(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 72397, 1721]*) (*NotebookOutlinePosition[ 73162, 1748]*) (* CellTagsIndexPosition[ 73118, 1744]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ \(\(<< cellerator.m;\)\), "\[IndentingNewLine]", \(complexLeft = "\<\>"; complexRight = "\<\>"; dash = "\<\>";\)}], "Input"], Cell[BoxData[ \("Cellerator\[Trademark] 1.4.3 (6-March-2004) loaded 17-Mar-2004 14:12 \ using Mathematica Version 5.0 for Mac OS X (November 19, 2003)"\)], "Print"] }, Open ]], Cell[CellGroupData[{ Cell["Field-Noyes Model of Belousov-Zhabotinski Reaction", "Section"], Cell[TextData[{ "Standard Abbreviations:\n\t", Cell[BoxData[ \(TraditionalForm\`\(\(X\)\(=\)\(HBrO\_2\)\(\ \)\)\)]], "(HBrO in model below)\n\t", Cell[BoxData[ \(TraditionalForm\`Y = \(Br\^+\)\)]], " (Br in model below)\n\t", Cell[BoxData[ \(TraditionalForm\`Z = Ce\^\(\(4\)\(+\)\)\)]], "(Ce in model below)\n\tA = Br", Cell[BoxData[ FormBox[ SubsuperscriptBox[ StyleBox["O", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], "3", "-"], TraditionalForm]], FontVariations->{"CompatibilityType"->0}], "(BrO3 in model below)\n\tP = HOBr" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FNModel = \ {{BrO3 + Br \[ShortRightArrow] HBrO2 + HOBr, \ k1\ }, {HBrO2 + Br \[ShortRightArrow] 2 HOBr, \ k2}, \[IndentingNewLine]{BrO3 + HBrO2 \[ShortRightArrow] 2\ HBrO2\ + 2\ \ Ce, \ k3\ \ }, {2\ HBrO2 \[ShortRightArrow] BrO3\ + \ HOBr, \ k4}, \ \ {Ce \[ShortRightArrow] Br, \ \ k5}}\)], "Input"], Cell[BoxData[ \({{Br + BrO3 \[ShortRightArrow] HBrO2 + HOBr, k1}, {Br + HBrO2 \[ShortRightArrow] 2\ HOBr, k2}, {BrO3 + HBrO2 \[ShortRightArrow] 2\ Ce + 2\ HBrO2, k3}, {2\ HBrO2 \[ShortRightArrow] BrO3 + HOBr, k4}, {Ce \[ShortRightArrow] Br, k5}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sys = interpret[FNModel, frozen \[Rule] \ BrO3]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["Br", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(\(-k1\)\ Br[t]\ BrO3[t] + k5\ Ce[t] - k2\ Br[t]\ HBrO2[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox["Ce", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(\(-k5\)\ Ce[t] + 2\ k3\ BrO3[t]\ HBrO2[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox["HBrO2", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(k1\ Br[t]\ BrO3[t] - k2\ Br[t]\ HBrO2[t] + k3\ BrO3[t]\ HBrO2[t] - 2\ k4\ HBrO2[t]\^2\)}], ",", RowBox[{ RowBox[{ SuperscriptBox["HOBr", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(k1\ Br[t]\ BrO3[t] + 2\ k2\ Br[t]\ HBrO2[t] + k4\ HBrO2[t]\^2\)}]}], "}"}], ",", \({Br, Ce, HBrO2, HOBr}\)}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(ics = {HBrO2 \[Rule] \ .001, \ Br \[Rule] .003, \ Ce \[Rule] .05, BrO3 \[Rule] \ .1};\)\), "\[IndentingNewLine]", \(\(r = {k1 \[Rule] \ 1.3, \ k2 \[Rule] \ 2*10^6, \ k3 \[Rule] \ 34, \ k4 \[Rule] \ 3*10^3, \ k5 \[Rule] \ 0.02, \ f \[Rule] 0.5, BrO3[t] \[Rule] .1};\)\), "\[IndentingNewLine]", \(s = predictTimeCourse[FNModel, frozen \[Rule] \ {BrO3}, \[IndentingNewLine]timeSpan \[Rule] \ 1500, \[IndentingNewLine]rates \[Rule] \ r, \ \[IndentingNewLine]initialConditions \[Rule] \ ics]\)}], "Input"], Cell[BoxData[ \("Warning: the following variables do not have initial conditions and \ will default to a value of 0 (zero) at t = 0: HOBr"\)], "Print"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "1500", ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"Br", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 1500.`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"Ce", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 1500.`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"HBrO2", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 1500.`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"HOBr", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 1500.`}}, "<>"]\), False, Editable->False]}]}], "}"}], "}"}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(pl = runPlot[s, \ plotVariables \[Rule] \ {Br}, timeSpan \[Rule] \ {400, \ 1400}, plotColumns \[Rule] \ 1, \ TextStyle \[Rule] \ {FontFamily \[Rule] \ Times, \ FontSize \[Rule] \ 14}, \ PlotLabel \[Rule] \ "\
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