(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 5966, 179] NotebookOptionsPosition[ 5684, 165] NotebookOutlinePosition[ 6027, 180] CellTagsIndexPosition[ 5984, 177] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"With", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"g1", "=", RowBox[{"Plot", "[", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[Rho]", "B"], RowBox[{"(", RowBox[{"1", "-", "\[Rho]"}], ")"}]}], RowBox[{"1", "-", SuperscriptBox["\[Rho]", RowBox[{"B", "+", "1"}]]}]], ",", RowBox[{"{", RowBox[{"\[Rho]", ",", "0", ",", "2"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", "Black"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"g2", "=", RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ FractionBox[ SqrtBox["2"], RowBox[{"wnd", " ", SqrtBox["p"]}]], ",", "p"}], "}"}], ",", RowBox[{"{", RowBox[{"p", ",", ".001", ",", ".5"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", "Blue"}]}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{"{", RowBox[{"g1", ",", "g2", ",", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"GrayLevel", "[", ".4", "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\<\[Rho]\>\"", ",", "\"\
\""}], "}"}]}]}], "]"}]}],
"]"}], ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"B", ",", "10"}], "}"}], ",", "1", ",", "100", ",",
RowBox[{"Appearance", "\[Rule]", "Labeled"}]}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"wnd", ",", "10"}], "}"}], ",", "1", ",", "100", ",",
RowBox[{"Appearance", "\[Rule]", "Labeled"}]}], "}"}]}],
"\[IndentingNewLine]", "]"}]], "Input",
CellChangeTimes->{{3.530935920639841*^9, 3.5309360257996264`*^9}, {
3.5309360573116813`*^9, 3.530936065517296*^9}, {3.5309401055615234`*^9,
3.5309401147646484`*^9}}],
Cell[BoxData[
RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"g1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Log", "[",
FractionBox[
RowBox[{
SuperscriptBox["\[Rho]", "B"],
RowBox[{"(",
RowBox[{"1", "-", "\[Rho]"}], ")"}]}],
RowBox[{"1", "-",
SuperscriptBox["\[Rho]",
RowBox[{"B", "+", "1"}]]}]], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Rho]", ",", "0", ",", "2"}], "}"}], ",",
RowBox[{"PlotStyle", "\[Rule]", "Black"}]}], "]"}]}], ",",
"\[IndentingNewLine]",
RowBox[{"g2", "=",
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
FractionBox[
SqrtBox["2"],
RowBox[{"wnd", " ",
SqrtBox["p"]}]], ",",
RowBox[{"Log", "[", "p", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"p", ",", ".00001", ",", ".5"}], "}"}], ",",
RowBox[{"PlotStyle", "\[Rule]", "Blue"}]}], "]"}]}]}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{
RowBox[{"{",
RowBox[{"g1", ",", "g2", ",",
RowBox[{"Graphics", "[",
RowBox[{"{",
RowBox[{
RowBox[{"GrayLevel", "[", ".4", "]"}], ",",
RowBox[{"Line", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",",
RowBox[{"-", "1000"}]}], "}"}]}], "}"}], "]"}]}], "}"}],
"]"}]}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<\[Rho]\>\"", ",", "\"\