1f4DtopumhYXkcIlVEEut6fBo6f7kR cz8eipRzl6gyf6ZYQFGJAtsAO1GvKw39oP4TH2Smlck0EkMuU4J23TOveBxI lsJoXmyAVjGJ1rP0x5T9UwLTbdh9UR6HsnAHqF3edYKOUjOvTCdkId0IY+eM tyW24vTtSoksnQ0R6jYNXEwbmXfNBMgAUhck7T1FxzVjchTHmSPRVFme076E xARzCTu/m48FZbrirFdVpATHmu6ITPDmJxnsRmAkZrSZgQTPgjjY4lt1O/J9 DlApibd97Yax2xnZxMCevXFbm0xJiczdtDs4V6gmqYitCiqhc1kOUGkJ6PKO 43TuhtnEkT5T6Y64m9q0RO7cSBNBg6bhoUsW3HbLgZ3efjRc2KeMCqeM5jIS HNvq8mvQBZ/X/hlTmk5CyKTFDNd1G4pWkK5I8QnGhlajaP/xSIVWiPWW7gnj sVlWAjp/PgnnStQhlTAXGNhzpOmatnQy2OmNJwWzzU1KiSlYAUEDJ4uNSnKA xE50p/1jth/M7J3W73IUZHEgO8BtStGmKYMzzbBMg83RxG7+MkKuPgOPb0lb CcU4wKKxeuDxnQc0F9I9gkI98yhrZu1BXPBl1i1XtMnLGG6Hx+Fi274U6jAM +4s1wvx5J+kkLZOMfQpz4CvSdxZKadm9nkfqdEOzJitpFzc5R2EhH2qJwB4j 6a7DRG02ZDTMrqKWbcbygSvRv840YuWBYGPMPQZ26I/rJ/xMR0R44PZtBb4z B6e4WeJJucr5IbPpVhHWowwnS9HY4znO9xmH0EtpePToWaw2dyImFzx++Bgh M5YLyX4jFhY4sfaCUbMNjJVfTsfaBYdJB0n7zuBh2q05DEpoc+uWINiT9CeU T9wPi8ENvxA6sJUSfhlXr95F6p7jSNx0QIgdk1ZvYRsHu8/B//wVRM1ZIZSx XCIrjvaaiH0z/8HhQ9EI/XokwnoOx6WvhtEdJgcmr6f7jVguFNS8uwATVv9z tlDSby5+FvowsnJjoYx9uyCyfF1s/mIcJk08hMR3ywokC5QRRLiStwQ21P0W /b75Fw/cs1FI+uhSeBeOMsTAPTsSdx6ne4wDG3SknmYnqdjgjM1aBLdZJC44 LnaTINsGSdh2jA57h2vrWETrRhna5WP+uPj9FHa7Nsa1X4QJFQeIuhbsTGCM bWeHlquPA9/NxtZ/LyF49ipE/fEPYoQQ915skukzaUg9vp+O+7FJeBAcTn/X fUOQnHAdKRFJgj7YWfusSPx7L9M6Qs7GIGjfRcTOWoqo6Uto5Ib+tAgHNp7D oZVHENx/ItNrz+EsT+o4AP/+fhi75m4TytjZWi8ENepMx02W/vQv/hy6kmkb EZUbIaLsx4gtVQ1z+q/Bwq7zyQgTvcqQN7qSuxgmdPwVP7eZQtvDd91z4IFb VtwX7GlAg5mYUmOYC4ntjN7VJpLdsl9OUtnq4p+SwsVf2mVrirW1KvPEGqkd m2HuuXgSyVTP/FhRvhvatl5L62tJOYo4IS53ScFqVtfsS6YRVrgyQkrWckJg 2XqCn1zz6XgMH7Yb0aVqIKFYJdr25JmMuDiQHzev3cOpk/E4/+Vg8m9sUUAe kczvNav7O9aU74wkwQmxeZndJB7w2TcI7PMjLq7agwv+V3BZGFzXzoUIk2oE 7Rqe1zapWpJTuZ92m02hFD8EV2hIMRA7lbm8TEc0rbeEsSAppggtxjwQlNG/ 6zqsajMe4aU/ou212HfLI7hRJxpjx/tMxt+Dl9FWcmDXIQjtPQpB30/G7i/G 4ETXHxE6fCZi+oyAT7vvcX7wLES06gHfz/ojqElX2o44L1yzslOdRojDOy/C xv2C0z3G4myv8bg0aCrOj1nIluHhM20Nob7U90ca8hcGTqPFUt8+P+Fq5bq4 9FkfcgEBn/TCxhnb8c/kfySTzIbg2u3IJJeP26SYZHi5uggvUgVBXhUxt+fv iknG5y/jxGxS0NbU9j9jdvNJZJFklcJcwsxjSN0pmFBrJHN8imn1/3AsxlT8 wcLcBlYZbVPGNsmMtJPLBJcviCFQFWyPedehdSdjUr2xSM5eSDRJthlTilid 2242c27FPhR8R0jpj5llYlH/lVjSfzn8q7VBQM22TnTMwRl/Tt3KFIQLrfsI IL7tB7J1iR6jaSz79Z0glAmqFigGDJ4B35V72VFwBM9YIVj7vPVC08ilmxG0 1x/BQSmS+/BA3EE/hO85h2jfSHLlKWGJuBV7FfdTbuDevcdDVKtUApo6kv9k qxYJmw8iZN5a/PN3EPb3mCRYW00akiysYnknGxjLSrRHs3q/m1lpTtqvYH0z qtsK/CJ4D9aFaVm9aA2XdXPwR21xrNMoLFvqC58vhyKoVlu6SzKgcRdmHp0H C1JuWXIU22cKnq9KM7a1JApfBscW78K2satx4IuRggNcSI4wZOpSUsa+0Utx /Ps5Ytn4hTjXph/dJMF+BzbrjouCJbK78oKbdMa5zwYg+vPeNAgCxy1CYjfB 6HuPxP4+0+E/egH8l+0UFTxTsMyhU3H5yz7w6TcFR76bRfhO7QrE2b9POdMA EQ+f7PM+hyNL9wu8M1adhd9n2W/pl17ZORz9bSfJ7Sx9M+l3z/nXTpmgpT+O yWXsTxxbginN3Yst4/+UfmmVuWD93H1UFlu9KVJKV5HB/dt+Q32zd9BCabi6 ILDO57hQvyPN2Dt6TafTi8JwNCui0XyuSisce68Z/Osq5SZnycBZ2+lTj2BL h7FsS6JCA8ZHlRY02atlnuZl5BSZk2MmxMbPjz9soeugwdNLabtWcRsxNy0y 3rrxAElCMBDYfwKCP2wB/y8HkT/ybdwdU8bsFqL2kYK3L01HWNKdPciZsJju kFctZtwmeY5jZfIcl42+3RGevYRcRn+xWQvTvCXAKk5DLgvIVVbB9UOVURjz 4VByIaIjccZ1jzwYUX8ypjRhU7k4scXmKokoIftjnmRh55+dyZG40N2fv32/ Gkv7LWFxtexA2E6epZctTJIy49j2635sX7SPPLPfNxNwcdgcsvMjf5/Dmc1n xTEzZzV7niIil/yNiyciEXAsHLGbDiJ+31nEH/GnoDA5Lg3JiTdwM+aquAB9 +yHzJEhPf2r6k9MTjejbixJk9mGB+I0AAa9/LC6eSxDG7h+0c8zO/wW06IHA eh2YT8TsUVuxrNMs6mvWI7fchTRdCOOYW9ldohlFAYnZCrmaBSDzy3S38Na/ lOkG76KfWAQlrBNZZwTnKMM2Z6hse8GGVJbqnsdkjm/a+30t8L3ZZZ7mZfTH lr/lWG1WtYF4IvwWAmfZ3tKEAJhpccN77YVfYtkdIVf+tM06eFfpZqIzgcII T8hVHF07/8XKSPssDkvOkt+8XGrrYtE2NVsBcc4WrLZgRYrPNtb5hqZGfpkL 4rzew6gBm7UHuDJLiU+ZyQs8fUoLC6nhiWSOaaHxZKZhe30RfcAPcYf8kfSH NwKmLkf46l2ImrgQQVOW4tKY+QgePgfB05ZS2cU566VJMwfi95zBOe/juLjl NOFK9Q8XJ8+gGKT6XqJJlMz/6jUy/ftJqXh2934sx/q7yllD2k1ltNy+ch3R a3awBSgnhp/tnEVcQYxfFEJ3+khclKCcJDLiOs7/eRgBK3axUsT/cwBBk5Yg bP0++h0ydgHC567CpdE/I3T0XAQJUsbP+J2kjfn7IJJ/WYH43/6E7+JtiNy4 H7HHAghnws6TSFq3DSlzlyD4j63wX7qD8EUFJiHGN4qtujjLrAkJSXJUsvTL WJksFntiFfmHG/fE7SqTs/xb+qVfxk7iMv3103b09N1Wq4L3YK83GxDKJ+Nv +6QlG2eFQlvLn9JjDtSlIgXc5Ky0dOHU0nfDjIFJ5+RLcOqlpz0LRa5a0PUz Biad2y6utHS3ZNRJAalvv4kkQQGl1E25clJgnLSga2YMzIaoKrWqdGdOLX1q ZAxMUhsZpIslUy4cPFYsV88YmD2i+nrSJKoPJhHNr9RLezwm6cGkzhxkVmUq smqZgsU4S/p9apQlA1gklvIpOlb382D+UbGog1GkRt82z3y1IlP1NeM3F8NK TCdOD2kaTdVXRSAxQkdsXDmdY4UxB4e842CSJymuVV/fDiDPc2fjlKnIjDaW 1MGbjzy1YBo60liSQCl9rW/atimgk93UX1a+TTUhF+XKVeG+kEEwKmNP5cEU kd4UpZF0pMHCKtRB7sSpVU3WdjTRp8ArIHdVaqeJuCcrBXRzjye7cnMYLa8d ffJnCnpDXLtaonBWSGmWaXJoFJVqC+Z8kSHkewVuHELA50E1j1fRiFEENjyo 9u/hsFKl/XmZG69XQGXD1zQFt6vDyOjKTeGr4CugsuFrhSM8qLqp/h+hx3Pn NTJKeSX7Z+Xn3DllmpRrGkRgNTG7aPPgpBgXzympPV7NIJiL0kkSvVVKgady 5crBbdVE1aeER9HEf3byXM3+qZNia+Wn+NYZ0xqFT/qome6yzKnPqxSoM4eq Y+lpFybLSdKkGZzxytRp3zpEV3rWVWlnFQVYQbgp9qhZq8mBxqTvrnLHD6+d dfRgNX8a5YenB14ZL3Ti4XNVal04ECoWXQlfgT4Ptu5bu3prV6/BrqRHzUt3 Qcgao19WyYOHJSO8tSheYGwrjAunvWUrhZzVfO1hn7CG5VgzZaUdVfUGBosu J7yMQG+hQTOrsBrrRhMZXlepAqi9bJQDHjX1dsK3xvLWWOzII70pgOdgrPyW vn1oXqmRJ28ljZflGEgjHKKrRvS2nceDNNZKP73IOCKV+Yyj1O8voz1nQEKe q3lrNm/Nxo6EOk7HKpD9n7Ue6YW4Gjw72sVmqUSGjcPDQRyZbQ2qDDyv8bbf /+/3u71hL6rIMsAxyqHj1qDW6unF3VArh6xDkyNH7USdaR23WHeDsJltDSrP 6oNh3prB/8dmYLHCYXNEwCqRexVb8OBrlNcDWTha8eSUGehvNbl00aLmah+z 5oRigAMDsK8l8CO69d926//FbpXONnKXJZWWtt2eQQeu5xA1HagDmVvmRH68 uYv+rBae6H/Gvb3mldUZKt4eqFEpjKJ6LQbGY4N+1eaUvbW2t9b2eqxNOlXN XRhV6BkzOu3VaEOLyVp9xhFdo4FDZqguONPZIXddjqzK3HU17MGBcHRR3UPh 3fGldAO2o0+XR4O7BPrWQN4aiHzFX/UQe1y1E860pnkc2O5iDi/0tMKm7nOr i25Wy28eShmvw9Rz5raceFjSV6/cLFXjqkuB0GZRrjQDXpVPdTBZTdT6+vS0 T0PVlNV4f9uP/6P9aD4sVSVa9V8TBbC4cvW9cpVTUUCPTMFSy4wl9WCfFbKK CmA+Dtp6ypXaTnwkLX8i6vwfpPXh6xFPbZfZwqjtJNbzWhKgqg+UK7W2mHKl oq2glKloO2UyPolNVe//0bOd/38V0MoW74GcktsRLvOqTVzMm7BrN6sGljic lIp8Wk1cFDJ5XgGL2kSTFyniES5/so/Fmkn27dC7P7PZb6xe5XCksSYbaocZ wKw2dkhUFUwVtbyZIfGeeqgqPp9WEzFxdTWvUMjm1QfiPH9RE8JF4SQTkWpC 5LGvkJ8cRqr2h1jGaZfVYaQqQ5n2+phXeT5uNq0mKp/OnCb6dK1h+cZmANxV uaKpyyQ+0sXquaZqo7xatVZUeO3clas8nFpiifxv7ozBWpXxsMgnccw5HWsQ H6+ns9uHpdfqZrXfjmc0DkHwaLhyyvRpqBByyGxPXisabmY+1HFT4nUQr8MN mIOmD7NqzJPzv2poPO4df8ey4wb03zc5niPRh9D04xl2Zu4cjLweVrHk49SK RuUiY2H/de3PRYsdaeVAA5bHrHrvcE/7Hao5Agx4LO4EbtCQ6JVaBrynFQ36 M2BIjpseb8Dqm7e8kGzVxeqttdJWheMm6JBH0veEUgLrgOvjWbPaKbwHq2eO EWoEXo6/uNyoG8tlsN3rc3ea05SBidmZa2u8pIXnrXhNNK2OlypkEEI1R4eQ OvQgfHUsaEPwo+WCopIEdfZymKADeYM+ItWQM+21eK/yZH9e8mLUjDXpZg6s Og6kt1hYjQP1VQDOiuFbvR5Av0x1rXkt27lalrkpNHjtCoq1sivUfEFBDk6t muHrv1uQB8tbYlG14axF10Ct2gXqkxvE15Nxn8f2XGmkLvi3NNjOEFp1808f rdpOB+0LpZG6UdHCYLtcdtBaCaeJ1qqdhJaWm9kWjzgs0tmVuhusCtfYYDsJ bSmRC3q+Liu+etjXxHUMnDLe8H3bzni7N4mXt+3YuwJgM6ibS+3YNXu3OvvF S1R5GQSv3X+i7E3i5U3n703ihY49W9mf+HZXxU1HLfmbTDF6+Za3LuU/1O5N 4uVtO3XomKwP+9ielTH33tFFKluAv6le4E3i5U3n703ixUMqM2CWVk49+Zgf WWjIj/NNxTiYeWVFDbZ7FVg1d+VnLeztOa9KI7Pl4PFsleqw9xOx4hMjfxW7 6lMzmY4WEc8SUgXnMeO//eqj1ps/Zpzeo/TkuSagT+2OfED2couUsyGagDGF KvIB2QGY6FVbNQFTshfUBrw08VctQKZP+rMGtKzgUDydtwp7xZktRd+8lXCo 73RNQHovRMp9W0D2as+ZM45pArJ32MfJb4g2BzxZoSX8KjbTBGQ6CJu13BaQ vQklOUdhXUD2QhkbwMAmXdnLTTQB2Zt8Aj77xhzQRQTsNZqw3ou/SnX5bWFP Fq2DPV/+yIH99W8cyV8T8WdCtWC/67cVo0fttYGVexOnTydowPIsQaR7Oz4F 8Z4F6f1sGnTZm2zuumW3hWUf9s4v9hItG1ixCXsFIlOJ/DqTNlbgqdneRUil Jlrg7I2JDPya3yUuOAsFYguW1wIPXb2L3lwYeeA8F/xQmx+wuUIHLfDY2Jtk 0MePxZqBuyrgq1aeR5NGK+jlpVSQzxbH3aQ0JHq+iwv9JnBx+I34GTfdctAL 5rVwsE+6iwcCG3ayxqH0PdNS4vajujjoRXvv1+XyEb/pAOEIn7NSC4dCK67A +1wc7P0VDEfgN+N0+TjYdhD+qdiRi4N99hWqj10/LOTgsNX98+cvxILWHEQ9 v/oHEycc0kXkP/ZX3HHNpr5elYfI/4NmiPUqq4so8jdvkj527Q6xgJ686viB PicOffaWH/bGGT36QvBB9FnwodK3Ds1VCpYV3F1gFURpZzLJp7voZdeM4MPk ayLBvGILAycSjcj9+PY9Qh/QcaBYQEwY3UPkph9uFkplb7JkBNibja3Zf41q 21mqJbb2nUu/qLKaQbm4myyqXIo2Wf3fRVrAf9NJc7kc2oLlqs/SJtl0NGrk Xsf6RmvfzlxB7B1BzO1u3uBvYVdGBdDWk6uNnpJyFXNMAI29ObN+MJcL1zzy 0htVMyCGEVUFNu1Gr62CbEvVebKr2HjG65hA7JWE7N1jGRDIAUqBfcbS0LwT naSKZeed4La8srmOXoAM3cGdafoJm72CuGavgWSfVhp8sV5jb8+z5sshAROO X4R3kZbw9T5mRszdhtjJaWuxrGQH3Ey5LVZIe6ulOTjv338ijrw/z+viPOuT SC93Dbtw2S5O9rnpnksZBWY41eBF+Fw5ep5eHntp/EJDOFkwE/ZebV0+2cuH aQrpNswQzvAyH9PbYVWclrt68rBj71BlL2+EPOwsNiLdbGRjLxpk7z21h5eF stFFKmngtZXvyNhlWFLyCzx+/Eys+EQH+dYuk/DLx0OMIz8cgxZ1FyM+PNk+ 8rVrLqDTx3PwNP2xIeTsbW0WmZse8pBxC6jxlf2nDSGn/IvFob3H2Ed+ecdx aixEAxzkfBizYFysNNuwtox2xFUKMuyALwYaJiAa98dcAkpjaZ7DNc98CKnc VG2ss38tE/jnsx+xoMmPxgisazsWc9vNcojAH7+dQY/684wR+H32YQyqO0WP gI1aA/uNp367FRprn4CQkVBjJcsyIAF79TvF8+t22icgN45Zs90wgbRzIQQT PGyWfQJy46DB0w0TePH0GZ6x/LxVL/sEWGMpmbdLQIZZXncgfu/3h9pvvKMQ 0syKRY3HYOGAVWrjnPYJTBm2FeM/m88loGYPUuOpAzdieoNxDhEIaP4VvaH5 xbPn9iU4UP1Leq/53bQ7hgmwt32zfrt+PtQ+Ad/h86ix4B0NE4hZ+S/BRC7e aJ9A8lEpRxw9T4uAolaZgJAYE0xAix72CTx//IRUpJicjgQyDNP/mfeaqP1W hX0ZvaXNiYNZWtXH1FYzMGPYZhVzDvvcxHiVRVTRKlbcOJQPqsGvnIrwmPv1 h7VYXGewQ8wxN3/dM68KU1khpRl7e9jTEnudMFvTfHL3gWFGhIiKJrUHKTcM M+LMqbVcWTILxOkFy5Sd7zhumKvzhy6hdZ1F9Ep3o1xxM3h7fSePo+CRcyyY c+hmTF6fyJKkXb6JRaW74MysDY5Jompaj3/m7FkGEti4iy3/mWjrsjgvX7xE OtHrrD2ojB6o5RGS9g8xscsSjBy0jX5RjSiRkRzV7jiJz1cakSWrq7ipTzSP euqxuX74GqwpZxZAGmfTsVEUXKU5bmbJrRJqpsNVUP+JlnOVca4yNIqYE3nk 5IaHqTfsMxfnvZeYE5LsDDFnbGCcPxmNxvWXqh5Ej6VHN+6Im0Gf97dg6VVO i+sxdz35DtYVawOf8UtsmFM6X7qNAynZ30VAFXGupsbZzJjLkNHesc56m3Ia y+TnjNuFjh022JDnuW+ZQFTRyvLegn0CBxbuwObCTXErPN4wAZazMTf0Ut40 0CMQ++cuMrjwuasNExCic6S650FqQJR9Amx1ghLDDgMMEwi9lEYrNCdPxGsT kA4wIDlHIYSWq6fqM6sNAcVsZAJPnz7H9sKNcLL3RPsEgqq2xMUCVfQI2EjN NrNDyzdQYZroENj6bwiJm5JyzzCBSxUaIi2blzECMb6ROORVC4EzVhomIO97 3Iu/akNA0adMgM20NPM17GSYQJQQ0kdmK46QTce0JcgiNxYGTXz+Mqq4nvYJ pKc/ReOGy9mqjX0CAa1747l5eKhDQJZ6T8V28Ktk5nwa6xAI/2UdLuQqh9D9 FwwTYCd4pRU1+wTkDQXvDQGGCbCRzDo59XSANgHpHbo4/F4LBFZorHKTxYaA jWFcOeADi1RMj0DQR23Z/p+aptoSsJFAaIuzXlWx41sDBELG/kLcJMhHMHQI yGod+P0ODPlhhyp1I464MoHb4XGis+s61DCBY51G0qTz9MEjGwJKY+m5EjhU oTVWtZuocuNhn0DotD9I6jjv3fYJLP7NB+0aL8ETmRsDBO7GXhGl7jzYPoHg RRuFcOIdBA2ZbpeArNarOYsgolRNVeqGOgTuRl8mcWMKVjBM4GCnMfilUl/1 jAMdtjD6VBheOCHdiobLuYvLZzfESnf73Bw5EoNWQoIX5Rdjxo1jm7V6+zl8 TgPafkNx3r2EZC1Obez9VswV8prCZCHClLMkxYtTre7Z02Mp/q99hP7i7DV2 lSd3PwsHIotXVRX+fgZZssk2ZArM5fRq8wcmTzxkmKuk3MVoiDy5+9AwV+5a tiVF3vAesBgnCn6keg43+4xc7PA9jY7opZscU48bB6nMSPjPawhp5G/ehhm5 fyWN1tCC2vYxM53M27Tkc8qOW1CgUv8Lu5zKVhj7bnnEFyhLv1SVad7eyOux HBKq0LJ1cC1rfhWVmPQYWVEx5m52j1qGH6qPxcOHT8XK+pzGMjcXB8+Ab+6K iA+5bMvN63Y3wYHJ6P/hjzi/Yrd9Tu/ceYSmjVdgxRIfC04dfwqIHktsYN9x y4HQKk21WcopNT5Q9ytcFXzNS3nKcHk1lmzcjcxVYPVWYlT0WDqpqr70RG0v cxUyai4stnOMc2XX3YRMXSriXrnFhhEb9bBVA7b2JqTSGVKPnrt5mHaTBrF/ sx7ajOSSuf6wOanv6X3J84oiZvYZCb7dzhnkTesDL1/CFCd2M4TkE/D3B5Yt A5486aLDe+i6vZhV9mucORJpy3uGHNDxf87SekLclkOmSCoTFP38ORAcDKxe Ddy6BewQol0PDydGibmjO3cUNJ10mH3+/AV6fLocazpNs2CW51pldh4mX6O9 u8Cm3Ux0IpitAgnKQkQE0Ls3kEvA7ulpEnkRWN27F4iKAkaOBP7+GwgLgxC0 8XSYWyIR0OpriiGUHVQnbbZk42UnLm555KZEJIDKBI3fuwfs3AlMmAC0agXk ywecPQscPy6MHSEEyCaY9hdfABs2iOy/fGnqocNXyskL0ob5AMN8hUwSz/LF LNtk8pP5SkoCtm0T+WrTBjh4EAgNpXZwEcytcmWgb1+xh589Y+Zn6sOhIT2E AhElqgmy51KDinfs8/Xo9n1E5SiBLT1mmM7I3XjjBrB/PzBtGnD4MJCWpnaj zNfWraL1+QhZYnr6dzpsRS7aQKuoPiMXarGlOEPZIufMPo7PWq5E+q17pmMy W3fvAkePAufOMcsRwo5yKltOwtWkSSLlVavENo8e/cAhIbPFlvxDc5ZGWK4y drUlsxVxKgw33HIipO+PpoNyLzKncOWK2HLoUKBCBZEdBt9RPFOEMWOAuXNF 9u/dk54G7krjJSXlHrZvC8X0aUcFVC9MvBGRV6J/9LPBEPNB6Vgjn13ZUGO9 yuJqbvHmlb30LYRw27cDAwcCtWqJxt+4sQj11VfAp5+Knc46/8YNiaw7O74j DN3rlN2sXnUeUyYdRt8+W9Ci2SqBSsP6y4TvBw+eKPR5vkYWgS0q3nPLhtBy 9Y2IEDB0NkmcsGababssQny8OFaHDRMmemGm//hjVYQcOUSRmMZ37VJEuH37 EQIDkrFzRxh+X3yWHQxFl04b2SqTYERMBA9acerW5S+MGb0PS4Q2u3aGC27i Mi5evMrSS17H5JPZFDIwtk2c6Btuemlfqsf3HuKWe06El6tr2izb0WUh+d2y ReS8QwfVnhi8p5C21a0rSsw+bCi8eCGNYnfGnWCCd+FzJhF/bQzE3NknMHDA drRtvVbqIHe0bL4K/fr+i6lTjmD9ugs4djQWcXE32YKqqZeOaPeTUtGnwVyM G3tATzR5WO3v/hPdJxKx7ZTJm8qEkXv9OrBnDzB5sujI5s1TR66b8Fezpuik Y2NFZ/f8eQ5JMiEaRkT4NRw8EIUVy/0w4aeD+LrnZjRrskKRrH27PzFsyC7M //kU/t0SAj+/JKSm3qepux+HVekxP/h3wT6cy/MB4v/eJz4PQ1+yqBMhlPac rdHOtFaW7MED4ORJdjJRdJUlSqiSOQvT6KVLQEgI8PvvEPhiUYMYvbjRgAkJ SSWL/HXRGQwftpsFHLJQLGb+qvs/+Gn8ASxb6ou9eyIQFprGjkCaftARio0v ZlqxBcvrCSUPR/+qrfHE2Q0PE6+alsuW+OQJc57iOGNTeaVKojAMns1RTKDO nYGffwZOnGDCS4G4mxCEpCNAGC87toeSVCOH70Gnjt6yVK1arkb/77Zh1sxj bLWTbRPgcuJtwShemIZz2PSS2JRPqbDjeM9tpFJ8uyxV/O7TNEMHd/jOtITK soldtXIl0L8/UL26aHje3uK48xIItW4tTiG7d0NwF56SAbLYiHHIOGUcM86Z BOrQciOp2GnzmTNEqdjxU8Gtj+VwKArkQudQ2NoYOxsnTHLPtHtKHoena3yO eR/2Z4vFpgWyTGwCiYwUveGQIaKPWLpUNEfWYywIa9YMGCvwEhgoy/To0TMB 6gbJtOHPAHIJfXpvEQbVSkUmFvsOG7obC345ha3/XoL/+StCHHB/EofDAhKH sRv3YkLF79lCpMmAQMz5tKz/O3YO+c00TzY9FhKx0IIxvHatOM9nzy6aXtas orv39hYxJSRQqOYuSSVMnnRHFDsXylwFGzndu/6NRg2WSS7enV2T22cuno2q A/ujEBlxnZLuGRxe35V4XTjzEDYXbY6kncdNT7VFkwfhuXqdKDi+cfqChNZV tDM2+e7YIbb+6CPVVbgK9T/8IJazQFl0gm6SZMLoEMbiLXLZa1b7Y9LEQ+jV YxPzEYpkzF+w24mYgxwqOMPVK8+TZEJfS9rlSeaCe4kpuCkEzOxE59P76U/s C5caEkf5YVSFuqbJsnBpacCFC2JLNml5eanC1RJP4+O334DFQhjs6wshpHC1 GmAnjsfRKd3JTLielsLJMzPrUta1LBBhXc3ipUUcVgtKrIbPX0d+IKJCfZOO ZLKXOddhkBheLVxrGidbZHq62IpNzSxJKF5ctMZixcTyWbNEJ8k8PEsqHj6U sk1JtMt3aJz9uf6i2TizFW38uANYvswXhw9FU6zFpmU6cPoqa0uFJMEii35I TF/sOcr02J4eXPD4wSPE5S6JjdV6MD5GUnE2cTBu2iT6/u7dgbJlxcHJyidO BMqUAboIYdL8+WxekLXAxmVMzE2STJ7CmaWad7A8Ln8cYzYuI6/TwfFZEqeG 1rQMrBkVkqR8cDlZcL/58cAlC0vpHmnrRXZw533iidOdI5aahsj2Iafg8tSy aJEIxZJKhqOgYIzt2wMzZ4qTquCxnMzsIyHhNt2/KY9rppkmjWzHNTN9Zh9M M+FCQMTG9c+WcmZwDa2wpI8bAeF04wC75fVu7JV0bX3IXnFHN3FWjpv2q2kA lbmpawDMS2/cKEJUrSo6A1dxRho5Uizetw9CcC3fI4abNx9S7LbRO5CyIWmo 8JzAyhXnyQmwOYTFDr9mUBM2S3eyMtj+xdECtTDy23+Yqh/aKEMBkh3poweP EVGgAt3udHP9pr6yPtjgCA+HwK4oNAvhc+YU9ZFNjETYh6mL/bElEkGF7E6X kOAUYbIIw8IFpym+/aztOnl2FkIqZQ5joTHzGMJYWWpfDU48d6LlP4pKsrGh 27/aOASWa8C22R9om0ZBCSLBJ5TWbh4LE8XTO/fp/msWSbNJkH3WrAHq1VNH iZeXWM5Gz4AB4oKWMKqYUpm1s+h3ye9nMXLEHjVIdkPrT9bg+/7bMW/uCYr8 WeQpxEerM2VcFJNECRo+W5xESlZH+vXb97WFlz3L6U8H0H5cfKmqePn4SVcq zs1sHfjpJ6BFCyB3bjH9ZrH2L7+IkdvgwRT0PPEPIOfHhjrrYOYUmXNUAxk3 lnqj3zf/UsjJxss5IU9NTbnvLXFlaGnUgA6KSxIFD51JOkjweg93IhPvaetA HEDOODNgOkFEftza9IWsALZEycLr6dNFn1i0qLjYxHwnW1iqWhX47ju8XLEC SdGpOCrEOytX+NHcyEa+mqy7M8dADmLK5MM0t7I5lqXAbB94k9LD2jerWXJd Qu7r6ctpR39GvdEI2eN3V1vOIhLEiU+/x8Ty32HdqvNsLhAfPyD4uORkyzXH 6GhxrY+hYKtDbO7s1g13giMRcDoa27z9yYr7f7uNZerm3p8FQ2xmYMERC5JY sMTuKvfhcFVS4ir6YgL2FGmIh84eCBg66449OVxpCYHlNtsLNkRC5Xp4ee++ qYVUR8KwfpsyRcxoz52TojsPZUHwyfFTiPKLxpm53lg69zCGDrZwWMIlpRNs 7WXfvkgpxHnhz+GolEQ15vBFhAsOlamMHci6E3vVdEsU5JU33YqaSX2k4why ValepfA4NNLUSJY6MVHMRZjEV6+ymVyVWkiunq9YhdiQK4gcOAG7xqzAlNE7 ZSuVR+knLVZjQP9t+HneSWzZHIIL/ldYhhzM4UjsGzfayQroOpRudVlc6WtB 7eGMyxtmgmdiLFRckvX42KW45+JJSwFJ85fT4hLduujE0iymZLbKyfxW3ryS Etzxcvx4XI6/iZQ2neHbbRRW9V6Ib7us44YvsgGzYXpVGKZsbSacw9B7khqu HDuPQQO34+8iQtKVqygiJv/GTkWKS9TO6mrRzZuSvWTShmIJSSEhBy7iQInG NIAiS9fE08BgE90HzzZA2BIWW9JiH7Zi8MknQP78ZKgvv+kn2Mpd3KzTFNGN O2Bbix8wuOZ4tGq4xDqOmTD+oBLHyMlMrMqSYtPi9rU7BVbBk5fQMQlGigUa ga2+pu2xv+TefPxY9LJsQfrmTZFFtmN1+DAebNmB9HXeuHbkLGUl18ZMQcrg sUjp9T2ufNkHIVP/QFivEbhSpyWSK9dBcoWPEPVRKyz85TSCa7XB/Wx5kO6R DS+cnHE5f2mafgILVyNewj7r86r9YBOKlZBM4caNh1hZtTfuC/b5/B1nXGnd GS8epovPKsouBtXsw5b9e/UCqlUT13aECYb1xL3KNXGzRHkEVG+NDXW/Rb/a 09RFji+88fmn64Vo8wj2C15JSjmSOIYhnnHwwHNhfF7oMZJusaRDlq5ZEVi/ Iy6dpHEqptoFxRUYlhQzIxUS4/vhsbQGfXPFBlxbtAKpU+cjadRURC7bQml9 fPfvEd+qC+JbfInEj5rjxLfTae5PLFsDqUXex7X8xXErd0EcbtiLVgqfubiZ aEVO+N5W7jO2HIUnTnKZF7yLfkJHCuk2boFN5uDYAF9d/FNsK9gIsVkL0xHO i7nex97CDQh+9Ye9cKR0Uxz64FMcqNoBm5oNoiBz/Vezse/zEQhYut14HzsU Z5aWTDzkaAiOVGiNqx75MPjzJfD5agzub9nJRpxkXtnFgIF9WCbKEq5GgsMu UADPa9el/rvxkTBqc3shtmwtHKjSHhOqDjGZh80shGSr+8yxsgXVBw+epHFY qij1d9SyzXRX0zWPPHS38bJKPRFUux1CxszH1QM+4u1RhcWBxz7x8Xh6KQwP T/rg9p4jSDsTQHNd0q9rkTBuDmKHT0Vsv9Hwm7aKVn4jW3al/r78QR0kvV8T Rz4fghnTjyKlQCncyuGFdPdseCj87azUHl07/8XMTun3fwo3oz4WEliprBQ2 SWXX3XJRf6d45BW0mR+LS31JMeO5AtVw4d2qOFf0Y5wq3QjLmoyggbynTg/s rvc19rb8HrvaDsWGwcto6W/30MXY9N0CLPpqEQ7O+xf7N/iQvZ7bFwR/IVe7 dCmVlpmYT2c7Wewoa3r608qZ6ZPLyENPSJeP7b2Efj3/Jgthdp3umQPXWrbH s0NHxNRDyNVTU8WMXDYSti3E0qzs2fGsZGlKMRMatcMjz5yIK1geh4o3wvwy 3Ultzer9Thk+M5QRw/bQmcrdu8LpWLtgKKbbHPbE2+Fd8ODmPVLNsbpd2RkH OeNNyFeaHo8TOGExWQJ7dJt4j0IxcVa9fZs22O4nJuPmCV/c+n0VUn7+A5dX b0HsrKUI+3MfTp2MR+TQqYjpNwpRX36L8HZ9cKr/DPIQoTVasaU4xJaqhstF KmBPgz7kIZLzFCfLeersSpraVbwZ7QEJblRxHIIjYFLfdckqGVAxiv9YWWS2 YkjwLIjI7MURnLccVlbqQQZ4vGwznCjXHD6VPsHxmh3xV6fJmCUkIUfbDcbx rmNwtPdknBgyH7vnbSMDP714B855H8eF7WcRcCQUEYFJNEyZa2abNMxghARb fKiRY0c7DJiOeK9GTmzb6I8/O07C4UJ16GFKC8t2x/hea3DXMzfSqtfH/QFD 8JKtTbJVPrZPw04nxMWxaV5anihGHUVbImx+ZXUsvD9wQLQxtrbJrtmnZk28 9MyKF8IfU/zTrNnpaVC+DTrjVvb8CCxQCVuKNMPc93oqNvdpm3W0YTd3zglK 506ciKO1DcFYHnLEEt/0mZtN/QjsORIhFRvRo8YeumSBX+6KhJbtbd91z4F7 7K6Yuu0R0n0oLk0X7CnoKtLCEvAsLIJ5LZP4BqNCtND5KCYBD4LDcf3wGVzb d4JGdvy+s0iYuwzxUxYhfuxsRA/8CYcORcNn6mpECHYY+mlvhDbqiNAGHSjO 3d15PNliXNFKuOxVGnHZi6Brl43Y/EFHPHT1lM+mPH3HRTzzXvQTk6tUJtue 4LykILMorc6xIJA5r9A879O6ZGS+9xFWuDJN5+yQ9xHBDn2qf4ZTdTvjVIs+ 2PrdfBoax76biVOD5sJn1CKcnboKZ1YfpBEavPMcwvb6IkbIVxKjUskW2eTM bJHlj9+YGaNDaaR42jcLbbD4nU3E0kUnMezzxfSMt5isRWgWZiYhpJjsIK6J vVOWJcmUFUp/Pu81IvdzKUcpOmvwb6HGWFi6C8ZWHEgPFPvi8/UkNEvW2KLh vr2RtLMtCCBtjVnyJD5lqxQlFkkXo2lVwefLYYgqUJ6OYj2UAhkW6bI7y7YU aiJFDM5kPyk5CmJd6zHY/35r+Jf4GJGVGyO49mfw+6gDRQns4XqBjTohrkBZ +DToivjCFejYdGLB9xFf4H1c/KAp/Jp0R2ShSoKvaulEN/DnwrFeE7D88ynw +7A13bTF0IZXakSJwqZWwxFZ7ENEF62CRMF9JgmujJ03+LtSZzxwy8oWlWQz Ys6a3XImHXiib2ZCa4u11SyjSEiYs9Oy5KWBt6LGN4jJW4ZMKqR4DZwqWFMY jDuwsdsM+DbuDr9mPeHbfiB8Ow+l7b1DC7fDf/QCRH8zEhGjZiNs7S7y0jE+ ETRiEoLikZxwnW2XkUmxXGeSaFK8DFycPwrT8ucF/6vYsTUE66dtx4xG47Cw 3jBsqtwJfnk/wP4CteGfu4IwwCvgWL7qOJOnMpaU7Iif3/sKG4q1wvj64/HT p/MwVvBrE8bvp6UhloUvWniGVpjZcuK1aw/Uk/IuHGbEZ5LmwO24ZCTsPU0n Ck7P/hOhpWshqEZrXKzbAcFCMv5Hh2k4WKwhonOWwOWcRZGa1QvhOUuJqnWm USsZNFsDFb7LkqGzc0AsLGF/x9+thQVlv0JylvxI9fSiI5lsdLPt/TUNfkCc V1mygoji1RBcrj4mTzyIP7vNhH/djmK3CEbFuoWN9J1TNsK3z0/wHzqHuiZw zhoa6YH7LyJ04yGE7T6L2NOhiDkfTaP9uqAH1jXPnr1Yod0zH4llghd+huTk u7TmTjV5OI3bSY3v3HlMjdlG/Slt3PTtyCNPtQAtKxx4yKo9QMcoQvlk/KXK NFs7KxTaWv6Uno1UUmFEATc5Ky1dOLX03TBjYNLdcCU49dLraUz8943Td/2M gUm3fxVXWrpbMuqkgNS330SSoIBS6qZcOSkwTlrQNTMGZkNUlVpVujOnlj41 MgYmqY0M0sWSKRcOHiuWq2cMzB5RfT1pEtUHk4iq72WTEm2T9ORvZw4yqzIV WbVMwWKcJf0+NcqSASwSS/kUHasLTTD/qFjUwShSo2+bh6pbkan6mvGbi2El phOnhzSNpuqrIpAYoUNWrpzOscKYg0PecTDJkxTXqq9vB5DnubNxylRkRhtL 6uDNR55aMA0daSxJoJS+wsxqv2Am+0fdY+XKuMNQYba0Lph0d4pwNVOEn6FU 0ba5VderI1l6pITZoLBSUgmDiFReZosYpysFdA+sJ7ty0+eF44JURoo5jM8Q S66WOqSrrPYp88CycOlRr+QzSEWzMR+32i9GJeA1tsGtGo+HrsA0oFQvXNwg mA29WQoeV11ACr3cFHqlDILZ0FujhVuVpd4r4dF0efYwrmX/nAxibMBp7Kao iI/RSekeVY91OU2yKOqQ8KxTCjw50C6WRifBKPy+VodqU0CnUlwVBlsrP5eK 9WsUPumjZj/LMqc+r1Kg+icXRUsaHldzwuaVOSsi8eYLJ6XWWaGqOcO4KSam WavJgUZY5a5yxw+59GYeNeZ0iB+eHnhlqkY0dahy4GrZcyqEikVXwlegz4Ot +9au3trVa7Ar6YUn8ovETWbzjFU+6mHJCG99wqrWiS+MC6e9ZSuFnNXc5mGf sIblWDNlpR1V9QYGiy4nKg09FfByQ55qeTEu78oqO7fqKlUAtZeNcsCjVvet sbw1FqPGIr2nhudgrPyWvn1oXqlvw+atrvByAh6sPg19WPVFw7adx4M01srq ylp3GUakMp9xlPr9ZbTnDEjIczVvzeat2diRUMfpWAWy/7PWQ3m85ihwtIvN UokMG4eHgzgy2xpUGXhe422//9/vd3vDXlSRZYBjlEPHrUGt1dOLu6FWDlmH JkeO2ok60zpuse4GYTPbGlSe1adevTWD/4/NwGKFw2bb2CqRexVb8OBrlNcD 6gq7WubJKTPQ32pyydsWVKclfcyaE4oBDgzAvpbAj+jWf9ut/xe7VTrvxl2W VFradnsGHbieQ9R0oA5kbpkT+fHmLvqzWnii/xn39ppXVudqNE+pGZDCKKrX YmA8NuhXbU7ZW2t7a22vx9qkk7bchVGFnjGj016NNrSYrNVnHNE1GjhkhuqC M514cdflyKrMXVfDHhwIRxfVPRTeHV9KN2A7+nR5NLhLoG8N5K2ByFf8VQ+x x1U74UxrmkdE7S7m8EJPK2zqPre66Ga1/OahlPE6TD17bMuJhyV99crNUjWu uhQIbRblSjPgVflUB5PVRK2vT0/7NFRNWY33t/34P9qP5sNSVaJV/zVRAIsr V98rVzkVBfTIFCy1zFhSz05aIauoAObjoFXPRqrtxAc38yeizv9BWh++HvHU dpktjNpOYj2vJQGq+kC5UmuLKVcq2gpKmYq2Uybjk9hU9W74XKbpnf8HSwND 8A==\ \>"]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Outer Solution: Matching ", "Section", CellChangeTimes->{{3.414200306241208*^9, 3.414200341859481*^9}, 3.414200537524205*^9}], Cell[CellGroupData[{ Cell["\<\ We have obtained expansion solution for the inner layer.\ \>", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414200355318046*^9, 3.41420041341429*^9}, { 3.4142005036045*^9, 3.41420052726393*^9}, {3.414223480759639*^9, 3.414223494569611*^9}}], Cell[TextData[{ "\nHowever, the ", StyleBox["magnifying glass", FontWeight->"Bold"], " can only look at a limited part of the solution, i.e., for ", StyleBox["\[Eta]", FontSize->22, FontWeight->"Bold"], " small.\n" }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414200355318046*^9, 3.41420041341429*^9}, { 3.4142005036045*^9, 3.41420052726393*^9}, {3.414223480759639*^9, 3.41422349456978*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.41422356060781*^9, 3.414223566789516*^9}}], Cell[TextData[{ "We need a ", StyleBox["telescope", FontWeight->"Bold"], " for looking at the outer solution, i.e., for ", StyleBox["\[Eta]", FontSize->22, FontWeight->"Bold"], " large.\n\nOf course, the inner and outer solutions should match up at the \ intermediate location." }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414200416209436*^9, 3.414200454528039*^9}, { 3.414200584369573*^9, 3.414200603318031*^9}, {3.414200692294842*^9, 3.414200714468395*^9}, 3.414223471663019*^9, 3.414223566789681*^9}], Cell[TextData[{ "The condition we use: \n\n\t", StyleBox["Limit \[Epsilon] \[Rule] 0 ", FontSize->24, FontWeight->"Bold"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["u", "inner"], "(", RowBox[{"\[Eta]", ";", " ", "\[Epsilon]"}], ")"}], " ", "=", " ", RowBox[{ RowBox[{"Limit", " ", "\[Eta]"}], "\[Rule]", RowBox[{"0", " ", RowBox[{ SubscriptBox["u", "outer"], "(", RowBox[{"\[Eta]", ";", " ", "\[Epsilon]"}], ")"}], " "}]}]}], TraditionalForm]], FontSize->24, FontWeight->"Bold"] }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414200721849345*^9, 3.414200753920838*^9}, { 3.414200789224611*^9, 3.414200985217729*^9}, 3.414201017612256*^9, 3.414223471663174*^9, 3.414223566789809*^9}] }, Open ]], Cell[CellGroupData[{ Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414223530848537*^9, 3.414223538722352*^9}}], Cell[BoxData[ GraphicsBox[{{{}, {}, {Hue[ NCache[{ Rational[1, 5]}, {0.2}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c8V98fB3AzRFYkmkaSlAYq4i0jycgqKqMkUfEVKlrIyNZQCRVRKPNe 2dkr4zPu55OVUfKVQvlW+CH1e3/+uo/n43w+95zzuufc877yrv/YnObh4uJa z83FxbkePD3GrP1irCf94mEl58pnKOczJKsEeWUhXErSSrDzaVIqKasBTD8D Bz1xDTDr7CYeyxrB2khCpnyJEdi7zb65K2sH+8oHiz78tIUB9VuGcbJu0FKY 2hNGOwVp0ociomX9IdYCZj+F+UGIILkxSjYM+mgRFU3TN8HhaHrB1H+JYH9B mr77zl0Q/hviaLL2KYhKTpMiYsmwwfrbWENMJnwJsLdKM02Dy7Q9kPQrByJ4 9T70eGSATLHEIDd3ASif+scnfP45lAwbdtD3EjB4Ten8vFc21J99vOroRDEE vzdQ84p6CdPKumJ5XqUg/PGExDfDXOCZeyW+akMFXDLYG7Mwlgdaf0+U2OZX wYq9xIlv+gXQEaZBa1atAXr412MJGoWw7vb4XM63WlBcZr+3o7YQxmeHBt9t q4dg+Q0RcTuKIPNrZZtofAO0RoSHWj4uAtE1Wd9HRhphua+vls5sEcR6vnZP U2qGAu+5HDMgYEb/1YhHUAuQZ+5k8d4koCpzPOVyWAtspf3+8hl9U1DNNiKq BeTTTj1qDyVAlJFbl3GvBY5+3KJ/J5wAZZf8J4NZLXC4dKZYOoqAI9eLHOwY LSA0xX+R9zYBr8tLO0C+FXQKXVf4PybAf0dj8YqGVuh36isrLSHAXWN92p3W VrgyFn40qpQAB61rMSK0VvjRt/LEsTICdLQ1XHl6W8H2kGLafDkBPAaZYt++ tcKbiiW/dr4hIME67GyT3FswCvNRi24g4KWP0Xp/37dQb5T8qZlOwFB+YwxT vg0ukU+l7owSwJjkm9ixsQ08Vk8Z6XwmoFbN2DxRrQ3WJAz9N4JOe9kkYr+r DQqikuq1vhDg+qI5rt+8DRgTR/azxwkYfdya8PlyGzhn1y+bnSJgMrbj3mJn G2gkyZoPzBOwcJadsulKO3zyb8rcs4wEOy2nO1uD2iH854PISnQu92jEzrB2 mCMEBXRFSXBOmr2gG98OEYs32XpiJNQ1yR2wftYOVRGtJboSJNxaf/JXQFs7 8Nfy1KpIk7C8a9K8Va4DfjDOr369moTN+wT+uFd2wP9gx6VCVRIKX77a2FPb AYOr0w0UN5OgIWVlbdrcAcZP7mXeR+/9nJS5mdkBK5qoTYFqJFjGqZpNjXZA 8CNn0NlKgm+vRVKgZCewCkIaXm0nofxC4o5Yz04QvRp1B3aToPd+t+OidyeU fPrp8xxdbzQQ7u3fCXPWahNL95DQJqPcaxXUCYwtbSVsdP+b0iDp+51QqSn0 7JQOCVxL33c8qe2ExfS6eW89EkyeyZ8pkqHB7fRKbl0jHG+SqHLzahrs3yLS chu9Pn5hpE+eBh1Dqtoj6PnAd658ajTo4vFQjTYmIc86ytlenwZ2sT+0qP2Y D/d/hxc9aBCdmrLe1pSEIZdaI9MKGghs9dCUtSSh43Aer3MNDRp/JCy4osvM kut9G2nQbinun4u+u8tfP5VGA01G1jW9QyQYi6ns/T5MgxPxQlPOViS8qk7Y eV+YDtet1t+4Y0PC5TUuCh8d6bAhMF2l+ggJrlbbjvSfpMMWNwvtRbRlKHd0 tzsdQgsv8u+1J0H5S8Z/nT50SJ0qay1Ds4vHaivC6GD+8OKSAgcStpn7uiTm 0oFfbiYw/hgJY1fCU01+04H4+1pGzpmEr0c2e6RzMWD/keJEK/SJqeU863gZ cHaMix6BNlP8V1NOkAF9PgtXf6AVom49FpdkwJAAUdHsQgLDruP84gYGZHb0 jrieJEFt4rBwtwUDTPVESs+6YR525jXRVgyI4K7heYw2fGPgp2fLgOuEFh8d fSxe/f1zBwY8UeTbtOM0CVHbhF75n2JAieufxV/oUf+qg5KBDHjW5fPr/BkS 0hYVoi0yGZBnzxbYeBb7c5fV485iwJpAEysrdClN7EdxDgMijXptAtG0p7+P ri5gwCpyKKINvbiva9N4OQNmbZTyPc9h/xFRbyPpDJi8W7Ei5Tw+b7EpwcZ5 BvDJG2i1e5NAvYm+ZbrIABtvOusL+u75DUvofxkQVSe+W/AfEiTbjvH28TGh 6vmKw0YchzctfhdlQvayv5/K0eILyT9WKTKhPevRuWQfzCtH80L6BiZYBLkH v0bfdmB8V1ZhgiDjhhMDLVbCP7l9CxNMNs348F8gQfSCz2eTXUyQOVL59zxa 5LNxv58ZE0aj7antvrj+7n84NmfBhNsJ4ZdN0bFGV3tvWDEhVjlm9ARa+Flh V9RhJujF3lBIQC91WsV86sIEHrt8qS9oQdZUU7sfEzZ9tJy960dCa0iMkfUl Jvy6ZG6chY7cptzQFcAErYJnzpVogfjjtR+vM+EGo/TnMHqJaXPF7C0mnOeW e6nuTwJfTUqBYioTwh8aOdag+/YaHRh6woQlJoFdTHRBxcSH5HQcn2O81Aj6 WImupGQWE7q56f0CF0koyhvy5yKYICzSn2aOjtgcuayqmAmHNu7XdUI75mx7 cbmUCduaAp94oQWfh3R/q2ICS7CoIA7tnKqoPdDChHrZcPF2tIZcB5XUxgR3 mZNdvWihJP9zdp1MKNw0cXIMXXyvKbWdYoK0WUgb3yXMK+bM3/IBJuwvqB3R RpcFvmp88JMJXmu2HUlFx8/aOtnMMKFXXjMsC33q4u/pZXNMOD2TE0hc4jwv i43hf5gwdMK6sgV92uN7lJ8QBd1BSanf0dqjDxXURShIyV4jNIcWd9Ov/CpK wdS/k7o8l0mocrkzcVKKAk+Dfi4ptKT9zkNW6yhYsnL0mwZ6jP3+s7ACBYY9 5Wl70W9swoJblCj4nVq4ygjtYfmuSE+Vgvvbfb1s0Hod1w/Oq1GQ5OJrdBS9 /KDyp9fqFJyz5PrXBV1tfFlqiyb2l6Ieeh6d2LAub2wXBYnf+UN80Z77Wo0z tSlInmIdCEBL6cpeXqVPwcyRWq1Q9NeKOrFuAwp+HlzuFImu3X02+64xBapC LRZx6HMalb1CZhS4+pfHP+C0M97lllng/ZnX2pPR0l5TQWesKOjJn2Y/Qdc8 36DcdJiCZrmzli84/Rnoz/k54O8zH1TncMYzeKxD4TgFdZl9C7mc+cjc9g0+ QYHd9aWDBGf+5Etj9VOY10/l0NecfA41rRw8TUG1bNV0KSfPiaHxWA/MS2FY swJ9JnK+WuccBRkaRYZVnPyVpO9+9cJ2j33rqtESdeqnH/lQUEN72VqDdnc6 uPuAHwXSnvz6dejKOTfh2YsUPFH3DK9Hiz8IGnweQEGA6LekBvTpHclFdlcp MBp9daURXUErDuO9QcHW2ArVJrTYObo9EUzB5NvtORy7CXxVPRlKQbvTphmO yzP4/ohFUJA/XybRjBbVX8esjqRA9sD/Fjjtp/r3ZHrFULBz+E8xx2UBdpdX x1PQcXRkL8fLpP852H6bwrqo9h6nf9eiqDVX7lGgMZFTzhlfqUXmlMoDChSm yvI54xf5Wt3QnUTBxww+P878Tkb0PohIQbtkLqlFlyj88tR8QoHLhQJPTj7C NaK6I2kUnJHTTeXkd+L4JvF7GRT03nF7wsn39azhp30vKPDl1fUpQy9NdC6Z yqagLWFAogTtsi0w6ukrCtzMnUJJdHHHPUfLfApyDFmNhWghz3z1xUJcX/5H uvLQZPqnd8dKcH5mHzyz0IJ6f7KFyin4XiY1kYF26lt5raySApPvRXppaIHl lgor6igQooUcTkI7FnhMNzZQYD/6UTYRXWQW2urXTEFRFn9BAvp4WJk3s52C 4LgfZhHowvWsfcE0CthtY7YhaP43k1LqTAr+DP9Wu4YumFaojO3C8Tr32FxA 856JEzjwEdefMe0fzn5z4M3um/mEeblv4LVF5z2tz3s+SsGeOnMPc7R9z6wt 7wQFw7fcsvXQr0xd06pncH81r+eRR2uoyevBHN5vXKVAlrNfRT+8r1mgYLVN soYkmsFykqnjYoHl/b+tnPfHL6ej8Q1LWfDvWK3sML5fruuvVDNaxoKPh7li e9FLFLvfNoqxoP62ZjcDLTtmx98sxYIr61v+V43W87W61rqWBQVN588+QrfY icmZyrPg0oz+iwS01S5a6VtFFiTF3K8MR7v+NvvZpsICqRQ+vwvoWxEmZzt3 sEDmZe8KEzQjWc+B2s+Cr4f27RvH9+3R64vTNqYsuBUuu2YIPexSdY9lxgLB mBAWhf6lpE1nW7Hgd7choxwtW6C5v/sYC5wfnhKOQLs2qGn0e7NAWzvygQx6 elxOfPQBC0rqsn3X4XmS+PhzS+ojFrD6icPL0DsPFQfZprIg0HmV2AKeVxcI i++16SwwVnLg70JPBgTTUnJZkBVEcEej/+UfjbWuZ8HSTgezr3g+vltXJPRm EvsX+fwqFs9ff+b1Or8p/D/fspCL6OWhBwNVf7KA/zavujPaevTT2MP/saBn R760Orozd0WrLy8b3lovFafj+d6051qEiiwbPrgYvxVAv7Y14U00YoO8mwrd EeuLSLOy8NUmbHjQK15jgHY03CT43JQNKt7seBU0z07hZSWWbOjj2kj76YX1 oCR9RY8DG04T8Z2R6DHGEdXVXmyYFZp/n4v1jJylu3XmfTYkEFeTB7D+CToQ /rR4lA0d1gczRtyxvnH2cNz2hQ3ebwyeNaCVLprJ5o6zoeJzRvgzdFu6xL2M KTbEmTPnXNBSC48j7s6zoWda7VEv1mfZeSVePqLvwGn51eoWrOcYkmM6alrv oPHw9EyCKwnyAwd7MsLfAXHR5SXlhOffrrBE2R1d4CPwcvNerHcd19LnuFld oGOSsWsG6+/ptrhhn5BuCHhYE6S7i4QkPmd/G6UeOOE3+cVSBfMefP2Mp7EH bi0m1uetxP14PcRuz4VeCLlEq6hagt8DOc4Fw5J9YJK/R0d1mgDf5II4yfo+ KDv7VsfmIwFvNkcKSni/BxvzIau1nQRIHPRVuynaD+8azAxI/B7s38JgBVb1 w+VnXFwymQQUPgGlEecBEDHsXeOXQIBTgZbEmj8DcPJ4RQ7rCgHB4ekh/S8H 4Zvf9GlxNwLyxtakiJoPAXuo9nGQJQHWEqK7W+aH4Aw99D+aFgHR/Dyr+tFb 9UZkOtCNc9OLU+grqYZ6b9FawwMNcgtDkLfxb3QDWo7MO+SN/hbgqVSGHraz OCP9ewhslwrbp6P9k2IfnFocAn2+m5V+6LzY4MAA9MZztR990KPB/o5xaPH6 RQFvtIOno0IpegYu2nmgdbXV8pf+GYJb1+wnHdFL+tubitBbf4+t3Y8GRk12 M1rk9ApjQ3RAIxnzHr252uCcPvprboo1/98h0N6XVKqNpl0/N+CAlojRslJH C/i61Hqh3S4dv6SG1ne3zbiJXmkTlLoJTVjqeOaiC/oaxhTR4wbq5nXo5Fsj ovJopV2K6l3oGSU+zbVo580ykuPoFkLh+Cr0w3XC03/Rotv1Q1ai/w/nxOwf "]]}}, {{}, {}, {Hue[ NCache[{ Rational[3, 20]}, {0.15}]], Thickness[Large], LineBox[CompressedData[" 1:eJwd1nk0Vd0bB3AppZQoEhki6iVThUrpK1QieakMDVIZMg+pSEIhFWUmFOFe 916ze++RQsqUSJGS8ZYkhWhQifTb7++vsz5rnXPW2ns/z3c/8se9LB35+fj4 BGbx8f33NHEcaq3+uGPbZjFpfk2HwG1zDKW8eZKKuKLfxRn8aIMNGSnpbEkt 9M8EPe9ln4Tp047SW5JG+CDwTWlktz+sHX5Wxknux7bMDW0bgi6j1lCqrCbd Cr5+mjVvtK5Cc5Ve8Xc5W+TSbqe0vImCYP/FLKvVdijyemC4QigWvRqXDaMl HSBXu6R5x0wiEjKWVysdckQE2/JPs1oyTBaztlalO6Hx2+ewDTYpoD43a4/J ueDuKdvYH7dScb1gyT8Wqz3he5j2I3fsNjLFzSOuSvqhrkKSk2yXjcCnybVW 9/xwdnZ16Mq2bFiFv+Ffdeg0OuZW8HMNc7Bwwif4fvoZbD24MVtBngb/9gT/ EbkAuN+U0PxWR8e+qF7qbnUATL5c9q5UyYW60eqJsGPn8Ox1Gq8tOhcD7DIf mexAyHYoRU3vZcAivst17+oLqLRNXylaxYSq6SqmVMMFbOrgVUyJsyA42/3D oHMwOI8efz3pzsLR8pmSB/tDsNKthBoQy4O4coy6TVIowjb/Gyh8IB+hguw1 VyTDoG5Raa+XXAiVXbGRpd5hOG+hb5LPK0RbuNfH7oYwVPqZfa5bXQTF2ap5 6mfC0WfXpbikpAj1f3LU29si0M0MzTl4qBheWy/d+KN8GSubZYdjzhVjeeCx 8dWhl9Fkb/1uw81iuPySKQ3QiET3lltJT9qLsfBbkrZc1BWo3roodWlHCbjr TicZv7uCNckFB53tS2Dnve+nj+5VbJPP8Wo+V4Ki0cXltUNX8Xhg1FyhsASW Q5FbXXdE4dSHabkti0uR0nvOkDtzHVeMSrq/VJRiu7RtTt+BG/jh2Pqt/3kp Ph3cKCBYcAOmdwSMTg+UQnYk4ESBWgyC7m5yC1vAhpeLjhJfTwzMJ6w0Ay3Z qI2kvUyYFwszx7HbOSfYWM4Qi1DeEAvB4zc3n/djo3rw66Dl1VjoVOm83ZLI xhKHIgZtUxwWhx+aUXzBhtMlWVtdhzg89EiYM/SWjftZ0fOf3YiDdaqXo8M4 Gw5v3Vx/DcbBtT7mwPWFHHDt/lE1TYxHp1VUYON2Dmxs7xSNf0kA88WGebxM Dsa69y/IkkrE5Ms11sJ5HETYCTruM0zEyfTwosVcDtgnvKSohEQM7DFJuvaY A2FPvfDAjUkoeqltEjTKAW18nKdqnwSjcvM5lj842HoqR7cvMgnlzXJ5MzMc uPoLjet3JZH9CDndv5iLuoudB+cGJWMyzMxmUIOLwwLR3DJaMtqr4oaiNnLx 9bK+iEtLMsqW+USKgIuV0bl1TXIpSJsTsb/EjIvzyac1Yx+loGIsTtbFhYv1 +aJzpQVTcXLLmhTlNC4a1evsn2qmYjp6udC7TC7sS/zvX7BNRe8XjIXSuYim eN5vWanwjnTr8CnhYqi6oJtulgY1D9q/q+u5CDY8pmNzJg2dO4bDJJq4WFYv Fjs/Iw09IemxX55xYdgUuNN9PA0a3YF1xzq5uP1yd8m6+HT0qV5YpzfMhbbN H6F399NxS6v1WfAYF81dxU4JA+kw37lsW+E3LiZ5EtI/tW/heKzB0LMpLvZ/ eh9R8foW7twNK9EQoiD0N/TwLtkMLBf7fo6+mkKKi7Wd6s4MqNr6XapQpqDY rmov6pmB2XOoJzWqFLYxO050V2Zg0mOtSO56CuXMJG6Zeib2DXRJNOhR4Dsa qsMyyITf7x9VHvoUdoq5l6VbZSJmxZvgeYYUXlzYXh56gbzvqqcibkxhdN9I hWlLJjx1M0duW1DQmt+ht60/E7EP9LUG9lE4V/WwSvNHJn6/mdCStaIwTzm5 Wlz2DlrWaMr7HKQgP7O9ludxBxmMB9zk4xQOMJKbTi3KQk394f5FPhTSj1zc 4ySfBePa6XS2L4X+JR5PbbSzoBa9vPxfPwpeQQbP9I5k4eCatQyfsxSuWI62 zSvIwtj7V/qWQRSez3u973d1Fnrjez5RFygsq3zUPtKehTKl50JiIRSy16S8 ap3OQoH2hfV3L1KonDboStuTDUt9p9N5lynMKVU7dN0+G4xsZb2OSAomzst7 QvyyUa3k7Dl9hUJH62ivY3o2PtzUCtoQReELPeWtxkg2ukRvbLeOobDp8KXj Cnw5cJ78bWYRS+GCqOc7MbEcdIYMJ++II+d33vD95JYcvHu7dqdMAgUli89D NddyIJJwKOtaMgWp4F26znfI972Z59xSKIgUZF5bUJaD73r/nNxxk8JvwX3q Fv05WNHCG/uQStZbXXaqbxMNd7WmYj7dolD3WaQudC8NDnM/T9y6TeGetOsy JQcaJFWu6+3JoEDzly53u0ED3fdb281Mcl6aoTO/3tNQqJoTO5VF9teuyzx9 igYrDberkdkUHKI23IEoHU863SVEcyiYD703jNhKR+obf4jTKBgtQ6KyJR0n N+3gjyXWNUoZbHamwy3mBUOQTuox0+TK0ng6jkp3jAwTS7Zkd1EMOqI6DIqs cykIT0+vPVhFx+J6+4wHxJPWRS2ZH+l4qzzbPIxBoWWxmJi6fi4eJ0bW9zMp 1Oh5OLYeyMUxTuCLdSwKd93qKT+3XFSfbogLIs5u8Le9n0TuMTMNR6E80h8T rSy7/Fwohf1NNCO+vmrt9KxHuchSiOdEEfsH9942Hs1F4Znwb7PyKXgU6IwP 8zMwrz1UYxPx8e4b228sZ0DVIDjGjdhm/se49eoMnFhYtCqd2GyjwcBLQwYS wwR+NBIbOKZpB9gyoC+zRWyCeFP89whpLwaMLjy9KlNAQWGMrnwilYHOW7wS J2IJGb7AucUMSKptO3eZeKGpbTOzjoEgtfInNGL+gFIZs24GrPrKCh8S/6QL eY2PM3C0yX1dN/FIu0N1/FwmnKpfHflK3M9fJbpRmomEuw+3zSsk9aopcaJr HRPmjQ19ksTNdt6coF1M/BC0NFYhfhTVKCB/hImjPjfDNxGX3VOwrvVlwrgq N9OIOH8okOEcyUTVLpvsvcRZy15OLrjNRNxrm2Qr4mQjddNCNhMTISoRh4mj fC+nWzQyscVRIcCe+GLmm9HvfUwMR7oGHCc+27IZKd+ZkEvij/nPwurc942C LLSoKXz77/2caM2oKWkWnoSE3DtCrDuat15tHQvy1YtGbYhb96zptNvBwiLV 9FhL4pP5WcExtixsTHxTaEI8IyS7+pEHC3XdvqbbiRPcbjZ/C2XBzL3FQ4d4 bZPYKaUkFuj3LKX/v36VGElrFgvZ9wyPSBPbXBWqjqxi4bnVE51FxJ8/Rjjd a2Nh5fvvhdNkf8N38y8aGWSh9GZZ0ydiaWYQW2aKhZSfI3EdxKWCk7bmi/Pw GFYLaoh5DWP00o15ON1utjKJ+MwaN7MB0zwYKw40Bv133pcHv4nb52GRzoPN DsSbd/bqB0TmYR3dIlSN+DnN5gMrPQ/LHa1PiBA7CbRH9xTnAa5Y+ZXUV3zt ky505iH/77FtpcQqijtDfUbzUHRRjxlDXH3p4ZrsWflo+6DH70k8anDXb65K Pu4JC8cqEe96SBN+ei4f2hnGtyNJP/StlCfjTD7Ehjb+tCP2C0k/pJmdj53/ Sh3TIr6DeEZ8Uz5khWvO9pB+m6oMMTgoXQBd13UyCsRF9w6d+VBZAOa15rMR pH93SnVIS7YVwL1zXYY5cU+AZY3JYAG07b1FlhPP37xbpFC4EM7vS3ropP9P lOmw/I4W4lTYlGcFyQsJjmjfrFlFUBHr+NBI8udw1NT+gWVFGFi6K+oScZbD +6Z61SL0cT5HbyVWFS8vv2ZThAeRZZx8kl8GZ+wTxYuL4B/xkxdO8k0n3Zqe oFGM52K7Z8mS/DtmRz/C6CtG6UA1Z4LkKdVv2PxsaykK/HWr6TdIfbjeWmE7 woFSbhfHidw3E6v1Fhd4lKEp5CWt8Sjpz8k8kRVK98Cn/tDp5Q7y/7/21L7C Crz/rTcnWI30W5hWS73KAxw9eboiVZyCXMzwJPNzNex7TY/nkft9+Cev76Xm Izz2kLA8+46LnE/3nwhfrwFv4XqWbiMXwjK5YwMDtThduLfMv4iLKBeuU6Zi PYwXqUmfSubih37ewMngBph7dGk5BnHht76Ws6zmMWZoPgVLHbngFdZea5V/ gmx/pZ5yEy6mXNvTlM81IanyfG+XJhdrt8+bcbrfjJrTZbi7nItdWfLOJRIt SLu43yaazGdnZY4qvD38DGtDelplBzlQHTkg1GH2HLGCq2TXtnCwdPG4YO3v 55BXb1mpweFgzoM0EoytOLrGMWwsjQM3rfud803bsKDV/nZuKAd5u49nVv1o w3rjFde6nDmYGJYSGUx6AcO0h68bzck8um/X7ASjdojcae4p1uYg2Dg8gzPY DsFLNdv3y3Ag32vyOjv8JY5tCAjwFeBAd2NYguT6V7ieFO8cOczGYdlnk7Ne vMKnlzepg2QenngS3e8d2gHJx3MqFMvZSJlj52ep+Br+SYcU8jLZWNrHzeKv fY1tG3wO5UeyIRAUun+zTydeXRw2oXmywce0K+pf0oWMQou0g1Zs+KYWRS95 1AXdaOmseVvZqFwbKSjq2Q1dXXqghgIboia+qheFe+Bes4JaSub7HrXnLwIq euD9d4I+NlaK4ttQHLDrBV2i4tfljlIcKdIRlZnpxfYZfZm0B6UICb8T2sPq Q2Gyyi8ajdThkEya8B4e9izi0/KILoWFqPCmht88VGjrrlY9VYqrAvwreoij djTwKxPXTk78GSc+dGA/T4lYp7+3RmqKh99+nilyxFLsAnNP4k2crAVLifv3 mzmLT/PAXi80NulbCr+UqKQTf3hgavSUNRAXRIUE+BMHwCWhlngwxO9wNLGx +Q/vh8Q2LocVyoiHPEVU7hPr6aoWLpjhQanQKL2QeG5PU10JcaZqQUgiMZ4/ YNQTe2/VPRJH7F/LvtZNjD0Nm28Qf8pPsxD4y0Of29uvkcQtQW69NsTSeeKO 54nn+R6t9iAevpe1PYBY32lf9kXi+080ZM8Ql+7d4pJPbPtpd4cX8bCBxp6H xMq/X7HdiRU3rtJ4RfxrvkOMC7HdWoklw8QNkl/cnYiT5YQm/hInK1/YfYL4 fxDDDpM= "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 10]}, {0.1}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV1Xk01PsbB3BbaLlEdQsh2xSGClkK77rqiFCWlMgWyj6YslWWaJ1KkiSl okW2zMx3vsq1z6VTVKQoW7miEEpTt43f5/fH5zzn9dezned8NPwjXQIlxMTE jpP3/2gf+L6t7sMm64VTF9xz1CqspWyUWf1K2uCOfKI3DHFgnJ+Tx1MygaJ7 vdb227kYXKqdEsuwho3R7qr5iTewpbWTe0VpIz71zGazX9yCNkf15oy6HYZL H0aVpN7FL/s9F/0YTjj4X3jUlSulGEnrEPplO8PR4BorSe0edgR8q85UckNi /n+HxNZWQGijTDfmueNipcnJMF0uVmlZ3fui7gHL9uo5eVNc5En4FukUeGKf xx6HHVd5kB1IveHO8Ebmv9mVyYZ8PHjT3tro5gtajTphfocP1rYAe69sPyg6 n5j6IUeBUSdq+tLpj9+Lr+XdD6TQu/KYzWmlANxuoDQ/lVHIyl9Sp+MZiCyj S7ZVYxTs5e9a1uQFwXFx8Ja+ZQKIJa277963F8+3hA6+chBAMN6yZkI9GGLl jsafowQI8/bmHvMLQbr5O0mLcwJoPpkwXFYQiuQA+asXigXoskoprhwMQ7N1 l8/jegHOlCqucGZEgMta7pzUIcAm1cLCD3sjkdtIv7IcFOBwU+78ejcWHKjm qvhPAngc/tfptIgF9fIc1qVfApiYMk97ZEfB5Q+nmYlZNOTH2Y91zKKxxnfM X/gHjZGb1bM/d0bjko3YOZeFNP7ZLb25Ji4GgxuqVrYq0bi2aOvRk0psiJ+R lfVRo5HYelHo/oANJS09a6YmDff0NxJanvsx8+KRh6sOjdVWuhsmfu7HraXy OuPLacwTRSVV5R2A6XWJYEU9GsMlD6qPWcViJLOR065PoyFA8pdrXyyC2r+q WBvQuLLUYe2ypDgox3ua+xvSiOvIihtTj0fKnarvditpuHJ6BZV18ZAu+1Yz TWy4kSFK80uATHFi9PFVNGb/ijB2lkiE788Fwo/Egzw6SrUgEYHDTR4mq2nU hord+2BzEF8ylnz3Jc7VshunBg/i25WholjiA93nmKnphxDn/Pp5IrHz+dch TozDqDTbvINFzNyiVaTcfBgcDeMbO4hlJcOGh/YmwXhqboMxcfTu15keUsmw /VIeLU3sc3+6otYtGfn6C/TbSD0Oi7TadG4mo2Hr1PILxGujbCdPiZKx5MBb tivxIt0Mw53ZKWBtGtvTQPqTSOc71gyl4MKETRCbePJNV5i2WSq2hTOPaBE/ ztEonuxMRfNx8+YEMq8UWd7yE0ppWC6vZfEnmaee7bnjXFYazrZ03+YyabSn R37obk5DuEypmROxtiSz2PBAOsSsAuyOkH00/S407Gg/is9+haJhXbK/qew1 6pwT+Gh62+42g0ZOb4INNX0G23YJIpYuo7HT43r55KcshKg8vCm5gMbcmRQv W7V8ZKpr2p75IYCO8/j7xlOFUJTWqzo/IEDsEwvkfCmCS372u4yHAizmK/SJ i5ejfuEEy/4euZcBm5anllxIWpVwf14QoCHkiorHGB8lxiualx8UQMSwki8N p5EmnWE5P0AAie/F81V0HmAVx2vfpJ0ApjO+AteyvzFvfKGIs1qAljSTJ016 tXBS47gVKgmgnjH6vWi8Dv7i+0J4MxRGv/X3vVjVgDt1K98eHqZQOFL1SO5M I2qNvOT+aqUgp3p7YnBQCKsYW7lkHgVOMBV0TbsJo2fVIhMuU/i6vnhwX1Iz wnx2HQ1LocA2EvL/bHwI1bmp08rBFPrLhKfaNB7herCcQb0ThZ8hHZd1Ex7j VLaH4YAJBf0NMtNBVS24lZ+RUbuUgu0Njb0Vi5/gvCezKEuCQqyqj+Zbr6e4 N8XTZIzwwRzbPrfT8RlMdv2IMGrnY4H8pKzwxzOcjLkZZVrJh1Tt5XKtvDYo BFu++JrPR6hJ1avZW9oRomA+UZbOR7Gd/7War+3QO/65+20oH6JR5flD2c+h 3J2j2+bKB+VqK5m1sQM9bwoMKi34SNqcns8f6sDThtxMTw0+NHrtuwrSX0A3 Ztuj+Nl8rDVLy1Iyegm3lyGVZyd48FJ7+l38+UtULIqS8e/kQfTo9AArpRNv ZHrmMat5yJHyZrtod8H6pVEMt5CHBX3UDQlhF6RiNpfwODzMOpTiZhH1CnkN DZdLonkQK/IuH1B8jcDxFWN+u3iIzi0/rdjwGmKtU5/l1vNQrX9cViGiG+IJ h1pMGTwo2EczU+V6YCw5Ja0ix0OPwbPn8X/3wAyt376S/+HeVWgPevcibMd5 u7PdXOwuN1VQne6FjPWSiBuNXCSnX0/pudsHdqe4XWkRF6XvVS/LOfRD0bEz jX2OC2cFOfPmH/04sl8h1jiWi5OzJFR6iF3Sr7quIhZ+F/2eJNa8oL/KgNh0 oLdR+Wc/6vibPjCIlXmlWyOIp6fiPZWJB9wc9y761Y+E6AGIE7NzONl7fveD FcmTfXqA5Ockx8cRr09a/+4x8VAy2+s0sfzZ1vqHxDuDvTRp4rKy4YQGYqu1 zLI50/0Y/ajykSKW7nn8TwVxUFhaWx4xntXeaSI2PahQdok4Tsg71U0szbl6 Mpt4pOSy86yZfhQWV9pkED85FNq7k3hgZIw6QiwT7VMXTsz9EZ+ZTLw+yLUg lThljkzkIWKu07rgEuJlehorYolH/1rpUE88YVEmxSbWNtNa+ZK4xm7dWxax t/5ixVHiMx4Pq8OJL6rPFc0Q7w7enhtC/D/8UBnq "]]}}, {{}, {}, {Hue[ NCache[{ Rational[1, 20]}, {0.05}]], Thickness[Large], LineBox[CompressedData[" 1:eJwV0Hs01HkfB/BJKrKmpM0z00qiKZfQitKWd0sd0UXiUTaNVShsUWvRbTWi pbCFZ9hMS7q5NszvN7/flsSTKVGEJuQ2NasbDj1nGYvwfPePz3mf1znvc97n fEwPROwO1uJwOEHk/kmP4A/N1R+3OFP3s8SjwW+dtV35kSqeOZ7MbKh7opHB PjdbQvHW4HNAgXAwlkHvV+aiGIEzxhwuR3QvYbGtoU12lbcZ6xQTgVs2sjBP Mb45beKO/TmtYVkuLD57HMwKFOxEQXrSo82uLPoSlIpAsRcGJLr8RcR7gkYr 03k+4O06ST8gfYUrn62R+MIuQPtRALGd2cayYRM/bHXYHTn9LQsddXy+r0CI crcIR2fibttfXFN5QQjyKcutAIvM3H9VL98XDIGwfew7Yo95RRseSEKQ68bx GXdmwQw+cxgyCcU5/V06TsRppQtWegmOYpl4KJLZwCLvS8/zF3hRcLlt41Lu xOJUQ5bC914UQpJ9JbuIfRNfa5nt+wkXwn/WDK1j8cXIsbgKSTRabBuLbIhj lZmxAyYncPCPI4Yljiy8MjrCdgp+xrm6kt5b9ixEOtSKZF4CFP2Wv0hWsbB0 u5wki0wA9b11tT1xS2LEx87aBFx/uWqs3pr8c6Z1sU10IkRVduFjViweT96w UbacBzIcPX0tyf5fYgeTlGTcXe9iNH8Fi+zuk67yqTRIk/1un1vKYq/fNemn /2Xiyoqk2jBDFnrTIn+3JbnIQ/PhkXEGy70GP9RcvAF9wauucTWDmEYnZA8X YnvVljl/P2FgRBv0zJghRcWa39PLyxgwatdnzzfIMOm/T3lAzOBh2NXFfgM0 bnm3fUg7zWBEsHFe6REWcQIIY4IYaI0Vz1+8/B4sS/Qu7PFg4Dj9PeN95z5m cxWLhlczeJawpvGxZRW2On8TrcdnYHKpf6xwsBr+pkYpfA6D/lFVz0u7h8h/ 3aP17r0cN/oq6rlpNbi7W8+usEEOrvHtod5eBdZmaGzfU3KkhMpD8swf4620 4dKbHDk0m4p7D8fVIiROt+CFSI6orxX0oponMLJavTQ+VA7VHcXFZtN65CRX 7lzpKcdEmDLH4uRTJDI6u9wd5LD6ds5USMUz5FVBJjCWwy3f9FC5USNST3XW T2jJEWMcsOyN/3MUGR7cnNpHw3rg33ptO5pgc7Lw0m8tNAznfdJRjDchIcMn 4+ofNLSrcqRmkmboJfdr9ufRCF9T8Up3WwuCVr+fv+g8jWL3A3kPNC0wL7g2 ufUHGiP9/PnvxC+wcMJt2zofGnJvt5mZm5Vo5Xh7mqynEbc1MZd+p0Sd2p1+ aErDtNuj/XriS5hlTPe/1qWxfm1CJu/rVnhqeB2aIQr+S56PzXjRimKHpRZ1 bRRG6lPVkaI2dKy4aJNRSSFbWxi127wdTpo3mbybFAx75PlainZMpY828FMp zDoj8nE69gpi9bFKwx8pcAqFUvWCDgRw2/XrvqNw/Io0dcHDDowP5C+M3kSh 0ipJx+BoJyZ+sx68KqBg4HHcOp7bhVVm+SvjuRS6VjW9OHG/C6sDTvOEwzKU /Q7zXmE3QmJcwjWdMuyXOhoYT3VjhrD2V12FDGcTr4m6inoQMVoWtrBIhtIP xjnc7SroHzl/q/OyDF4G3HW14yqc+U919pUYGS7M0lrcRbz95o6fsogVYyOT n4i/knd4ZRI7qrtr+BMq3FMOz00j5lOlnkeJ/za0OCMiVvvsOPTlZxWi0i8H HiaOyk4RH5xUIezXA5aOxKUpZ0/EEjvlDs22J353Nso/lVhXevpPW+K9of7L WOKCRrHEgnjjeus7c6dUeKv/lGtMPLvr6aNy4sAU+79mEqOpquAxsZ2k+jmH OFZBXewk5pTsKJmMlqGvJMdr1rQKuU8PBY8SN54J795L3DVX0tZHPOd4QPUR 4hK+Bf2eeFOI9/V44lOWzKVeYtnOb0JLiPkeTe49xP0uttv/S/zRb7+gk9h8 rZltK/Hd0D6tdmKhldGCfuKkEzEqJXGWid7INPGeZO37zcT/B+yaE/o= "]]}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, Frame->True, FrameLabel->{ FormBox[ StyleBox["\"Time: \[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"Inner Solution\\nComplex:\\n v(\[Eta])\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm]}, ImageSize->{658., 411.}, PlotLabel->FormBox[ StyleBox["\"\[Epsilon] = {1., 0.1, 0.01, 0.001}\"", Large, RGBColor[1, 0, 0], StripOnInput -> False], TraditionalForm], PlotRange->All, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}, RotateLabel->False]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{3.414223538722545*^9}, TextAlignment->Center] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Outer Solution: Matching", "Section", CellChangeTimes->{{3.414223457098705*^9, 3.414223459933837*^9}}], Cell[CellGroupData[{ Cell["Limit of Inner Solution", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414201163408683*^9, 3.414201169260671*^9}, { 3.414223592788749*^9, 3.414223596428618*^9}, 3.414223761865378*^9}], Cell[BoxData[ RowBox[{"InnerOrder0Limit", "=", RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"u", "[", "0", "]"}], " ", ",", RowBox[{"v", "[", "0", "]"}]}], "}"}], "==", RowBox[{"Limit", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Sigma]", "]"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Sigma]", "]"}]}], "}"}], "/.", "Order0Solution"}], ")"}], ",", " ", RowBox[{"\[Sigma]", "\[Rule]", " ", "Infinity"}], " ", ",", " ", RowBox[{"Assumptions", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"K", ">", "0"}], ",", " ", RowBox[{"\[Lambda]", " ", ">", "0"}], ",", RowBox[{"\[Epsilon]", ">", " ", "0"}]}], "}"}]}]}], "]"}]}], "]"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{ 3.414201519731799*^9, {3.414218775456345*^9, 3.41421879554577*^9}, 3.414223761865615*^9, {3.414232065101065*^9, 3.414232065904703*^9}}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Equal]", FractionBox["1", RowBox[{"1", "+", "K"}]]}]}], "}"}]], "Output", CellChangeTimes->{3.414232068247262*^9}], Cell[CellGroupData[{ Cell["Forming ODE and IC for Outer System", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414223609419831*^9, 3.414223637605252*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"OuterODESys", "=", RowBox[{"Join", "[", RowBox[{"NewTwoDEnzymeODE", ",", " ", "InnerOrder0Limit"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "TableForm"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414218802903173*^9, 3.414218820854982*^9}, 3.414223637605503*^9}] }, Open ]], Cell[BoxData[ TagBox[ TagBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{"u", "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{ RowBox[{"\[Epsilon]", " ", RowBox[{ SuperscriptBox["v", "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{"v", "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{"u", "[", "\[Eta]", "]"}], " ", RowBox[{"v", "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Equal]", "1"}]}, { RowBox[{ RowBox[{"v", "[", "0", "]"}], "\[Equal]", FractionBox["1", RowBox[{"1", "+", "K"}]]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.414232110291977*^9}], Cell[CellGroupData[{ Cell["Write Expansion Equations", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414223653839561*^9, 3.414223670315363*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"LHSOuterODEIC", " ", "=", " ", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"First", "[", "#", "]"}], "&"}], ",", "OuterODESys"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"u", "\[Rule]", " ", "uExp"}], ",", " ", RowBox[{"v", "\[Rule]", " ", "vExp"}]}], "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"RHSOuterODEIC", " ", "=", " ", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"Last", "[", "#", "]"}], "&"}], ",", "OuterODESys"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"u", "\[Rule]", " ", "uExp"}], ",", " ", RowBox[{"v", "\[Rule]", " ", "vExp"}]}], "}"}]}]}], ";"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414197874911858*^9, 3.414197947582309*^9}, { 3.4141979793562*^9, 3.414198016265418*^9}, {3.414198051110632*^9, 3.414198108272088*^9}, {3.414218940192351*^9, 3.414219009071665*^9}, 3.414219054311462*^9, 3.414223670315616*^9}], Cell[BoxData[{ StyleBox[ RowBox[{ RowBox[{"\[Epsilon]Order", " ", "=", "0"}], ";"}], FontColor->GrayLevel[0]], "\[IndentingNewLine]", RowBox[{ RowBox[{"LHSCoefficientList", "=", RowBox[{"Coefficient", "[", RowBox[{ "LHSOuterODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"RHSCoefficientList", "=", " ", RowBox[{"Coefficient", "[", RowBox[{ "RHSOuterODEIC", ",", " ", "\[Epsilon]", ",", " ", "\[Epsilon]Order"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Order0ODEIC", "=", " ", RowBox[{"Thread", "[", " ", RowBox[{"LHSCoefficientList", " ", "==", "RHSCoefficientList"}], " ", "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "ColumnForm"}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414197874911858*^9, 3.414197947582309*^9}, { 3.4141979793562*^9, 3.414198016265418*^9}, {3.414198051110632*^9, 3.414198108272088*^9}, {3.414219038258375*^9, 3.41421904299727*^9}, 3.414223670315759*^9}] }, Open ]], Cell[BoxData[ InterpretationBox[GridBox[{ { RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{ RowBox[{"-", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "+", RowBox[{"K", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "-", RowBox[{"\[Lambda]", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "+", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{"0", "\[Equal]", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], "-", RowBox[{"K", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "-", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}]}]}]}, { RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "0", "]"}], "\[Equal]", "1"}]}, { RowBox[{ RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "0", "]"}], "\[Equal]", FractionBox["1", RowBox[{"1", "+", "K"}]]}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], ColumnForm[{Derivative[1][ $CellContext`u[ 0]][$CellContext`\[Eta]] == -$CellContext`u[0][$CellContext`\[Eta]] + K $CellContext`v[ 0][$CellContext`\[Eta]] - $CellContext`\[Lambda] $CellContext`v[ 0][$CellContext`\[Eta]] + $CellContext`u[ 0][$CellContext`\[Eta]] $CellContext`v[0][$CellContext`\[Eta]], 0 == $CellContext`u[0][$CellContext`\[Eta]] - K $CellContext`v[0][$CellContext`\[Eta]] - $CellContext`u[ 0][$CellContext`\[Eta]] $CellContext`v[ 0][$CellContext`\[Eta]], $CellContext`u[0][0] == 1, $CellContext`v[0][0] == (1 + K)^(-1)}], Editable->False]], "Output", CellChangeTimes->{3.414232148732833*^9}], Cell[CellGroupData[{ Cell["Obtaining Solution", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414223683515355*^9, 3.414223716147724*^9}}], Cell["\<\ We note that the 2nd equation is an algebraic relation; we can elimiate v[0][\ \[Eta]].\ \>", "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219066325649*^9, 3.414219087683463*^9}, { 3.414219118444265*^9, 3.414219132913197*^9}, 3.414223716147978*^9}], Cell[BoxData[ RowBox[{"elimiatedODE", "=", RowBox[{"Eliminate", "[", RowBox[{ RowBox[{"Order0ODEIC", "[", RowBox[{"[", RowBox[{"1", ";;", "2"}], "]"}], "]"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "]"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219097033849*^9, 3.414219097729864*^9}, { 3.414219136443207*^9, 3.414219163012296*^9}, {3.414219214749168*^9, 3.414219220905997*^9}, 3.414223716148125*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"K", "+", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], ")"}], " ", RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "\[Equal]", RowBox[{ RowBox[{"-", "\[Lambda]"}], " ", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}]}]}]], "Output", CellChangeTimes->{3.414232250151314*^9}], Cell[CellGroupData[{ Cell[TextData[{ "Rewriting this, we see the ", StyleBox["Michaelis-Menten", FontWeight->"Bold"], " rate rule we wanted to obtain:" }], "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414221122210028*^9, 3.414221167547122*^9}, 3.414223716148397*^9}], Cell[BoxData[ RowBox[{"u0ODE", "=", RowBox[{ RowBox[{ RowBox[{"Solve", "[", RowBox[{"elimiatedODE", ",", " ", RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}]}], "]"}], "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "/.", RowBox[{"Rule", "\[Rule]", " ", "Equal"}]}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414220981529705*^9, 3.41422102782134*^9}, 3.414223716148521*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Equal]", RowBox[{"-", FractionBox[ RowBox[{"\[Lambda]", " ", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], RowBox[{"K", "+", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}]}]]}]}]], "Output", CellChangeTimes->{3.41423226560667*^9}], Cell[CellGroupData[{ Cell["An expression for the solution may be written down:", "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414221201412455*^9, 3.414221217215041*^9}, 3.41422371614879*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"Order0ReducedODEIC", "=", RowBox[{"{", RowBox[{"elimiatedODE", " ", ",", RowBox[{"Order0ODEIC", "[", RowBox[{"[", "3", "]"}], "]"}]}], " ", "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"u0OuterSoln", "=", RowBox[{ RowBox[{"DSolve", "[", RowBox[{"Order0ReducedODEIC", ",", " ", RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], " ", ",", " ", "\[Eta]"}], "]"}], "//", "Flatten"}]}]}], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219206769951*^9, 3.414219254443387*^9}, { 3.414220086202676*^9, 3.414220088966626*^9}, {3.414220293366918*^9, 3.414220295342697*^9}, {3.414221185736694*^9, 3.41422119350568*^9}, 3.414223716148914*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"InverseFunction", "::", "\<\"ifun\"\>"}], RowBox[{ ":", " "}], "\<\"Inverse functions are being used. Values may be lost for \ multivalued inverses. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/InverseFunction/ifun\\\", ButtonNote -> \\\ \"InverseFunction::ifun\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.414232372930748*^9}], Cell[BoxData[ RowBox[{ RowBox[{"Solve", "::", "\<\"ifun\"\>"}], RowBox[{ ":", " "}], "\<\"Inverse functions are being used by \\!\\(Solve\\), so \ some solutions may not be found; use Reduce for complete solution \ information. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/Solve/ifun\\\", ButtonNote -> \ \\\"Solve::ifun\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.414232373079107*^9}], Cell[BoxData[ RowBox[{ RowBox[{"Solve", "::", "\<\"ifun\"\>"}], RowBox[{ ":", " "}], "\<\"Inverse functions are being used by \\!\\(Solve\\), so \ some solutions may not be found; use Reduce for complete solution \ information. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/Solve/ifun\\\", ButtonNote -> \ \\\"Solve::ifun\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.414232373086626*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], "\[Rule]", RowBox[{"K", " ", RowBox[{"ProductLog", "[", FractionBox[ SuperscriptBox["\[ExponentialE]", RowBox[{ FractionBox["1", "K"], "-", FractionBox[ RowBox[{"\[Eta]", " ", "\[Lambda]"}], "K"]}]], "K"], "]"}]}]}], "}"}]], "Output", CellChangeTimes->{3.414232373093456*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u0OuterSolnDeriv", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Derivative", "[", "1", "]"}], "[", RowBox[{"Head", "[", RowBox[{"#", "//", "First"}], "]"}], "]"}], "[", "\[Eta]", "]"}], "\[Rule]", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"#", "//", "Last"}], ",", "\[Eta]"}], " ", "]"}]}], ")"}], "&"}], "/@", "u0OuterSoln"}]}]], "Input", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219524860257*^9, 3.414219683596512*^9}, 3.414223716149856*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"u", "[", "0", "]"}], "\[Prime]", MultilineFunction->None], "[", "\[Eta]", "]"}], "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"\[Lambda]", " ", RowBox[{"ProductLog", "[", FractionBox[ SuperscriptBox["\[ExponentialE]", RowBox[{ FractionBox["1", "K"], "-", FractionBox[ RowBox[{"\[Eta]", " ", "\[Lambda]"}], "K"]}]], "K"], "]"}]}], RowBox[{"1", "+", RowBox[{"ProductLog", "[", FractionBox[ SuperscriptBox["\[ExponentialE]", RowBox[{ FractionBox["1", "K"], "-", FractionBox[ RowBox[{"\[Eta]", " ", "\[Lambda]"}], "K"]}]], "K"], "]"}]}]]}]}], "}"}]], "Output", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219595934426*^9, 3.414219616265833*^9}, { 3.41421965104971*^9, 3.414219684615302*^9}, 3.41421972444686*^9, 3.414220014741463*^9, {3.41422021565283*^9, 3.414220245269228*^9}, 3.414223716149993*^9}], Cell[BoxData[ RowBox[{"v0OuterSoln", "=", RowBox[{ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"Order0ODEIC", "[", RowBox[{"[", "2", "]"}], "]"}], "/.", "%"}], ",", " ", RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}]}], "]"}], "/.", "u0OuterSoln"}], "//", "Flatten"}]}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414219329165277*^9, 3.414219400667017*^9}, { 3.414220342199737*^9, 3.414220346101795*^9}, 3.414223716150125*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"v", "[", "0", "]"}], "[", "\[Eta]", "]"}], "\[Rule]", FractionBox[ RowBox[{"ProductLog", "[", FractionBox[ SuperscriptBox["\[ExponentialE]", RowBox[{ FractionBox["1", "K"], "-", FractionBox[ RowBox[{"\[Eta]", " ", "\[Lambda]"}], "K"]}]], "K"], "]"}], RowBox[{"1", "+", RowBox[{"ProductLog", "[", FractionBox[ SuperscriptBox["\[ExponentialE]", RowBox[{ FractionBox["1", "K"], "-", FractionBox[ RowBox[{"\[Eta]", " ", "\[Lambda]"}], "K"]}]], "K"], "]"}]}]]}], "}"}]], "Output", CellChangeTimes->{3.41423238733503*^9}], Cell[CellGroupData[{ Cell["Plot Solution", "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10003.}, CellChangeTimes->{{3.414223728786439*^9, 3.414223737774669*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"u", "[", "0", "]"}], "[", "\[Eta]", "]"}], "/.", "u0OuterSoln"}], "/.", "ParamRule"}], ",", " ", RowBox[{"{", RowBox[{"\[Eta]", ",", "0", ",", "10"}], "}"}], ",", " ", RowBox[{"Frame", "\[Rule]", " ", "True"}], ",", RowBox[{"Axes", "\[Rule]", " ", "None"}], ",", RowBox[{"FrameLabel", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", " ", "Large", ",", " ", "Brown"}], "]"}], ",", " ", RowBox[{"Style", "[", RowBox[{ "\"\\"", ",", "Bold", ",", "Large", ",", " ", "Brown"}], "]"}]}], "}"}]}], ",", " ", RowBox[{"RotateLabel", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"800", ",", "500"}], "}"}]}]}], " ", "]"}]], "Input", CellGroupingRules->{GroupTogetherGrouping, 10003.}, CellChangeTimes->{{3.414220795479577*^9, 3.414220900716272*^9}, 3.414223737774897*^9}] }, Open ]], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwV02tUzHkYB/CZpgtJmrR0oZlpZnVRiIOwPL+t1pQhKSNCNENSSdmim78U MmxmyiwVGVFarZE5W9sWpZt0L03bRY2uo1WYtppNSzv78+I53/M55/vi++Zh 8E56HdUikUge+L5mJsHTdTxydUuJcHWzRqOCajl9uw/9OJjsEy+4MaUCTU1Z Ip0eDTl+l7VXvVNBZnkyTYcuALbhTp2TbSoI2Rx5YpqWDmfcI9hmOSqQfw4U j9MeQv+uQ9NLOSrQ6xm0/kArBsNHbO5A+kfIqpeEj9Hq4HZ3+IC58wd4nC/o CVnxGlzrrBXlSaNwDF6lvz81BHtkgR3hq/+CUKXtUMHjd0C5S1GKTd+CPuOC dZ/TOLT6zIoLtIbhmlGDXdbhSRC+VKy6tmkQeD27n1Ma/4G09FhyZnQ/hL+4 wDtp/S9o++6ZCG1VgCzMwNvUfRbOtjtubPm2B7Jig0dX+ZCQX59vV39iFyRI vuyaek9GCYm99d3sDiDJ+9GzGAoqK113xNatHZZFBETtttNB3BC5zGtnGwyr b+6ZV6qLbPpM3BPut8I2ZdDZ1PA5KIK6Y+T8bBN4DIuWW1rqo8wvQvId4wYY reLF10rnoVQDB5sfM2phBbVjqcuh+egAMVpSYF8D+qD27500RNLijW56tGpg f/CdtuIaoX6eUBFpUQldlUfIvvZUpE7Kjx7wKofCy9V+dDUVycOmFjjdK4UA ncj+5mZj1HZR9AtTWgL8U7GFBhkL0Ylrabkahz9g5bHlzdv9TdAUqTJfW10I Lcb28yI3fIMsyyCCU/MbPH2ccMuesgg9nbsuteKjDGLJdp6NikVov6ds32v6 E9DvjXELLViM4qT6qhIjKSgfMMSSOFN0OTjowMFDeSC2MdMu5poht0mrzeFP c0GUEfDSn26O1vZ93hB6Pgd8xQebDUbMkVBQ8Z5/6T58cs2ZkZRZoPqh1okC cRYMKZ2jKpOWoFMt6irtQQnc2+xo0eS/FKkLP60nP7oN0ouR1GMOlihGXdpp PZ0OSVw+h6K2RNRh07ofhDdhbW/Ww6QmGhr/fRM1bM3PkGZ7S9rEoaOircZG Yeuuw7ny5DROMR3FN+iVJ7imwA4Lbk49i4F0fyVmPMyE8H3oy/1UAQNZPNxW nrfmJ5As4bEa1QzEko+9cT0oAFZV7g2P/VZIS+6ZsmzmEogcKu3ayqwQ239k wLD7AgRMar+qs2OiGwvPBUdXJQBPNkEXCJnoz5TOzgryeaitn5P47AsTfZpc cJ1/nYAQlwFRHXaQ7ohCk0qA0bPiOx3YMSSK3W3svdKgknHskYy5Ne0pBIwI G/9mzeK+2nP+VhEBulzR4WRs6+zqLptkAlz6Fm/x+4+JsnWYfNUlAt76jHOC sQMMhB1Xsa+01u6Lwn5yGjg22G0V0ZGp2HFHTzj5XySAl93zqAY7xmmWIU8k IP64xGKlhomUpu8ci+IJYA2esf0O2zAovdgbu9bXc707dmdvsvP4Obx/O9mb j920yGWvLbZkBf/KTezZwDept84S4Jy7KS0bu907n+WE/ZZm8kCG7QnVRe1x BP6HFxUN2B16JQPzsdsEmS1d2Hd7M6LyYgk4rXVaocS+l/XciI1tHusxNoFd 5GWTNxRDQNnkshkNdtVYu2s89v+DD0+P "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->None, AxesOrigin->{0, 0}, Frame->True, FrameLabel->{ FormBox[ StyleBox["\"Time: \[Eta]\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm], FormBox[ StyleBox["\"Outer Solution\\nSubstrate:\\n u(\[Eta])\"", Bold, Large, RGBColor[0.6, 0.4, 0.2], StripOnInput -> False], TraditionalForm]}, ImageSize->{800, 500}, PlotRange->{{0, 10}, {0., 0.9999999072356254}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}, RotateLabel->False]], "Output", CellChangeTimes->{3.414232395533552*^9}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Conclusions", "Section", CellChangeTimes->{{3.414221225517534*^9, 3.414221229857129*^9}}], Cell[CellGroupData[{ Cell["\<\ We have seen the main ideas regarding singular perturbation analysis:\ \>", "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414221380681097*^9, 3.414221383464336*^9}, { 3.414221437817287*^9, 3.414221450891951*^9}, 3.414222044211017*^9}], Cell[TextData[{ "Magnifying the boundary layer: introduce \[Epsilon]-dependent scaling, ", StyleBox["\[Sigma]=", FontSize->24, FontWeight->"Bold"], Cell[BoxData[ FormBox[ FractionBox["\[Eta]", "\[Epsilon]"], TraditionalForm]], FontSize->24, FontWeight->"Bold"] }], "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, 3.414222044211284*^9}], Cell["\<\ Solve the corresponding inner solution\ \>", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221629601949*^9}, 3.414221697128062*^9, 3.4142220442115*^9}] }, Open ]], Cell[CellGroupData[{ Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414223812448637*^9, 3.414223812872829*^9}, 3.414223868341679*^9}], Cell[TextData[{ "Take the limit of the solution ", StyleBox["\[Sigma]", FontSize->24, FontWeight->"Bold"], StyleBox["\[Rule]\[Infinity] ", FontWeight->"Bold"] }], "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221693429293*^9}, 3.41422204421171*^9, 3.414223868341926*^9}], Cell["\<\ Use the above limit of the inner solution as the initial condition for the \ outer solution\ \>", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221730983939*^9}, 3.414222044211925*^9, 3.414223868342147*^9}], Cell["\<\ Now the equation and initial conditions for the outer solution are \ consistent, which can then be solved\ \>", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221759569481*^9}, 3.414222044212143*^9, 3.414223868342362*^9}] }, Open ]], Cell[CellGroupData[{ Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414223838230247*^9, 3.414223862416649*^9}}], Cell["\<\ Since we typically do not observe very small time scales, only the outer \ solution is of interest\ \>", "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221795820274*^9}, 3.414222044212355*^9, 3.414223862417395*^9}], Cell[TextData[{ "We have derived the Michaelis-Menten rate, valid when the enzyme \ concentration is much smaller than subsrate (i.e., \[Epsilon] = ", Cell[BoxData[ FormBox[ FractionBox["e0", "s0"], TraditionalForm]]], "\[LessLess]1):" }], "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414221467324987*^9, 3.41422146936901*^9}, { 3.414221518814931*^9, 3.414221593160197*^9}, {3.41422162436166*^9, 3.414221823783145*^9}, {3.414221874765567*^9, 3.414221974735746*^9}, { 3.414222007227935*^9, 3.414222044212572*^9}, 3.414223862417619*^9}], Cell[BoxData[ RowBox[{ RowBox[{"u0ODE", "/.", RowBox[{ RowBox[{"u", "[", "0", "]"}], "\[Rule]", " ", "u"}]}], "//", "TraditionalForm"}]], "Input", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.414221839926388*^9, 3.414221862422041*^9}, { 3.414221977140235*^9, 3.414221994080766*^9}, 3.414222044212775*^9, 3.414223862417822*^9}], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["u", "\[Prime]", MultilineFunction->None], "(", "\[Eta]", ")"}], "\[LongEqual]", RowBox[{"-", FractionBox[ RowBox[{"\[Lambda]", " ", RowBox[{"u", "(", "\[Eta]", ")"}]}], RowBox[{"K", "+", RowBox[{"u", "(", "\[Eta]", ")"}]}]]}]}], TraditionalForm]], "Output", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{ 3.414221863615739*^9, {3.414221980098174*^9, 3.414221994920763*^9}, 3.414222044212923*^9, 3.414223862417969*^9}] }, Open ]], Cell[CellGroupData[{ Cell["", "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.414222080110633*^9, 3.414222084445242*^9}}], Cell[TextData[{ "In the first computer assignment, you will be asked to do similar \ perturbation analysis:\nderiving from cooperative enzyme reactions, to obtain \ the ", StyleBox["Hill-function", FontWeight->"Bold"], " rate rule." }], "Item", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.41422054669793*^9, 3.414220573636279*^9}, { 3.414221289197289*^9, 3.414221365243086*^9}, 3.414222084445995*^9}] }, Open ]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]] }, AutoGeneratedPackage->None, ScreenStyleEnvironment->"SlideShow", WindowSize->{1286, 985}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, ShowSelection->True, ShowGroupOpener->True, ShowCellLabel->False, CellLabelAutoDelete->True, ShowCellTags->True, Magnification->0.75, FrontEndVersion->"6.0 for Linux x86 (32-bit) (April 20, 2007)", StyleDefinitions->Notebook[{ Cell[ StyleData[ StyleDefinitions -> FrontEnd`FileName[{"Creative"}, "PastelColor.nb", CharacterEncoding -> "iso8859-1"]]], Cell[ StyleData["Title"], FontSize -> 28], Cell[ StyleData["Item"], FontSize -> 24, FontWeight -> "Plain"], Cell[ StyleData["Subitem"], FontSize -> 22, FontColor -> GrayLevel[0]], Cell[ StyleData["Section"], FontSize -> 22], Cell[ StyleData["Input"], FontSize -> 22], Cell[ StyleData["Output"], FontSize -> 22, FontWeight -> "Bold", FontColor -> RGBColor[0.5, 0, 0.5]], Cell[ StyleData["Text"], FontSize -> 20], Cell[ StyleData["Subsection"], FontSize -> 22], Cell[ StyleData["Subsection"], FontSize -> 22], Cell[ StyleData["Item"], FontSize -> 26, FontColor -> RGBColor[0.6, 0.4, 0.2]], Cell[ StyleData["Subsubsection"], FontSize -> 22]}, Visible -> False, FrontEndVersion -> "6.0 for Linux x86 (32-bit) (April 20, 2007)", StyleDefinitions -> "PrivateStylesheetFormatting.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "SlideShowHeader"->{ Cell[590, 23, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[5200, 164, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[35585, 1022, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[98488, 2211, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[128053, 2909, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[197798, 4197, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[206922, 4496, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[212942, 4685, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[229395, 5180, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[267052, 5986, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[363151, 7663, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[383816, 8081, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[406254, 8730, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"]} } *) (*CellTagsIndex CellTagsIndex->{ {"SlideShowHeader", 414028, 8959} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[657, 26, 157, 3, 48, "Title"], Cell[817, 31, 206, 6, 52, "Subtitle"], Cell[CellGroupData[{ Cell[1048, 41, 158, 2, 62, "Section"], Cell[CellGroupData[{ Cell[1231, 47, 180, 5, 37, "Subsection"], Cell[1414, 54, 460, 8, 33, "Item"] }, Open ]], Cell[CellGroupData[{ Cell[1911, 67, 228, 6, 37, "Subsection"], Cell[2142, 75, 142, 1, 33, "Item"], Cell[2287, 78, 205, 6, 32, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[2541, 90, 193, 3, 62, "Section"], Cell[CellGroupData[{ Cell[2759, 97, 366, 9, 33, "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[3128, 108, 303, 4, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[3434, 114, 350, 5, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[3799, 122, 588, 16, 14, "Input", CellOpen->False, InitializationCell->True], Cell[4390, 140, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[5200, 164, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[5289, 169, 112, 1, 62, "Section"], Cell[CellGroupData[{ Cell[5426, 174, 137, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[5588, 179, 5184, 148, 381, "Input", InitializationCell->True], Cell[10775, 329, 211, 2, 18, "Print"], Cell[10989, 333, 2117, 60, 62, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[13155, 399, 174, 2, 37, "Subsection"], Cell[CellGroupData[{ Cell[13354, 405, 212, 3, 31, "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[13569, 410, 6233, 132, 395, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[19839, 547, 113, 1, 31, "Subsubsection"], Cell[CellGroupData[{ Cell[19977, 552, 42, 0, 35, "Input"], Cell[20022, 554, 1488, 45, 71, "Output"] }, Open ]], Cell[21525, 602, 302, 5, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[21830, 609, 1636, 46, 125, "Output"], Cell[23469, 657, 200, 4, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[23672, 663, 1442, 45, 66, "Output"], Cell[25117, 710, 776, 23, 66, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[25896, 735, 1219, 37, 63, "Output"], Cell[27118, 774, 202, 4, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[27323, 780, 990, 30, 63, "Output"], Cell[28316, 812, 1199, 19, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}, InitializationCell->True], Cell[29518, 833, 1006, 29, 35, "Output"], Cell[CellGroupData[{ Cell[30549, 866, 273, 6, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[30825, 874, 598, 14, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[31438, 891, 1306, 39, 58, "Output"], Cell[CellGroupData[{ Cell[32769, 934, 271, 6, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[33043, 942, 541, 15, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[33599, 960, 773, 24, 58, "Output"], Cell[34375, 986, 373, 8, 81, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[34751, 996, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[35585, 1022, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[35674, 1027, 155, 2, 62, "Section"], Cell[CellGroupData[{ Cell[35854, 1033, 139, 2, 35, "Input"], Cell[35996, 1037, 1548, 45, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[37581, 1087, 115, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[37721, 1092, 157, 2, 31, "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[37881, 1096, 6602, 152, 455, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[CellGroupData[{ Cell[44520, 1253, 99, 1, 31, "Subsubsection"], Cell[CellGroupData[{ Cell[44644, 1258, 1470, 39, 146, "Input"], Cell[46117, 1299, 51522, 883, 667, 32568, 570, "CachedBoxData", "BoxData", \ "Output"] }, Open ]], Cell[97654, 2185, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[98488, 2211, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[98577, 2216, 155, 2, 62, "Section"], Cell[CellGroupData[{ Cell[98757, 2222, 142, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[98924, 2227, 2035, 50, 141, "Input"], Cell[100962, 2279, 25482, 575, 318, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[126493, 2860, 98, 1, 37, "Subsection"], Cell[126594, 2863, 432, 13, 58, "Text"], Cell[127029, 2878, 199, 4, 32, "Text"], Cell[127231, 2884, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[128053, 2909, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[128142, 2914, 106, 1, 62, "Section"], Cell[CellGroupData[{ Cell[128273, 2919, 117, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[128415, 2924, 165, 2, 31, "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[128583, 2928, 135, 2, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[128721, 2932, 7886, 178, 477, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[CellGroupData[{ Cell[136644, 3115, 99, 1, 31, "Subsubsection"], Cell[CellGroupData[{ Cell[136768, 3120, 1334, 37, 146, "Input"], Cell[138105, 3159, 58844, 1009, 667, 46348, 802, "CachedBoxData", "BoxData", \ "Output"] }, Open ]], Cell[196964, 4171, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[197798, 4197, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[197887, 4202, 197, 3, 62, "Section"], Cell[198087, 4207, 816, 25, 85, "Text"], Cell[198906, 4234, 355, 12, 35, "Text"], Cell[199264, 4248, 716, 25, 98, "Text"], Cell[CellGroupData[{ Cell[200005, 4277, 115, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[200145, 4282, 940, 25, 81, "Input"], Cell[201088, 4309, 1616, 46, 58, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[202753, 4361, 102, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[202880, 4366, 417, 11, 35, "Input"], Cell[203300, 4379, 1145, 35, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[204482, 4419, 513, 14, 58, "Input"], Cell[204998, 4435, 876, 27, 58, "Output"] }, Open ]], Cell[205889, 4465, 208, 4, 32, "Text"], Cell[206100, 4471, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[206922, 4496, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[207011, 4501, 149, 2, 62, "Section"], Cell[207163, 4505, 439, 13, 35, "Text"], Cell[207605, 4520, 212, 4, 32, "Text"], Cell[207820, 4526, 275, 8, 60, "Text"], Cell[CellGroupData[{ Cell[208120, 4538, 73, 1, 35, "Input"], Cell[208196, 4541, 1548, 45, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[209781, 4591, 164, 3, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[209948, 4596, 214, 4, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[210177, 4603, 1616, 46, 58, "Output"], Cell[211796, 4651, 333, 8, 81, "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[212132, 4661, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[212942, 4685, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[213031, 4690, 141, 1, 62, "Section"], Cell[213175, 4693, 792, 24, 192, "Input"], Cell[213970, 4719, 115, 1, 32, "Text"], Cell[CellGroupData[{ Cell[214110, 4724, 99, 2, 35, "Input"], Cell[214212, 4728, 240, 7, 35, "Output"] }, Open ]], Cell[214467, 4738, 1057, 29, 80, "Input"], Cell[CellGroupData[{ Cell[215549, 4771, 103, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[215677, 4776, 974, 25, 124, "Input"], Cell[216654, 4803, 1681, 47, 105, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[218372, 4855, 551, 15, 59, "Input"], Cell[218926, 4872, 602, 20, 68, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[219577, 4898, 104, 1, 37, "Subsection"], Cell[CellGroupData[{ Cell[219706, 4903, 1020, 25, 124, "Input"], Cell[220729, 4930, 2780, 74, 105, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[223546, 5009, 373, 9, 37, "Input"], Cell[223922, 5020, 247, 7, 35, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[224206, 5032, 443, 11, 58, "Input"], Cell[224652, 5045, 3906, 107, 102, "Output"] }, Open ]], Cell[228573, 5155, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[229395, 5180, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[229484, 5185, 107, 1, 62, "Section"], Cell[CellGroupData[{ Cell[229616, 5190, 159, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[229778, 5194, 699, 18, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[230492, 5215, 4576, 128, 122, "Output"], Cell[235071, 5345, 145, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[235219, 5349, 469, 14, 58, "Input"], Cell[CellGroupData[{ Cell[235713, 5367, 184, 3, 31, "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[235900, 5372, 2073, 51, 191, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[237988, 5426, 17032, 299, 393, "Output"], Cell[255023, 5727, 521, 14, 87, "Text", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[CellGroupData[{ Cell[255569, 5745, 158, 2, 31, "Subsubsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[255730, 5749, 2127, 52, 191, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[257872, 5804, 8367, 156, 393, "Output"], Cell[266242, 5962, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[267052, 5986, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[267141, 5991, 107, 1, 62, "Section"], Cell[CellGroupData[{ Cell[267273, 5996, 201, 3, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[267477, 6001, 4445, 103, 349, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[271937, 6107, 887, 21, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[272827, 6130, 89511, 1507, 507, 64885, 1101, "CachedBoxData", "BoxData", \ "Output"], Cell[362341, 7639, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[363151, 7663, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[363240, 7668, 136, 2, 62, "Section"], Cell[CellGroupData[{ Cell[363401, 7674, 293, 6, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[363697, 7682, 449, 13, 81, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[CellGroupData[{ Cell[364183, 7700, 134, 2, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[364320, 7704, 564, 14, 81, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[364887, 7720, 818, 24, 82, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[CellGroupData[{ Cell[365742, 7749, 135, 2, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[365880, 7753, 17111, 301, 326, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[383006, 8057, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[383816, 8081, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[383905, 8086, 109, 1, 62, "Section"], Cell[CellGroupData[{ Cell[384039, 8091, 236, 3, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[384278, 8096, 1138, 30, 80, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[385431, 8129, 286, 9, 64, "Output"], Cell[CellGroupData[{ Cell[385742, 8142, 176, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[385921, 8146, 378, 9, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[386314, 8158, 1761, 53, 116, "Output"], Cell[CellGroupData[{ Cell[388100, 8215, 166, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[388269, 8219, 1092, 30, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[389364, 8251, 1100, 27, 124, "Input", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[390479, 8281, 2313, 64, 118, "Output"], Cell[CellGroupData[{ Cell[392817, 8349, 159, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[392979, 8353, 302, 6, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[393284, 8361, 526, 12, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[393825, 8376, 481, 15, 35, "Output"], Cell[CellGroupData[{ Cell[394331, 8395, 292, 8, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[394626, 8405, 559, 15, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[395200, 8423, 456, 14, 66, "Output"], Cell[CellGroupData[{ Cell[395681, 8441, 211, 3, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[395895, 8446, 787, 19, 58, "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[396697, 8468, 463, 9, 18, "Message"], Cell[397163, 8479, 490, 10, 18, "Message"], Cell[397656, 8491, 490, 10, 18, "Message"], Cell[398149, 8503, 442, 14, 70, "Output"], Cell[CellGroupData[{ Cell[398616, 8521, 642, 19, 14, "Input", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[399261, 8542, 1104, 31, 14, "Output", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[400368, 8575, 555, 14, 35, "Input", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[400938, 8592, 701, 22, 100, "Output"], Cell[CellGroupData[{ Cell[401664, 8618, 154, 2, 37, "Subsection", CellGroupingRules->{GroupTogetherGrouping, 10003.}], Cell[401821, 8622, 1143, 29, 126, "Input", CellGroupingRules->{GroupTogetherGrouping, 10003.}] }, Open ]], Cell[402979, 8654, 2462, 50, 393, "Output"], Cell[405444, 8706, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[406254, 8730, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[406343, 8735, 96, 1, 62, "Section"], Cell[CellGroupData[{ Cell[406464, 8740, 284, 5, 33, "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[406751, 8747, 481, 13, 31, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell[407235, 8762, 324, 6, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]], Cell[CellGroupData[{ Cell[407596, 8773, 161, 3, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[407760, 8778, 442, 11, 25, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[408205, 8791, 379, 7, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[408587, 8800, 393, 7, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[CellGroupData[{ Cell[409017, 8812, 135, 2, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[409155, 8816, 386, 7, 24, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[409544, 8825, 593, 12, 29, "Subitem", CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[410140, 8839, 395, 10, 14, "Input", CellOpen->False, CellGroupingRules->{GroupTogetherGrouping, 10002.}], Cell[410538, 8851, 555, 15, 70, "Output", CellGroupingRules->{GroupTogetherGrouping, 10002.}] }, Open ]], Cell[CellGroupData[{ Cell[411130, 8871, 135, 2, 32, "Text", CellGroupingRules->{GroupTogetherGrouping, 10001.}], Cell[411268, 8875, 439, 10, 57, "Item", CellGroupingRules->{GroupTogetherGrouping, 10001.}] }, Open ]], Cell[411722, 8888, 761, 18, 62, "PreviousNext"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)