diff options
Diffstat (limited to 'plots.nb')
-rw-r--r-- | plots.nb | 1609 |
1 files changed, 1609 insertions, 0 deletions
diff --git a/plots.nb b/plots.nb new file mode 100644 index 0000000..2df6f03 --- /dev/null +++ b/plots.nb @@ -0,0 +1,1609 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 12.0' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 62035, 1601] +NotebookOptionsPosition[ 57527, 1519] +NotebookOutlinePosition[ 57859, 1534] +CellTagsIndexPosition[ 57816, 1531] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ +Cell[BoxData[ + RowBox[{"<<", "\"\<VariationalMethods`\>\""}]], "Input", + CellChangeTimes->{{3.7705578793146677`*^9, 3.770557893242214*^9}}, + CellLabel->"In[50]:=",ExpressionUUID->"11c1c939-5ea7-4e35-820b-196b7afc7932"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"fo", "=", + RowBox[{ + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{"r", " ", + SuperscriptBox[ + RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}], "+", + RowBox[{"c", " ", + SuperscriptBox[ + RowBox[{ + RowBox[{"\[Eta]", "'"}], "[", "x", "]"}], "2"]}], "+", + RowBox[{"d", " ", + SuperscriptBox[ + RowBox[{ + RowBox[{"\[Eta]", "''"}], "[", "x", "]"}], "2"]}]}], ")"}]}], "+", + RowBox[{"u", " ", + SuperscriptBox[ + RowBox[{"\[Eta]", "[", "x", "]"}], "4"]}]}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"fe", "=", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{"\[Lambda]x", " ", + SuperscriptBox[ + RowBox[{"\[Epsilon]x", "[", "x", "]"}], "2"]}], "+", + RowBox[{"\[Lambda]a1", " ", + SuperscriptBox[ + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], "2"]}], "+", + RowBox[{"\[Lambda]a2", " ", + SuperscriptBox[ + RowBox[{"\[Epsilon]a2", "[", "x", "]"}], "2"]}]}], ")"}]}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"fi", "=", + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{"b", " ", + RowBox[{"\[Epsilon]x", "[", "x", "]"}], " ", + RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", + RowBox[{"e1", " ", + SuperscriptBox[ + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], "2"], + RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", + RowBox[{"e2", " ", + SuperscriptBox[ + RowBox[{"\[Epsilon]a2", "[", "x", "]"}], "2"], + RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", + RowBox[{"h1", " ", + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], + RowBox[{"\[Epsilon]x", "[", "x", "]"}], " ", + RowBox[{"\[Eta]", "[", "x", "]"}]}], "+", + RowBox[{"h2", " ", + RowBox[{"\[Epsilon]a2", "[", "x", "]"}], + RowBox[{"\[Epsilon]x", "[", "x", "]"}], " ", + RowBox[{"\[Eta]", "[", "x", "]"}]}]}], ")"}]}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "=", + RowBox[{ + RowBox[{"fo", "+", "fe", "+", "fi"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Lambda]a2", "\[Rule]", "0"}], ",", + RowBox[{"e2", "\[Rule]", "0"}], ",", + RowBox[{"h2", "\[Rule]", "0"}]}], "}"}]}]}], ";"}]}], "Input", + CellChangeTimes->{{3.770556239149859*^9, 3.770556315944047*^9}, { + 3.7705578472891817`*^9, 3.770557967428043*^9}, {3.770565309038463*^9, + 3.770565318491414*^9}}, + CellLabel->"In[51]:=",ExpressionUUID->"98997921-fc2d-40a3-b750-05550f4b5c59"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"s\[Epsilon]", "=", + RowBox[{"Solve", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"VariationalD", "[", + RowBox[{"f", ",", + RowBox[{"\[Epsilon]x", "[", "x", "]"}], ",", "x"}], "]"}], + "\[Equal]", "0"}], ",", + RowBox[{ + RowBox[{"VariationalD", "[", + RowBox[{"f", ",", + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], ",", "x"}], "]"}], + "\[Equal]", "0"}], ",", + RowBox[{ + RowBox[{"VariationalD", "[", + RowBox[{"f", ",", + RowBox[{"\[Epsilon]a2", "[", "x", "]"}], ",", "x"}], "]"}], + "\[Equal]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Epsilon]x", "[", "x", "]"}], ",", + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], ",", + RowBox[{"\[Epsilon]a2", "[", "x", "]"}]}], "}"}]}], "]"}]}], + ";"}]], "Input", + CellChangeTimes->{{3.770554820338584*^9, 3.770554829738276*^9}, { + 3.770554860325389*^9, 3.770554886102066*^9}, {3.770557979668975*^9, + 3.77055802659697*^9}, 3.770560903908511*^9}, + CellLabel->"In[58]:=",ExpressionUUID->"2ebc8031-6231-481f-b049-707f66f906b6"], + +Cell[BoxData[ + TemplateBox[{ + "Solve","svars", + "\"Equations may not give solutions for all \\\"solve\\\" variables.\"",2, + 58,17,33203065702852886569,"Local"}, + "MessageTemplate"]], "Message", "MSG", + CellChangeTimes->{3.770565319391838*^9}, + CellLabel-> + "During evaluation of \ +In[58]:=",ExpressionUUID->"42656e0b-6b9d-4ade-a02a-1e1a2c506fba"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"s\[Epsilon]", "/.", + RowBox[{"e1", "\[Rule]", "0"}]}]], "Input", + CellChangeTimes->{{3.770565327531459*^9, 3.77056532843566*^9}, { + 3.77056537362363*^9, 3.770565376951768*^9}}, + CellLabel->"In[60]:=",ExpressionUUID->"b1ffed5d-b41b-4c8d-9f41-b0dd65eaa34f"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"\[Epsilon]x", "[", "x", "]"}], "\[Rule]", + FractionBox[ + RowBox[{"2", " ", "b", " ", "\[Lambda]a1", " ", + RowBox[{"\[Eta]", "[", "x", "]"}]}], + RowBox[{ + RowBox[{ + RowBox[{"-", "4"}], " ", "\[Lambda]a1", " ", "\[Lambda]x"}], "+", + RowBox[{ + SuperscriptBox["h1", "2"], " ", + SuperscriptBox[ + RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]]}], ",", + RowBox[{ + RowBox[{"\[Epsilon]a1", "[", "x", "]"}], "\[Rule]", + RowBox[{"-", + FractionBox[ + RowBox[{"b", " ", "h1", " ", + SuperscriptBox[ + RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}], + RowBox[{ + RowBox[{ + RowBox[{"-", "4"}], " ", "\[Lambda]a1", " ", "\[Lambda]x"}], "+", + RowBox[{ + SuperscriptBox["h1", "2"], " ", + SuperscriptBox[ + RowBox[{"\[Eta]", "[", "x", "]"}], "2"]}]}]]}]}]}], "}"}], + "}"}]], "Output", + CellChangeTimes->{3.77056532898451*^9, 3.7705653771424007`*^9}, + CellLabel->"Out[60]=",ExpressionUUID->"c2d3dc1c-b8ea-46f2-b457-b0dbb99b7d7d"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"f\[Eta]eff", "=", + RowBox[{"Expand", "[", + RowBox[{"f", "/.", + RowBox[{"s\[Epsilon]", "[", + RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}], ";"}]], "Input", + CellChangeTimes->{{3.770561243988637*^9, 3.770561256154991*^9}, { + 3.770561337365841*^9, 3.7705613556017838`*^9}}, + CellLabel->"In[33]:=",ExpressionUUID->"d2d5bc38-647e-41ae-9585-f6514cd2c6c7"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"\[Chi]", "=", + RowBox[{ + RowBox[{"D", "[", + RowBox[{ + RowBox[{ + RowBox[{"VariationalD", "[", + RowBox[{ + RowBox[{"f", "/.", + RowBox[{"s\[Epsilon]", "[", + RowBox[{"[", "1", "]"}], "]"}]}], ",", + RowBox[{"\[Eta]", "[", "x", "]"}], ",", "x"}], "]"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Eta]", "[", "x", "]"}], "\[Rule]", + RowBox[{ + RowBox[{"\[Eta]", "[", "x", "]"}], "[", + RowBox[{"\[Eta]", "[", "xp", "]"}], "]"}]}], "}"}]}], ",", + RowBox[{"\[Eta]", "[", "xp", "]"}]}], "]"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"\[Eta]", "[", "x_", "]"}], "[", + RowBox[{"\[Eta]", "[", "xp_", "]"}], "]"}], "\[RuleDelayed]", + RowBox[{"\[Eta]", "[", "x", "]"}]}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"\[Eta]", "[", "x_", "]"}], "'"}], "[", + RowBox[{"\[Eta]", "[", "xp_", "]"}], "]"}], "\[RuleDelayed]", + RowBox[{"DiracDelta", "[", + RowBox[{"x", "-", "xp"}], "]"}]}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Derivative", "[", "i_", "]"}], "[", "\[Eta]", "]"}], "[", + "x", "]"}], "\[RuleDelayed]", + RowBox[{ + RowBox[{ + RowBox[{"Derivative", "[", "i", "]"}], "[", "DiracDelta", "]"}], "[", + RowBox[{"x", "-", "xp"}], "]"}]}]}], "}"}]}]}], ";"}]], "Input", + CellChangeTimes->{{3.7705609237352962`*^9, 3.7705609537314863`*^9}, { + 3.770561084362817*^9, 3.770561153048244*^9}, {3.770561183376079*^9, + 3.770561205422473*^9}, {3.7705615497853127`*^9, 3.7705616904555693`*^9}, { + 3.770561744959778*^9, 3.770561935829486*^9}}, + CellLabel->"In[48]:=",ExpressionUUID->"0f544c33-f435-459c-a473-d005863f95f2"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FourierTransform", "[", + RowBox[{"\[Chi]", ",", "x", ",", "q"}], "]"}]], "Input", + CellChangeTimes->{{3.77056193699454*^9, 3.770561944259122*^9}}, + CellLabel->"In[49]:=",ExpressionUUID->"b4dcf7cc-1bf9-49f0-a9af-a4dcf6893896"], + +Cell[BoxData["$Aborted"], "Output", + CellChangeTimes->{3.7705619589957113`*^9}, + CellLabel->"Out[49]=",ExpressionUUID->"639ccfaa-595b-4074-8a0f-26ae9b6470cb"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"1", "/", + RowBox[{"(", + RowBox[{"\[Lambda]", "-", + RowBox[{ + RowBox[{"b", "/", "2"}], "/", + RowBox[{"(", + RowBox[{ + RowBox[{"b", "/", + RowBox[{"(", + RowBox[{"2", " ", "\[Lambda]"}], ")"}]}], "+", + RowBox[{ + RowBox[{"2", "/", "b"}], " ", "/", "\[Chi]t"}]}], ")"}]}]}], ")"}]}], + "//", "Simplify"}]], "Input", + CellChangeTimes->{{3.770567125728854*^9, 3.770567177945568*^9}, + 3.7705674449229307`*^9}, + CellLabel->"In[64]:=",ExpressionUUID->"5b3333e0-2528-421d-98d3-c7414514d461"], + +Cell[BoxData[ + FractionBox[ + RowBox[{ + RowBox[{"4", " ", "\[Lambda]"}], "+", + RowBox[{ + SuperscriptBox["b", "2"], " ", "\[Chi]t"}]}], + RowBox[{"4", " ", + SuperscriptBox["\[Lambda]", "2"]}]]], "Output", + CellChangeTimes->{{3.770567175117193*^9, 3.770567178165471*^9}, + 3.770567445208769*^9}, + CellLabel->"Out[64]=",ExpressionUUID->"81ba9537-513b-4bf7-9467-d533e9b63498"] +}, Open ]], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"Fu", "=", + RowBox[{ + FractionBox["V", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{"r", " ", + SuperscriptBox["\[Eta]", "2"]}], "+", + RowBox[{"2", " ", "u", " ", + SuperscriptBox["\[Eta]", "4"]}]}], ")"}]}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Fm", "=", + RowBox[{ + FractionBox["V", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{"r", "+", + RowBox[{"c", " ", + SuperscriptBox["q", "2"]}], "+", + RowBox[{"d", " ", + SuperscriptBox["q", "4"]}]}], ")"}], + SuperscriptBox["\[Eta]", "2"]}], "+", + RowBox[{ + FractionBox["3", "4"], "u", " ", + SuperscriptBox["\[Eta]", "4"]}]}], ")"}]}]}], ";"}]}], "Input", + CellChangeTimes->{{3.77057072935113*^9, 3.7705707715959597`*^9}, { + 3.7705708106509323`*^9, 3.770570826028399*^9}}, + CellLabel->"In[55]:=",ExpressionUUID->"19f1d159-2940-4211-a220-00ea16b951c8"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Fm", "/.", + RowBox[{"{", + RowBox[{"q", "\[Rule]", + SqrtBox[ + RowBox[{ + RowBox[{"-", "c"}], "/", + RowBox[{"(", + RowBox[{"2", "d"}], ")"}]}]]}], "}"}]}]], "Input", + CellChangeTimes->{{3.7707358225505323`*^9, 3.7707358412169533`*^9}}, + CellLabel->"In[59]:=",ExpressionUUID->"7886c291-33ec-4ace-a89c-ce01acce2fe0"], + +Cell[BoxData[ + RowBox[{ + FractionBox["1", "2"], " ", "V", " ", + RowBox[{"(", + RowBox[{ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox[ + SuperscriptBox["c", "2"], + RowBox[{"4", " ", "d"}]]}], "+", "r"}], ")"}], " ", + SuperscriptBox["\[Eta]", "2"]}], "+", + FractionBox[ + RowBox[{"3", " ", "u", " ", + SuperscriptBox["\[Eta]", "4"]}], "4"]}], ")"}]}]], "Output", + CellChangeTimes->{{3.770735834827647*^9, 3.7707358414325438`*^9}}, + CellLabel->"Out[59]=",ExpressionUUID->"691b31d2-84e5-47dc-abab-1a896d8bf522"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"eq", "=", + RowBox[{"FullSimplify", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"Fm", "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"q", "\[Rule]", + RowBox[{"Sqrt", "[", + RowBox[{ + RowBox[{"-", "c"}], "/", + RowBox[{"(", + RowBox[{"2", "d"}], ")"}]}], "]"}]}], ",", + RowBox[{"\[Eta]", "\[Rule]", + RowBox[{"Sqrt", "[", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"c", "^", "2"}], "-", + RowBox[{"4", " ", "d", " ", "r"}]}], ")"}], "/", + RowBox[{"(", + RowBox[{"12", " ", "d", " ", "u"}], ")"}]}], "]"}]}]}], "}"}]}], + ")"}], "/", + RowBox[{"(", + RowBox[{"Fu", "/.", + RowBox[{"\[Eta]", "\[Rule]", + RowBox[{"Sqrt", "[", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"c", "^", "2"}], "-", + RowBox[{"4", " ", "d", " ", "r"}]}], ")"}], "/", + RowBox[{"(", + RowBox[{"16", " ", "d", " ", "u"}], ")"}]}], "]"}]}]}], ")"}]}], "//", + "Expand"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"r", "<", "0"}], ",", + RowBox[{"c", "<", "0"}], ",", + RowBox[{"d", ">", "0"}], ",", + RowBox[{"u", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.7705719684602833`*^9, 3.7705719897201157`*^9}, { + 3.770572024010268*^9, 3.770572030983783*^9}, {3.770572061179989*^9, + 3.77057207487043*^9}}, + CellLabel-> + "In[103]:=",ExpressionUUID->"4da03829-80f7-4d3c-b1df-3061c9d0fa86"], + +Cell[BoxData[ + RowBox[{ + FractionBox["2", "3"], "-", + FractionBox[ + RowBox[{"4", " ", + SuperscriptBox["c", "2"]}], + RowBox[{"3", " ", + RowBox[{"(", + RowBox[{ + SuperscriptBox["c", "2"], "+", + RowBox[{"4", " ", "d", " ", "r"}]}], ")"}]}]]}]], "Output", + CellChangeTimes->{{3.770571971025888*^9, 3.77057199001871*^9}, { + 3.770572027244319*^9, 3.770572031316922*^9}, 3.770572075525268*^9}, + CellLabel-> + "Out[103]=",ExpressionUUID->"de2415bd-ffa4-42c0-a20c-1aaf19c5b3cd"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"-", "T"}], " ", + RowBox[{"D", "[", + RowBox[{ + RowBox[{ + RowBox[{"Fm", "/.", + RowBox[{"\[Eta]", "\[Rule]", + RowBox[{"Sqrt", "[", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"c", "^", "2"}], "-", + RowBox[{"4", " ", "d", " ", "r"}]}], ")"}], "/", + RowBox[{"(", + RowBox[{"12", " ", "d", " ", "u"}], ")"}]}], "]"}]}]}], "/.", + RowBox[{"r", "\[Rule]", + RowBox[{"a", + RowBox[{"(", + RowBox[{"T", "-", "Tc"}], ")"}]}]}]}], ",", + RowBox[{"{", + RowBox[{"T", ",", "2"}], "}"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.770642179466674*^9, 3.770642237343441*^9}}, + CellLabel-> + "In[264]:=",ExpressionUUID->"deee272c-c109-48f7-a88d-1ee72a679856"], + +Cell[BoxData[ + FractionBox[ + RowBox[{ + SuperscriptBox["a", "2"], " ", "T", " ", "V"}], + RowBox[{"12", " ", "u"}]]], "Output", + CellChangeTimes->{{3.77064218035308*^9, 3.770642237571024*^9}}, + CellLabel-> + "Out[264]=",ExpressionUUID->"d46cf980-3684-47bc-a454-7e432e809dda"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"ss", "=", + RowBox[{"Solve", "[", + RowBox[{ + RowBox[{"eq", "\[Equal]", "1"}], ",", "c"}], "]"}]}], ";"}]], "Input", + CellChangeTimes->{{3.770571271302767*^9, 3.77057133636125*^9}, { + 3.770572037947668*^9, 3.7705720404974947`*^9}}, + CellLabel-> + "In[104]:=",ExpressionUUID->"67413114-8b38-4eff-8a22-b1615b0ea9bb"], + +Cell[CellGroupData[{ + +Cell[BoxData["ss"], "Input", + CellChangeTimes->{{3.770572089368773*^9, 3.770572089551257*^9}}, + CellLabel-> + "In[106]:=",ExpressionUUID->"415b3bc6-5bea-472c-b832-a17a204ee60e"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"c", "\[Rule]", + RowBox[{"-", + FractionBox[ + RowBox[{"2", " ", "\[ImaginaryI]", " ", + SqrtBox["d"], " ", + SqrtBox["r"]}], + SqrtBox["5"]]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"c", "\[Rule]", + FractionBox[ + RowBox[{"2", " ", "\[ImaginaryI]", " ", + SqrtBox["d"], " ", + SqrtBox["r"]}], + SqrtBox["5"]]}], "}"}]}], "}"}]], "Output", + CellChangeTimes->{3.770572089716961*^9}, + CellLabel-> + "Out[106]=",ExpressionUUID->"c4009c3e-79a6-4a49-aa2e-fc55f5e134e4"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FullSimplify", "[", + RowBox[{ + RowBox[{"c", "/.", + RowBox[{"ss", "[", + RowBox[{"[", "1", "]"}], "]"}]}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"r", "<", "0"}], ",", + RowBox[{"c", "<", "0"}], ",", + RowBox[{"d", ">", "0"}], ",", + RowBox[{"u", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.770570828320014*^9, 3.770570953489955*^9}, { + 3.7705709875289993`*^9, 3.770571005837789*^9}, {3.770571136462347*^9, + 3.770571146581094*^9}, {3.770571270289277*^9, 3.770571299891721*^9}, { + 3.7705713595269117`*^9, 3.7705713613770313`*^9}}, + CellLabel-> + "In[105]:=",ExpressionUUID->"7dbbfd98-b060-4a55-86f6-4759247a6580"], + +Cell[BoxData[ + FractionBox[ + RowBox[{"2", " ", + SqrtBox[ + RowBox[{ + RowBox[{"-", "d"}], " ", "r"}]]}], + SqrtBox["5"]]], "Output", + CellChangeTimes->{ + 3.770570862632203*^9, {3.770570908731566*^9, 3.770570919950509*^9}, + 3.770570954410015*^9, 3.770570989007962*^9, {3.770571132154612*^9, + 3.770571142707281*^9}, 3.770571266388103*^9, 3.77057139945437*^9, + 3.770572044736827*^9, 3.770572078258441*^9}, + CellLabel-> + "Out[105]=",ExpressionUUID->"de6f3c84-c35e-4336-9744-7ae8779837e0"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"sp", "=", + RowBox[{"FiniteGroupData", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"\"\<CrystallographicPointGroup\>\"", ",", " ", "15"}], "}"}], + ",", "\"\<SpaceRepresentation\>\""}], "]"}]}]], "Input", + CellChangeTimes->{{3.770571376872231*^9, 3.7705714181475554`*^9}, { + 3.770571458262583*^9, 3.7705714653390207`*^9}, {3.7705715375305443`*^9, + 3.7705716215777903`*^9}}, + CellLabel->"In[90]:=",ExpressionUUID->"68ae3535-4b40-4f87-b02a-90936fba2195"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output", + CellChangeTimes->{{3.770571400483303*^9, 3.77057141869128*^9}, { + 3.770571538202324*^9, 3.770571621806196*^9}}, + CellLabel->"Out[90]=",ExpressionUUID->"aa33fa6c-e061-4c62-a7cd-54f992e9b260"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(", + RowBox[{"sp", ".", + RowBox[{"{", + RowBox[{"\[Delta]x", ",", "\[Delta]y", ",", "\[Delta]z"}], "}"}]}], + ")"}], "[", + RowBox[{"[", + RowBox[{"All", ",", "3"}], "]"}], "]"}]], "Input", + CellChangeTimes->{{3.770571623707589*^9, 3.770571653620319*^9}}, + CellLabel->"In[94]:=",ExpressionUUID->"32ce610b-fed3-46f7-bf71-317ac1393c49"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + "\[Delta]z", ",", "\[Delta]z", ",", "\[Delta]z", ",", "\[Delta]z", ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", + RowBox[{"-", "\[Delta]z"}], ",", "\[Delta]z", ",", "\[Delta]z", ",", + "\[Delta]z", ",", "\[Delta]z"}], "}"}]], "Output", + CellChangeTimes->{{3.7705716421912518`*^9, 3.770571653803969*^9}}, + CellLabel->"Out[94]=",ExpressionUUID->"29074888-bd44-4674-a7b9-f356fb297e11"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"pp1", "=", + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Piecewise", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"c", "\[GreaterEqual]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"c", "^", "2"}], "/", "4"}], ",", + RowBox[{"c", "<", "0"}]}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"c", "\[GreaterEqual]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"c", "<", "0"}]}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"\[Iota]", ",", + RowBox[{"c", "\[GreaterEqual]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"-", "5"}], + RowBox[{ + RowBox[{"c", "^", "2"}], "/", "4"}]}], ",", + RowBox[{"c", "<", "0"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"c", ",", + RowBox[{"-", "1.2"}], ",", "1.2"}], "}"}], ",", + StyleBox[ + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1.1"}], ",", "1.1"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.3"}], ",", "0.3"}], "}"}]}], "}"}]}], + FontWeight->"Bold"], + StyleBox[",", + FontWeight->"Bold"], + RowBox[{"Frame", "\[Rule]", "True"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "2", "]"}], ",", + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "1", "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "1", "]"}], ",", + "Dashed"}], "}"}]}], "}"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.3"}], ",", "0.3"}], "}"}]}], ",", + RowBox[{"FrameLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + "\"\<\!\(\*SubscriptBox[\(c\), \(\[UpTee]\)]\)\>\"", ",", + "\"\<\!\(\*OverscriptBox[\(r\), \(~\)]\) \!\(\*SubscriptBox[\(D\), \(\ +\[UpTee]\)]\)\>\""}], "}"}]}], ",", + RowBox[{"FrameTicks", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"False", ",", "False"}], "}"}], ",", + RowBox[{"{", + RowBox[{"False", ",", "False"}], "}"}]}], "}"}]}], ",", + RowBox[{"FrameTicks", "\[Rule]", "False"}], ",", + RowBox[{"ImageSize", "\[Rule]", "150"}], ",", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Inset", "[", + RowBox[{"\"\<Unordered\>\"", ",", + RowBox[{"{", + RowBox[{"0.5", ",", "0.16"}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<Uniform\>\"", ",", + RowBox[{"{", + RowBox[{"0.5", ",", + RowBox[{"-", "0.16"}]}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<Modulated\>\"", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.67"}], ",", + RowBox[{"-", "0.06"}]}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<(b)\>\"", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.9"}], ",", + RowBox[{"-", "0.25"}]}], "}"}]}], "]"}]}], "}"}]}], ",", + RowBox[{"LabelStyle", "\[Rule]", "Black"}], ",", + RowBox[{"Filling", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"1", "\[Rule]", + RowBox[{"{", "3", "}"}]}], ",", + RowBox[{"2", "\[Rule]", "Bottom"}], ",", + RowBox[{"3", "\[Rule]", "Bottom"}]}], "}"}]}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.770582847772399*^9, 3.7705832223990307`*^9}, { + 3.770583287222756*^9, 3.7705833378257504`*^9}, {3.7705834138103867`*^9, + 3.770583430268839*^9}, {3.770583514179763*^9, 3.770583514808462*^9}, { + 3.770583827834421*^9, 3.770583883010873*^9}, {3.770583914572714*^9, + 3.770584064549211*^9}, {3.770584799621869*^9, 3.770584875260147*^9}, + 3.770585053921783*^9, {3.770585084166893*^9, 3.7705850850093603`*^9}, { + 3.774042541938417*^9, 3.7740425632301273`*^9}, {3.774042733486842*^9, + 3.774042741015345*^9}, {3.774042828843865*^9, 3.774042831009488*^9}, { + 3.774042888527259*^9, 3.774042888711533*^9}, {3.7740429724914083`*^9, + 3.77404298458764*^9}, {3.7740433130185966`*^9, 3.7740433133040457`*^9}, { + 3.77404363278094*^9, 3.77404383606604*^9}, 3.774044155463279*^9, { + 3.774044195194737*^9, 3.774044285426847*^9}, {3.7740443306428967`*^9, + 3.77404434744316*^9}}, + CellLabel-> + "In[395]:=",ExpressionUUID->"5b48adc3-c181-4ba9-8919-787aedf6881e"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJxl2Hk01N//B/BBqWzZkn1LSKRQKZmLijZZsmQNUfYQhZDQ2Gls2UtCKsre +xzIvRMnaCC1KStZKki1J38/vd9yZ7+n7/mfO89zlzH3Nmft6zEjYnTN0YCQQ +CEcYCIT/exUyY5dWVv4Byv//vEAkb/V38V8YcIbgl4tUz/2PiTj75b/Nq343 +Bc6JNmsvPKUid/bCXftEpyDwAcO1kn3PUWF/Dml11iTYhhW+cT3cgZr5bNWP +CXyFpbANipM+raj5wMvPwj6fofI32Uk3/in6Dj3G11+Nw1zf5HnpwSbkWqFp +1WY6BsXs1RM5YY2oNcvBMrJyBNZZ9QhxiNWji4SfC4QdwxCYF5KrylWL9B/y +GEiWDcEFn2JOHc1HiO3E8M0O3o/gOe5YOe5ejjZ6SMcpJQwCa3/cfOaWEsRO +UB/RGngH9xd5GT8M3kP7q9VkvAveQKVc/epI5Xy00Ukgl//OS3iyTtWNLzAH +lf2256Ce7YEsE00teeZ09JUUX75kTYWWHvIY29sE1P9ZL8lXrh3IkS9to1sj +UORyVlF2RTPwXF7a1OkdiEZnTviZnAL4Wu2a/KLBHfWHbjIGvVJ4VTj289eM +ERJOrvHsuZgKZgVb7C9XSKJ2pEAQMb+OCCvPyueDcP31tfw/nBnqhrhIaR+d +YynoTUDVsqp3F2RViUX3TMQhpdm5m6xTLbAkMSwmeC4UBS1tmr1d2gj9a8Oa +6l77INtatdGol49AkVKluHToNJJ0SvAsd7sDtt3pj5nztRDBeJj/Yr8mcFkV +2ItNnicy3vw2n5H3AjgUchNXiaeioluzaTExz4Fd+GDvZxEyInnkCmrFtoLk +sOXi4hoSCvttQ5VQaYLsiaizyyF+6PYrnYceQrUgxqJSK/zQEbk++hKbRiqG +KT0GnhRRXdQEIXIPmSPhCqf2He8EJmReHvrsZFcHCMp+8uJsjkYDfkdkeg2f +gpiGR/fYn2Dk92uEX3ZHA3S9Ht3L5ueFRG8qiuYlVsC+4m/vh/it0CsBVeMu +o1uwplKNNYmwE0ltOKOj2Uai1fPNcbnQSuYe4Oaa5G/jTEMdSVoFTbPPwSLS +1/3QIhltL/YzfWfRBtv7/fax24cj5qDLaHCmCYKtU+x6vC6hJyMdSafr6uBz +r+qpvFwXtHaKjYP07CGEcWafnMs0QJf9g/anBCaArzXxtYv1BpSeKvKpJacT +armEs6MMY1FElbi9h0QLDBtFhR9VCkFLl1aHj3xvAEJGhPAJcW+kUVzBmLqz +CliJGtr2vTYoUNNhSNM2D14fHZDKJO9DPfCyN7LIh3aekNaGtkC/aogytb6/ +Z9QBPb0Gf6T978HpQXGBmes6iHcDV+ZZKX8wtWFpMbAYJp75tCHun2vZkPEk +w3tihwJS3DxFHThFpu2nnf+0Zf/uHsgv4DMbi0pD79jHi2zkqKB73vFBoHMC +Yu74NCv3uA1MM+q7lzdEoEOUuAvIuBl2CgS1xngGoL6vnGus4ihwYPjL07MK +bmh6T2rJrZgS4Kv6PVCETqDONVnmFf7JYJIbuelZrzCqjnL+TmDtgs1u9pnG +InHIqi+akRLRAmdu65k6dIUg9VpeykHDRji5VD3/eNEb6VcseJOZH8GsYEpE +/zo7pN97Se7SaD7MPfDre2GvgVQ21EwLep2mnSeRuop48UgNFOkOXTHRPovS +pfq0bQhF8LPt6pXiQ0eQTN7BJU+2UEjpP+qQWjRHZCZJcKR03oRDKsV+1wt2 +oAbFXJ/LzTG0/WzfwMlJQjyoEoa6O9ZxoLtFxzPX9udCtOPc5ESuKgpflBVg +ogbT5peDwuW+U64gNFfv0Cf7jNhQO/ZHOywDVEg7080LZVBQKcf4b8sk2vwl +gxSXKL0e4K2N9nVoSUMOR/aVFB+gguDsLJtgbgLysBRsps61QQmbUs33cxHI +0ZqP+9zVZqi7wGKWOR2ArD2V6l/PUeC4KU/IoTk3NDJgxbRjsgSmnnwQYOQ3 +Qj7H5UcO/EwBQRM9H6MgcdTKxLWQibrgcnlZMiU0DrU4NFDta1vAwyrY8oto +KLK2zDTzCWmEnUVf4IGTD3qlKriN49wjaDkf+4Dvjh3aI7am8/rdAhBzHy14 +GqyJhI2l53+U1oCIspfXp59nUai77UTA4yIYqxbPWyo+ii4o2fOQ15GAve1+ +kZH5MvFb1/2SUnIOrNdT9G09ooxeKX+rYv5zDfwl15pMsnOjpPnXaHP2bRAq +v418yXvRxcUXblvkvOHd88D7fU6viUn6f7SDWbJgt/m7aVYLOSTdwN61eSkR +Nqjwnj81x49ebZQZNlwfDDcMnS6Wi04RuXVzNLuYYqBmckb6Hmkt8o8qkzR3 +sYE/S9MxYa8fEl8V/K4tsuiB676id9BoGiocGy7tNaCCigDjvQhIQNJSFfJ5 +nO1QcphSuSUrAvlue/OelNUMsc1zc9eUA5Gk8mNh/q0AE3fT6h9ZuCObEg35 +BdFSYBjQMJ64aoRavv+4F/PoOoheNYz2SpZAhhr2vybMuiBFdGRKuSoOBSpY +7lHta4GDRNczk9qhyF3eRiY2vREe5N3zT8jxQZmLd6OO5f5b/70BUioLdmhb +U7uYNNsdCHLxbVfn1qL1b9mabXoWvDPqg3xVJ5RGa8ClXv7YPSNH5Msjs491 +czHc1W+ZvuFwDIn4/cgWjwiHTKORn991GdAnby8mzR85wCwgdc5ykwqSf1kZ +eJxCBm3dLiNiEQ+KyLxBLvtzG7z4Hp7aHa+GnoRPhx2SuQiPWa763qkfJAam +R01kdmSBZV1aXG/DVuRv35vkVpMEIQv+EZvfCaJg60qPj7FX4Ggry2kXrR/E +6sTtHdYhscDDdWDeehcr2pg3pZ/qcAbSCtTnR82A2Pm5J5whOgyCSfJBajaL +RFm3ChMWBU8onz7XqOLRTbS7pVhGkgiEreOdB0bDJojV77+M7f5oBFkl4Uos +WhnEv/spx2THQFlnKS2X/sObwDNOoWXheepjMtMT+rhlwPPp8+20fNW1vKxy +L5WWJ5pq19sE9NByiezI9hTSS1qWmCb0+155Q8utvUXJOnXvaNnlY10U1WaQ +ltlHvxr6MH2kZRvP4sBTUUO0HFE8+uXGumFabl9wsjcpHKHlhpYA4gmFMVru +znsl/oQ6TsuPdhbpxLt/pmW9o9zU7G9faJnRvd5OijxJy0rRl7f6sk7Rcqdq +v05kKz0vuFo49qZ9p+XFoU3VByym/8cvOGNP4hyVzT+l9pQ+H3sAZy1NUWMN +Mn38737e/Ys7evdv+jjuvzhnc+eEa12gj//dP7d1JNft+Ugfx/0S5wty107u +5Ke/f9y/cD526ePNx4709X/3n7c7X/ZV99DHcb+hnSeR6lnJQt8f9xeccf/A +uaXhOCrfTJ+fqxiqsMqOvv/YZSYz/zldWlaeuHj6Vwd9/JKO1/IcE3292IVv +bTOi9OzFXlx6Xv6/zhv54vxta/r658b7gpl3ydKy9YGWwoxW+nh+TuOB6wT6 ++iPPEXeyED1nnV1e4NlCz9plVq4vFOn5r98jQPO6sG5OjCsVsNftd27Xcalv +A+x1VTbSWsu3zYC9LtnnWNi/vx6w1xcPV0pyJlYB9vqsi+7ebb+LAXvdtSuw +j+B0C7DXe2ZOq0vtSQTs9eM9dgt7lfwBe12RS0X9vZ0O7XPBD/b59FYPQ7P3 +NYB93tj9o6/JsAywzy85DxQMHvn33l7xOTdr3k4F/QzAPq8pylNTE4oA7POf +pCveEXpnAfvcWIWqXjCeSsE+N1yIfrRalgLY55ynU1rPOFQA9rmz6Myjn5H3 +APtcO8+NgTJ0A7DPC9g0P296GwfY53PUwbZ/ezjg72NOkmk310VZwD7nTOvU +kbMoAexzGX22NUMoD7DP9z/POay38d8+t+LzkfZZlzjFEMA+j8xl4fhHw3zl +PDtWzhNBwT43Sd7y/rcRAPZ56T2+qDe+lYB9vmSQGs2pXgTY55y/suqaZHIA ++7zsaqiFjjYZsM/zkponlVddAHw/8M3FdjFX7gXsc75o6q2UE6WAfS464eo0 +QMkH7PP6hrtDZ2XTAPs8Tve5aR3LVcA+d/zGcp2h3xaC/5jmKT3bCxqjlu7q +DxIo2OeuX302rrWNBuzzAH4nse+BboDvG7cFtr3SpSyAfS5h+SFCCRmu1Edi +pT6+FOzzawaW5259BcA+F7+mJSSyugqwzxUaPcKDhIoB+7yhK255/kkOYJ8f +WT/z1mZfAmCfv5WqM0lb7wv4fuNj3lWZtVoLsM93N1GuGHeXAvZ5cOymImJo +AWCfu9cUznrvSQfs89KcGmfDGBJgn88I8bevDbKHeiOyC6cGglb2jSZe7ckU +7HN+CUvJLxtjAfs84MYPTjc3D8D3ZUB3dtDySWHAPjdvEDgZyGWyUm+5lXqH +UPD9uWmwI1f8iRJgnxczlt8dbrcGjbui740Md4HzlYPsXFLxFHy/3lLe8Yf1 +/DcK9nnDaKNGSaLuSv25VurvSME+jzE2dUEi9YB9buOlfG3waBVgn7+LX94y +GV0M2Oe7ovKrcjbeAuxzMt8xg6//JAD2+X1V85uMon6AfX5za27CeNYBwD7v +0r8mYspdBtjn7d43zxeMFAD2ecir0QdCTemAfV793MNC2DAcsM8LDn8g/xx0 +AOzzT8ARb7UQC9jnVG+VUStdT8A+H1uO/uK9IAnY5y8k1fgCRU4C9jn/1qjP +TuRdgH1Onnoi8zndBrDPeQ9mmR5r+kPBPrc72Xpx1FcfsM8FNV/rzSsjwD7X +KdifbCvNC9jnznKlU8Z3tgH2OapVfDi8vpeCfW7NyvMsfHs9YJ9fudHY63yu +CrDPRd66SXk3FQP2ua+aefpejVuAfd7NYuN74mcCYJ9f2UCesC/wA+zzM9Iy +27oWDwL2ueiL+AvBSmWAfd6nu4Zwl/8OYJ8LxZsIzK/LAOxz/8MZCpqV4YB9 +bk1KQR0pZwD7fNppUdJLQICCfU6a2i3W5xQH2OfOSnXzoeAJ2OePx0/5uuds +BuzzQ2Jfo5TlzQD7PFWcaSI2VRWwz9dwdGaE7LEF7HNv3fyU7qlVgH1uzifu +t9nMALDPDfqP+exu1QDs84GADjVmHn7APr8fFWX+i2EHYJ/XR5AWt6cOUbDP +OXv6t20OEAfsc9tvrD802eYp2Oc1BgzRnImcgH3O2JV0SntdA4X0MN/ak/Sd +9v+jMwN/Q4nee1r//w+GRpOo + "], {{{}, {}, {}, + {RGBColor[0.368417, 0.506779, 0.709798], Opacity[0.2], EdgeForm[None], + GraphicsGroupBox[ + PolygonBox[{{168, 3, 27, 167, 201, 194, 200, 188, 193, 199, 179, 185, + 192, 198, 173, 177, 183, 191, 197, 169, 171, 175, 181, 189, 195, 166, + 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, 153, + 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 172, 176, 182, 190, + 196}}]]}, {}, + {RGBColor[0.368417, 0.506779, 0.709798], Opacity[0.2], EdgeForm[None], + GraphicsGroupBox[PolygonBox[CompressedData[" +1:eJwl0MVOHgEYBdDBgwQCobj9FClS3N0KhCWPwAPQbd8RlxR3Da5Bgp0/LE7u +vd8sJjOhib/jk5FBEETwjzElvNvkphyVVQyRyjBl9PLi+YisYIBE/lBMJwee +V8pBkimhmxv3X7I//C5yaGDZPU2W08ernSR/0sWpnSJL6eHRjpOFtLJhP5Og +h+hg374Of5+eTT1L9gkPxNoFtLBuPxGvF9HOnn0VfP+gLOpYNI+5J8bOp5k1 +e5dLPsl0q2VBP+KOaDuPJlbtHS74IMOthnn9kFui7FwaWbG3OeedH26/mdP/ +s8UZb6S7VzOrzzDNFF8wgDiG + "]]]}, {}, {}, {}, {}, {}, + {RGBColor[0.880722, 0.611041, 0.142051], Opacity[0.2], EdgeForm[None], + GraphicsGroupBox[PolygonBox[CompressedData[" +1:eJwl02VvlFEQBtAuVKhAaWlLC3UX3F3qFAjQQCA4xa3F3d1/GG7B3YNrkGDn +ph9OZp55N7t5750taGlrbu0QFRUV4TdnaRLOqee5wEV6maVF2j/zmvvc4BK9 +zdP5o3/DA24y0KwnHfkkP+MyfeQM/urf8pBbDDLLJprP8nOu0Ffuzj/9Ox5x +m8FmOcTwRX7BVfrJmZH2l3qvPGa4Pp94vst3GKLPJZav8kuu0V/OIsIH+Qkj +9AUk8EO+y1B9HnF8k8eoJSTzSh6lFpHEL3mcWkYq1+UBag86MJ5yPpqPVovp +Qg2VPDUfqRZSRyLVVNDAT8/HqqXUk0ItVTRyz/Nh6h61kDOs5wQzOcUaDofv +4TRtHGMaJ1nBfipYx3Gms4qD4Txp5SiNLGQbWcxiLUfCOdDMSg6EfWAGqzkU +3pPJLGU3BeFsmcpy9lEe7p8GFrCVzLCL4a6YxBJ2kR/OlCksYy9lYd+oZz5b +6B72POwKE1nMTvIoDftMHfPYTAZV4VxpooUd5FIS7pda5rKJdCrD3jCBRWwn +h+Kwd9Qwh42kkU0R/ahmNhvoRiopdCWZLnQmiUQSiKcTccQSQ3T4/Uj7f/4/ +metfjw== + "]]]}, {}, {}, {}, {}, {}, {}}, {{}, {}, {}, + TagBox[ + {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], + Opacity[1.], LineBox[CompressedData[" +1:eJwt0VcvHgAABdCvCTVbeyXU3jS1V4zYM0YIsau09qhNa1MUv9mReDi59+0+ +3MyFrZHND4FA4JoeJUgG85EQQgkjnAgi+cRnoogmhlji+M0krXwjm1Ti2WWK +NsrIIY1jvr/tU0MRCewxTTvl5PKFExbopZZiEtlnhg4qyCOdU37QRx0lJHHA +LJ1Uks85PxmkkQz+sEg/9ZSSzCFzdFFFARf8YogmMvnLEgM0cMMaY3zlihVG +aOGODSZI4Yh5uvnHJtXvn60yygPbFHLJMv8Z5p4tnmnmlnWeGOeRHV7I4oxX +/v0n8w== + "]]}, + Annotation[#, "Charting`Private`Tag$56945#1"]& ], + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], + Opacity[1.], + LineBox[{168, 196, 190, 182, 176, 172, 143, 144, 145, 146, 147, 148, + 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, + 163, 164, 165, 166, 195, 189, 181, 175, 171, 169, 197, 191, 183, + 177, 173, 198, 192, 185, 179, 199, 193, 188, 200, 194, 201, 167}]}, + Annotation[#, "Charting`Private`Tag$56945#2"]& ], + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], + Opacity[1.], Dashing[{Small, Small}], LineBox[CompressedData[" +1:eJwVz0VOBUAUBMD/0SCBQHB3d3e3sOQIHACWHBKX4O7BNUiwYlHp7jeryZ+c +npgKBgKBGcaVWTnHPAtUuSXxpV+xxzqLVLsn861fs88GjW6ZhPJon7JEjZ3C +j37DAZs0uWURxpN9xjK1diq/+i2HbNHslk04z/Y5K9TZaf+f4U4c0a7nEcWb +vU2LnkMEL/YFq9Tb6QS5t4/p0POJ5t3eoVXPJZJXu0cWE8+l3SULieXT7pOl +JLJmN8gMQuinjAf3bllEHINUcOLeKQsYJoYByhnlw3uvLGGEBIaoZIxd723y +D7rNOIE= + "]]}, + Annotation[#, "Charting`Private`Tag$56945#3"]& ]}}], {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Epilog->{ + TagBox[ + InsetBox["Unordered", {0.5, 0.16}], "InsetString"], + TagBox[ + InsetBox["Uniform", {0.5, -0.16}], "InsetString"], + TagBox[ + InsetBox["Modulated", {-0.67, -0.06}], "InsetString"], + TagBox[ + InsetBox["(b)", {-0.9, -0.25}], "InsetString"]}, + Frame->{{True, True}, {True, True}}, + FrameLabel->{{ + FormBox[ + "\"\\!\\(\\*OverscriptBox[\\(r\\), \\(~\\)]\\) \ +\\!\\(\\*SubscriptBox[\\(D\\), \\(\[UpTee]\\)]\\)\"", TraditionalForm], + None}, { + FormBox[ + "\"\\!\\(\\*SubscriptBox[\\(c\\), \\(\[UpTee]\\)]\\)\"", + TraditionalForm], None}}, + FrameTicks->{{False, False}, {False, False}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->150, + LabelStyle->GrayLevel[0], + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}, "AxesInFront" -> True}, + PlotRange->{{-1.1, 1.1}, {-0.3, 0.3}}, + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.770583979557695*^9, 3.770584065228504*^9}, + 3.770584805738936*^9, {3.770584844594309*^9, 3.7705848756879*^9}, + 3.770585054700766*^9, 3.7705850854671583`*^9, {3.774042734852344*^9, + 3.774042741539318*^9}, 3.774042831455653*^9, 3.774042889186082*^9, { + 3.7740429740628643`*^9, 3.77404298508883*^9}, 3.774043313781547*^9, { + 3.774043658001062*^9, 3.774043668608696*^9}, {3.774043699098453*^9, + 3.7740438365753107`*^9}, 3.774044196466015*^9, 3.774044286339246*^9, + 3.774044356017893*^9}, + CellLabel-> + "Out[395]=",ExpressionUUID->"4b43f08e-8622-44ca-8076-254d5e591534"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"pp2", "=", + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Piecewise", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"c", "\[GreaterEqual]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"c", "^", "2"}], "/", "4"}], ",", + RowBox[{"c", "<", "0"}]}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"c", "\[GreaterEqual]", "0"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"c", "<", "0"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"c", ",", + RowBox[{"-", "1.2"}], ",", "1.2"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1.1"}], ",", "1.1"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.3"}], ",", "0.3"}], "}"}]}], "}"}]}], ",", + RowBox[{"Frame", "\[Rule]", "True"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "2", "]"}], ",", + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "1", "]"}]}], "}"}]}], + ",", + RowBox[{"Filling", "\[Rule]", "Bottom"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.3"}], ",", "0.3"}], "}"}]}], ",", + RowBox[{"FrameLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\<\!\(\*SubscriptBox[\(c\), \(\[UpTee]\)]\)\>\"", ",", + RowBox[{"Style", "[", + RowBox[{ + "\"\<\!\(\*OverscriptBox[\(r\), \(~\)]\) \!\(\*SubscriptBox[\(D\), \(\ +\[UpTee]\)]\)\>\"", ",", + RowBox[{"Opacity", "[", "0", "]"}]}], "]"}]}], "}"}]}], ",", + RowBox[{"FrameTicks", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"False", ",", "False"}], "}"}], ",", + RowBox[{"{", + RowBox[{"False", ",", "False"}], "}"}]}], "}"}]}], ",", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.012", "]"}], ",", + RowBox[{ + RowBox[{"ColorData", "[", "97", "]"}], "[", "1", "]"}], ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"Inset", "[", + RowBox[{"\"\<Unordered\>\"", ",", + RowBox[{"{", + RowBox[{"0.5", ",", "0.16"}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<Uniform\>\"", ",", + RowBox[{"{", + RowBox[{"0.5", ",", + RowBox[{"-", "0.16"}]}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<Modulated\>\"", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.55"}], ",", + RowBox[{"-", "0.14"}]}], "}"}]}], "]"}], ",", + RowBox[{"Inset", "[", + RowBox[{"\"\<(c)\>\"", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.9"}], ",", + RowBox[{"-", "0.25"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}]}], ",", + RowBox[{"ImageSize", "\[Rule]", "150"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "Black", "}"}]}]}], "]"}]}]], "Input", + CellChangeTimes->CompressedData[" +1:eJwdz08sQgEAx/EYBxeL5d9s+TfMKC4O9RxkHDDazJ+9Q7UiS2mczBySZBws +zXRpLjbPMqzMgcrKoRnTQZZNzaywQs1crJo99HuH7z7nb41iZkiZy2KxKrNB +3Wk6fluWFD36/KWBrIHqOBeuTwvroePTyYfD1qs26DESAij28rpg+IYegFt8 +Sg7tnSWTkM0xMp4T0mVY4aRWoWnCvAddG6YDeJ9J2eHhfpUDblOjbrg0P+uB +1ovMA1QNCkOQ/Dl5goboGaPeWBuHVL7yAxIvsi/YH6NTUJ3nyrnDR+yS0TxW +J1Zzk6L0YjEJBVG5HH6bVYxv5ZYp+Lowp4Uym94CCy3XbqijWoPwOdHHSPw1 +hOB4U1EYStYaI/Bot5tROtL7DjcD/ASMtBzTUEVyfmGQtrE1WX3tXsawoqAZ ++rUSHtQbvB1wRbPTA/8Bk8fcvQ== + "], + CellLabel-> + "In[407]:=",ExpressionUUID->"b3b4cd09-afae-4511-b396-8eb0b0793210"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJxd1wk01GsfB/CJe1W2W7aQLCUkUpabSvNDoltJCSVLiNK1ZN/KEhq7GlmS +pSSkGtm5th8hE6GRNZfrJmsSypJU733fc+c/7+l/zpw5n/N9nmfm+c85833+ +UjaXDO3YSCRSyz+v/75vNOWRUVH5iCr/u15BUM8yw/VAPflf4785MO2b/WdW +xcAM/n7Tao1XEwOceXJ/1RCfQf8nq24UaLyE3P4Mys9p02gdmvva8bdWaBSy +3n9U5D2uhAoqTXs2Q6NOzzsxz3dY+pV6Uf96E8xip3FS7wQudE+7yww1gGOJ +lkXLqXHM46mYzAh9Cs1pduYRpaO41qJzI69ELXiTPi+Rdo2gf1Zwpvr6Kjie +z39ic9EwennmrdPTKgfukyN3WwXeoOuEfemEczFscJGJVY4bQq7+2MXUbQXA +Q9o/qj04gI+XBdj+HnoEByr2yXrkvMZS+dqfI1SyYcNFkUzhBz34bK26k5B/ +BhR9teVlXOjENBMtbQWO2/Cecr14xZKB9E7qOPefcdD/ziDeR/4FUiN6rKOa +wyHiWxotvaQR+QNXtrR5+MPYp5O+JmcR31c4Jryqc4b+kC3GaFCIvbnjn798 +MgKxhErXTu9baJqzzTawZDO8AEXSpjNJQPr3+uH3wePafn+fH+7A2AgZT72j +ifD6Stk3dY92TCuTiOqcjAXl+YW7XDN0XJEakRC9FAIBK1vm7xc+xf41oQ3V +fZ5gXbVvLLKnHJVqypRWDp2DzRfjXIudHqB1x+16jmxtIBmPCHv3a+F6ixxb +iWl3MsVj/8D1qVXE57Pd/bCYkvUKeRUzb/4keQto9+aTo6NfIo/Ywa53m6hA +cckU1Y5pxs0j5svLqykQ+tWKIaXagOmTkRe+BfvC/V69fJeNVSjBqVollm8P +juVTMcmUPJwxWMWfKK4PDRgsn88RgVfX6T7wiGOHM8Uhz0+3t6Ko3Fu3dY1R +MOh7WLbLsAklNF06xr8Hge+XUWG5XXXY3je2l9vXDcTvKoln3SxBjbwPfw0L +W0CviLpxu9E9XF26jyuepAbSguf1tFooxP19fUw+pJSjE/nWTwu3rEuG1njt +nIb5l2gW4eN8aJkKO/N8Tw2YteDOfl8NHtsw4AgIhKFPDRhkmWjT6XYZno22 +xp+rrsZ3XepnszIdYM0MNy/leT6Grks/vZB6AgL9Ag4k+sehjyW5z8FSEG7f +2vSWntGGVevF0iMNYyC8TNLWRYqOI0aRYUeUg2Hl8s9ho7N1SEoJFzsp6QGa +eSVst9TKkIusqWvbZQX+WnbDWtZZ2HdkUDqVqgGd2NMVQfMk9hPcXNfi71uB +kacsH+8Zs4OmG/hdxu8RnhuSFPmUpAcCgutTL0j74SkrTvoJsxHy+beCsX/c +SMeUZykek7sUQWnrDGPwLJVYTze7iX5gdydm5wiZjkcmwwDPBM1KnoH67vZP +/H+PA47Wt/Py9S14KqW245tgOByqifUC40ZUEwlojna9At3v1622iK1BnZGp +pguKTjC351bBvegCFCr7OkiDk9C2Ou1MiV8CmmRGbHneJQYVkb/PkrjacauT +barxpliw6I5iqwmn4/n7Bqfs2oNhf5VAzUHDp3h6pWKxftkDjpcseVA5ynFe +NDG8f60NHO+6LH95LBsXnvh2v7LVBFXByjlRt3PEfm4yfiJ7H65Emv7wVRPd +C3BbulvXikTDzy3XruYdOgyyWQdXXLlDMLH/iN0t2gKZgyLFm9h2Fw+p5vkm +5eyCOqVMz8DGaGI969d4epp0HdVJwx2ta3nhIe1Y6pr+TIyyX5iezFSHsGU5 +EXZGEDG+GBUDu8864saFWrtuuefkuqrx77qhKahKUbt9JlcWAgp5J76axxPj +V04kOkQadKJAVZSPHT0Z7A5rFOTpMFB0fp5bNDMOXMxFGxkLLVjArVw5eykc +7C2F+C5da8RqL07T1LkrYOmqXNu3UIPHTvEHH1pwgtFBC/Zd0wU48+xvETZh +I/A8pjCq8zkRRU0MPI0CJKGZff1SKrRjYHFRQk1ILNDt6hi2VXR0sQgynxIP +AUvzVFPP4KeoRpvCJxc9oVdddAfvpXKku8c8EXpgA3skVrclPcxBCeexnKYg +LRAzlln8WFiJm1Tc3N5+vgAhztaTV+ppOF4hmbWSdwS8lG35qWspyNPymGZ0 +5hv5Q/vjgkJqBv5ioOTTfFgFelU+lHF8v4F+m9eYTPPwQfxiH2xNv48bi++D +D3UveC+/ctom74EDL/0fd1/sI8cf/64bxJmGu88MzHGZyYNMHU/71pWbKKgq +4H52QRh6N8iOGP4ShHcML3oXi8+Q+fQztNrZo7Fy+pPMI8oa8Iss2nzGwQq/ +r8xFh/blk3tzvlbRzDoxyUf8AYwlQ+74SGHXCQaqirA9Csc4kJEuUcha9wIL +fqsp3ZYWDj47Xv9FSWvEmMaFhRsq/rBZpV5MeDvi5MPk2nIzZ7Aq0FRYEi/E +VYOaxpPXjIA++/FRdHkSil8zjHJLkAJDTdsvk6btmCg+OqNSFgv+iuZ71Lvp +eJDseH5aNwScFaxkY24/xSdZj/ziMjwhdflh5NHMf+7/3ivSqks2sKPhhYQM +9wMMcPB5sZ9PG5j/33KVOwzMBD7tHxIqO6k8VokOtQpHHxnZgw+/rAbX1jx8 +eJw+d8fuKGzy/ZguGR6GqUajn2f1V8FbDzd2rY8ZyCEifcl8iyoo9JT6H6uh +oq5+uxGZxg/hqXeoRd/vo5tQ/tnd1/fBs7C50EOy3ljPec3nQe0Q2f925GRq +axqaVyfHdtVtBz/brninyngMXvIL3zogCkGWpS5vYq7ikWbOcw7aH8kVN3e2 +WgbHIP96nUXLX7lgQ9bM8Vt25zE5Z//imCmS2951hq2KCsUgikLAPqtlspxT +iQmnoisWz116qurSQba5p1REkfLH7RNtOmOhk+SKv6bGd78xwrSCMGVO7RTy +j/3KO906WNRWSLjwD4E4/okawmKLjHoq+zNWbn7l5Zz7C8LXHIuLSvcyCE82 +VP1idaWTcIHc6M5ESg9hqTlSv8/V14Sbu2gJetUDhB3eVEcyrIYI84y9N/Rk +f0PYyjXP/2zkMOHwvLGpO2tHCL9YumhrkjtKuI5+hXxScZxwR1av5DPGBOFy +NZreded3hA2O8DHSP0wRZnOutZGmThNWjgrc7sM1Q7hNvV8vopnlJUcz+67k +WcLLw1sqdMzmfjzPEGaeN5mOTBee2dfEGs88DzCtrSVurEll5T/2eccXvqjd +X1k5s3+ZTufLCNP2YuU/9ueO1oTqPW9YObMvmfaSv3FaTZj1/Zn9xfTRy2/u +1tuz5v/YP3+q9XRXdLJyZt8Q+7nJcC3lZK3P7Bemmf3BNL3uGBRvZY3PVApR +/MmGtf54ILup34I+YZVJ73NfWln5ZT23bwvsrPkSXh9aPomz7MaTV+iu8H/7 +jXjlft+SNf+lsUYQx69yhC116Lkpzaw8O+OpThKJNf/wS+BL2Mhy2oVvS/zb +WNYtsnB8pcQyJT/b0pUySzyf/AfZzGA+ + "], {{{}, + {RGBColor[0.880722, 0.611041, 0.142051], Opacity[0.2], EdgeForm[None], + GraphicsGroupBox[ + PolygonBox[{{1, 27, 35, 127, 34, 143, 114, 139, 88, 141, 109, 134, 64, + 142, 112, 137, 82, 140, 105, 130, 42, 113, 138, 85, 107, 132, 55, + 111, 136, 73, 97, 121, 25, 89, 110, 135, 65, 83, 106, 131, 47, 86, + 108, 133, 60, 78, 102, 126, 33, 63, 81, 104, 129, 41, 54, 72, 96, + 120, 24, 46, 59, 77, 101, 125, 32, 62, 80, 103, 128, 40, 53, 71, 95, + 119, 23, 45, 58, 76, 100, 124, 31, 39, 52, 70, 94, 118, 22, 44, 57, + 75, 99, 123, 30, 38, 51, 69, 93, 117, 21, 43, 56, 74, 98, 122, 29, + 37, 50, 68, 92, 116, 20, 28, 36, 49, 67, 91, 115, 19, 18, 17, 16, 15, + 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 203}}]]}, {}, + {RGBColor[0.368417, 0.506779, 0.709798], Opacity[0.2], EdgeForm[None], + GraphicsGroupBox[ + PolygonBox[{{169, 2, 3, 168, 202, 195, 201, 189, 194, 200, 180, 186, + 193, 199, 174, 178, 184, 192, 198, 170, 172, 176, 182, 190, 196, 167, + 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, + 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 173, 177, 183, 191, + 197}}]]}, {}, {}, {}, {}, {}, {}}, {{}, {}, + TagBox[ + {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], + Opacity[1.], + LineBox[{203, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, + 19, 115, 91, 67, 49, 36, 28, 20, 116, 92, 68, 50, 37, 29, 122, 98, + 74, 56, 43, 21, 117, 93, 69, 51, 38, 30, 123, 99, 75, 57, 44, 22, + 118, 94, 70, 52, 39, 31, 124, 100, 76, 58, 45, 23, 119, 95, 71, 53, + 40, 128, 103, 80, 62, 32, 125, 101, 77, 59, 46, 24, 120, 96, 72, 54, + 41, 129, 104, 81, 63, 33, 126, 102, 78, 60, 133, 108, 86, 47, 131, + 106, 83, 65, 135, 110, 89, 25, 121, 97, 73, 136, 111, 55, 132, 107, + 85, 138, 113, 42, 130, 105, 140, 82, 137, 112, 142, 64, 134, 109, + 141, 88, 139, 114, 143, 34, 127}]}, + Annotation[#, "Charting`Private`Tag$57747#1"]& ], + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], + Opacity[1.], + LineBox[{169, 197, 191, 183, 177, 173, 144, 145, 146, 147, 148, 149, + 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, + 164, 165, 166, 167, 196, 190, 182, 176, 172, 170, 198, 192, 184, + 178, 174, 199, 193, 186, 180, 200, 194, 189, 201, 195, 202, 168}]}, + Annotation[#, "Charting`Private`Tag$57747#2"]& ]}}], {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Epilog->{{ + Thickness[0.012], + RGBColor[0.368417, 0.506779, 0.709798], + LineBox[{{0, 0}, {0, -2}}]}, { + TagBox[ + InsetBox["Unordered", {0.5, 0.16}], "InsetString"], + TagBox[ + InsetBox["Uniform", {0.5, -0.16}], "InsetString"], + TagBox[ + InsetBox["Modulated", {-0.55, -0.14}], "InsetString"], + TagBox[ + InsetBox["(c)", {-0.9, -0.25}], "InsetString"]}}, + Frame->{{True, True}, {True, True}}, + FrameLabel->{{ + FormBox[ + StyleBox[ + "\"\\!\\(\\*OverscriptBox[\\(r\\), \\(~\\)]\\) \ +\\!\\(\\*SubscriptBox[\\(D\\), \\(\[UpTee]\\)]\\)\"", + Opacity[0], StripOnInput -> False], TraditionalForm], None}, { + FormBox[ + "\"\\!\\(\\*SubscriptBox[\\(c\\), \\(\[UpTee]\\)]\\)\"", + TraditionalForm], None}}, + FrameTicks->{{False, False}, {False, False}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->150, + LabelStyle->{ + GrayLevel[0]}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}, "AxesInFront" -> True}, + PlotRange->{{-1.1, 1.1}, {-0.3, 0.3}}, + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{ + 3.770585024257648*^9, 3.77058510255801*^9, {3.774042750307012*^9, + 3.7740428248367243`*^9}, 3.774042891583301*^9, {3.774042957269361*^9, + 3.774042988112692*^9}, {3.774043309563458*^9, 3.774043314171821*^9}, + 3.7740433496116037`*^9, {3.774043421473955*^9, 3.774043554482444*^9}, { + 3.7740438106739063`*^9, 3.7740438187563467`*^9}, {3.774043851505499*^9, + 3.77404385681668*^9}, {3.7740439824529047`*^9, 3.7740439937194433`*^9}, + 3.77404414494704*^9, 3.774044294797976*^9, {3.774044507760159*^9, + 3.774044523599522*^9}, {3.77404466973039*^9, 3.7740447173709927`*^9}}, + CellLabel-> + "Out[407]=",ExpressionUUID->"a81cbc8a-e488-404d-9dc1-7ceb38914c26"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/hidden_order/doc/overleaf/phases_scalar.pdf\>\"", ",", + "pp1"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.774042988914166*^9, 3.774043016730563*^9}}, + CellLabel-> + "In[408]:=",ExpressionUUID->"d728fcff-b9a2-4c71-8171-a8abdc435944"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/hidden_order/doc/overleaf/phases_vector.pdf\>\"", ",", + "pp2"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.774042988914166*^9, 3.774043031548027*^9}}, + CellLabel-> + "In[409]:=",ExpressionUUID->"8bbe13fa-dece-41bc-bbeb-237206d26e81"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Indexed", "[", + RowBox[{"x", ",", "2"}], "]"}]], "Input", + CellChangeTimes->{{3.7706319874834423`*^9, 3.7706319901051188`*^9}, { + 3.7706320530589314`*^9, 3.770632080595777*^9}}, + CellLabel-> + "In[235]:=",ExpressionUUID->"8ad43851-a145-489f-ad2a-d1403083b3c5"], + +Cell[BoxData[ + TemplateBox[{"x","2"}, + "IndexedDefault"]], "Output", + CellChangeTimes->{ + 3.770631990380934*^9, {3.770632054776945*^9, 3.7706320809112253`*^9}}, + CellLabel-> + "Out[235]=",ExpressionUUID->"c8927003-4b47-4284-860c-9cf89f4a8999"] +}, Open ]], + +Cell[BoxData[ + FractionBox["\[Lambda]", + RowBox[{"1", "+", + RowBox[{ + RowBox[{"c", "/", "\[Lambda]"}], "/", + RowBox[{"(", + RowBox[{"1", "+", + RowBox[{"d", " ", "\[CapitalDelta]t"}]}], ")"}]}]}]]], "Input", + CellChangeTimes->{{3.770634393156534*^9, + 3.7706344878251953`*^9}},ExpressionUUID->"312f4d6a-918c-4fea-a12a-\ +40cac090528c"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{"b", "^", "2"}], "/", + RowBox[{"(", + RowBox[{"4", + RowBox[{"\[Lambda]", "^", "2"}]}], ")"}]}], + RowBox[{ + RowBox[{"d", " ", + RowBox[{"qs", "^", "4"}]}], "+", + RowBox[{"a", " ", "\[CapitalDelta]t"}]}]], "+", + RowBox[{"1", "/", "\[Lambda]"}]}], ")"}], + RowBox[{"-", "1"}]], "/", "\[Lambda]"}], "//", "FullSimplify"}]], "Input",\ + + CellChangeTimes->{{3.770634171474904*^9, 3.770634238386848*^9}, { + 3.7706342843863277`*^9, 3.770634298943604*^9}, {3.77063434913536*^9, + 3.770634349567974*^9}}, + CellLabel-> + "In[243]:=",ExpressionUUID->"dcfed889-f347-4169-bc6d-e488d9f5ad66"], + +Cell[BoxData[ + RowBox[{"1", "-", + FractionBox[ + SuperscriptBox["b", "2"], + RowBox[{ + SuperscriptBox["b", "2"], "+", + RowBox[{"4", " ", "d", " ", + SuperscriptBox["qs", "4"], " ", "\[Lambda]"}], "+", + RowBox[{ + "4", " ", "a", " ", "\[CapitalDelta]t", " ", "\[Lambda]"}]}]]}]], "Output",\ + + CellChangeTimes->{{3.770634227655197*^9, 3.770634238785038*^9}, + 3.770634286362319*^9, {3.770634345136135*^9, 3.770634351688837*^9}}, + CellLabel-> + "Out[243]=",ExpressionUUID->"2c29099a-a822-4c55-a6db-afd274e085fa"] +}, Open ]], + +Cell[BoxData[ + RowBox[{"Integrate", "[", " ", + RowBox[{ + RowBox[{"\[Eta]", " ", + RowBox[{"Cos", "[", + RowBox[{"qs", " ", "x"}], "]"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "L"}], ",", "L"}], "}"}]}]}]], "Input", + CellChangeTimes->{{3.770637095208066*^9, + 3.770637109523609*^9}},ExpressionUUID->"bec159f7-aa33-4944-8826-\ +33d1e5fac3c1"] +}, +WindowSize->{614, 764}, +WindowMargins->{{2, Automatic}, {Automatic, 2}}, +FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[558, 20, 218, 3, 31, "Input",ExpressionUUID->"11c1c939-5ea7-4e35-820b-196b7afc7932"], +Cell[779, 25, 2633, 77, 206, "Input",ExpressionUUID->"98997921-fc2d-40a3-b750-05550f4b5c59"], +Cell[CellGroupData[{ +Cell[3437, 106, 1188, 31, 78, "Input",ExpressionUUID->"2ebc8031-6231-481f-b049-707f66f906b6"], +Cell[4628, 139, 353, 9, 23, "Message",ExpressionUUID->"42656e0b-6b9d-4ade-a02a-1e1a2c506fba"] +}, Open ]], +Cell[CellGroupData[{ +Cell[5018, 153, 282, 5, 31, "Input",ExpressionUUID->"b1ffed5d-b41b-4c8d-9f41-b0dd65eaa34f"], +Cell[5303, 160, 1144, 32, 62, "Output",ExpressionUUID->"c2d3dc1c-b8ea-46f2-b457-b0dbb99b7d7d"] +}, Open ]], +Cell[6462, 195, 400, 9, 31, "Input",ExpressionUUID->"d2d5bc38-647e-41ae-9585-f6514cd2c6c7"], +Cell[6865, 206, 1838, 47, 124, "Input",ExpressionUUID->"0f544c33-f435-459c-a473-d005863f95f2"], +Cell[CellGroupData[{ +Cell[8728, 257, 251, 4, 31, "Input",ExpressionUUID->"b4dcf7cc-1bf9-49f0-a9af-a4dcf6893896"], +Cell[8982, 263, 158, 2, 35, "Output",ExpressionUUID->"639ccfaa-595b-4074-8a0f-26ae9b6470cb"] +}, Open ]], +Cell[CellGroupData[{ +Cell[9177, 270, 589, 17, 31, "Input",ExpressionUUID->"5b3333e0-2528-421d-98d3-c7414514d461"], +Cell[9769, 289, 386, 10, 59, "Output",ExpressionUUID->"81ba9537-513b-4bf7-9467-d533e9b63498"] +}, Open ]], +Cell[10170, 302, 1027, 32, 90, "Input",ExpressionUUID->"19f1d159-2940-4211-a220-00ea16b951c8"], +Cell[CellGroupData[{ +Cell[11222, 338, 365, 10, 41, "Input",ExpressionUUID->"7886c291-33ec-4ace-a89c-ce01acce2fe0"], +Cell[11590, 350, 622, 18, 62, "Output",ExpressionUUID->"691b31d2-84e5-47dc-abab-1a896d8bf522"] +}, Open ]], +Cell[CellGroupData[{ +Cell[12249, 373, 1710, 49, 101, "Input",ExpressionUUID->"4da03829-80f7-4d3c-b1df-3061c9d0fa86"], +Cell[13962, 424, 502, 14, 65, "Output",ExpressionUUID->"de2415bd-ffa4-42c0-a20c-1aaf19c5b3cd"] +}, Open ]], +Cell[CellGroupData[{ +Cell[14501, 443, 795, 24, 55, "Input",ExpressionUUID->"deee272c-c109-48f7-a88d-1ee72a679856"], +Cell[15299, 469, 278, 7, 58, "Output",ExpressionUUID->"d46cf980-3684-47bc-a454-7e432e809dda"] +}, Open ]], +Cell[15592, 479, 359, 9, 31, "Input",ExpressionUUID->"67413114-8b38-4eff-8a22-b1615b0ea9bb"], +Cell[CellGroupData[{ +Cell[15976, 492, 177, 3, 31, "Input",ExpressionUUID->"415b3bc6-5bea-472c-b832-a17a204ee60e"], +Cell[16156, 497, 600, 20, 63, "Output",ExpressionUUID->"c4009c3e-79a6-4a49-aa2e-fc55f5e134e4"] +}, Open ]], +Cell[CellGroupData[{ +Cell[16793, 522, 737, 18, 55, "Input",ExpressionUUID->"7dbbfd98-b060-4a55-86f6-4759247a6580"], +Cell[17533, 542, 505, 13, 63, "Output",ExpressionUUID->"de6f3c84-c35e-4336-9744-7ae8779837e0"] +}, Open ]], +Cell[CellGroupData[{ +Cell[18075, 560, 488, 10, 55, "Input",ExpressionUUID->"68ae3535-4b40-4f87-b02a-90936fba2195"], +Cell[18566, 572, 4926, 157, 381, "Output",ExpressionUUID->"aa33fa6c-e061-4c62-a7cd-54f992e9b260"] +}, Open ]], +Cell[CellGroupData[{ +Cell[23529, 734, 385, 10, 31, "Input",ExpressionUUID->"32ce610b-fed3-46f7-bf71-317ac1393c49"], +Cell[23917, 746, 647, 14, 59, "Output",ExpressionUUID->"29074888-bd44-4674-a7b9-f356fb297e11"] +}, Open ]], +Cell[CellGroupData[{ +Cell[24601, 765, 5043, 133, 360, "Input",ExpressionUUID->"5b48adc3-c181-4ba9-8919-787aedf6881e"], +Cell[29647, 900, 11145, 212, 118, "Output",ExpressionUUID->"4b43f08e-8622-44ca-8076-254d5e591534"] +}, Open ]], +Cell[CellGroupData[{ +Cell[40829, 1117, 4385, 120, 360, "Input",ExpressionUUID->"b3b4cd09-afae-4511-b396-8eb0b0793210"], +Cell[45217, 1239, 8970, 169, 118, "Output",ExpressionUUID->"a81cbc8a-e488-404d-9dc1-7ceb38914c26"] +}, Open ]], +Cell[54202, 1411, 326, 8, 78, "Input",ExpressionUUID->"d728fcff-b9a2-4c71-8171-a8abdc435944"], +Cell[54531, 1421, 326, 8, 78, "Input",ExpressionUUID->"8bbe13fa-dece-41bc-bbeb-237206d26e81"], +Cell[CellGroupData[{ +Cell[54882, 1433, 287, 6, 31, "Input",ExpressionUUID->"8ad43851-a145-489f-ad2a-d1403083b3c5"], +Cell[55172, 1441, 245, 6, 35, "Output",ExpressionUUID->"c8927003-4b47-4284-860c-9cf89f4a8999"] +}, Open ]], +Cell[55432, 1450, 356, 10, 50, "Input",ExpressionUUID->"312f4d6a-918c-4fea-a12a-40cac090528c"], +Cell[CellGroupData[{ +Cell[55813, 1464, 780, 23, 52, "Input",ExpressionUUID->"dcfed889-f347-4169-bc6d-e488d9f5ad66"], +Cell[56596, 1489, 533, 14, 62, "Output",ExpressionUUID->"2c29099a-a822-4c55-a6db-afd274e085fa"] +}, Open ]], +Cell[57144, 1506, 379, 11, 31, "Input",ExpressionUUID->"bec159f7-aa33-4944-8826-33d1e5fac3c1"] +} +] +*) + |