(* 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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    "], {{{}, {}, {}, 
      {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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         "]]]}, {}, {}, {}, {}, {}, {}}, {{}, {}, {}, 
      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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    "], {{{}, 
      {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"]
}
]
*)