(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.3' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[      7880,        224]
NotebookOptionsPosition[      6860,        191]
NotebookOutlinePosition[      7405,        214]
CellTagsIndexPosition[      7334,        209]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\<\
Migrating Populations : now we consider u_t = -cu_x, u (x, 0) = u0 (x)
\
\>", "Section",
 Evaluatable->False,
 CellChangeTimes->{{3.760366941524991*^9, 3.760366945568947*^9}, {
   3.760367111299034*^9, 3.7603671228974*^9}, {3.761037532746563*^9, 
   3.761037534511614*^9}, {3.7610433232013807`*^9, 3.761043326040297*^9}, {
   3.7610433729954967`*^9, 3.761043375686651*^9}, 3.761043597401373*^9},
 CellLabel->"In[77]:=",ExpressionUUID->"55693a20-c381-4b7f-a6a5-454b39e3d16b"],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.761045990842964*^9, 3.7610459937156*^9}, 
   3.76104680292583*^9},
 CellLabel->"In[11]:=",ExpressionUUID->"95d36ad6-be1a-41b5-b01f-be49482aeb05"],

Cell[BoxData[
 RowBox[{"DynamicModule", "[", 
  RowBox[{
   RowBox[{"{", "U", "}"}], ",", 
   RowBox[{
    RowBox[{"UMigration", "=", 
     RowBox[{
      RowBox[{"U", "[", 
       RowBox[{"x", ",", "t"}], "]"}], "/.", 
      RowBox[{"First", "[", 
       RowBox[{"DSolve", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"D", "[", 
             RowBox[{
              RowBox[{"U", "[", 
               RowBox[{"x", ",", "t"}], "]"}], ",", "t"}], "]"}], "\[Equal]", 
            
            RowBox[{
             RowBox[{"-", "c"}], "*", 
             RowBox[{"D", "[", 
              RowBox[{
               RowBox[{"U", "[", 
                RowBox[{"x", ",", "t"}], "]"}], ",", "x"}], "]"}]}]}], ",", 
           RowBox[{
            RowBox[{"U", "[", 
             RowBox[{"x", ",", "0"}], "]"}], "\[Equal]", 
            RowBox[{"PDF", "[", 
             RowBox[{
              RowBox[{"NormalDistribution", "[", 
               RowBox[{
                RowBox[{"Evaluate", "[", 
                 RowBox[{
                 "Input", "[", 
                  "\"\<Please input the the mean of your distribution\>\"", 
                  "]"}], "]"}], ",", 
                RowBox[{"Evaluate", "[", 
                 RowBox[{
                 "Input", "[", 
                  "\"\<Please input the standard deviation of your \
distribution\>\"", "]"}], "]"}]}], "]"}], ",", "x"}], "]"}]}]}], "}"}], ",", 
         RowBox[{"U", "[", 
          RowBox[{"x", ",", "t"}], "]"}], ",", 
         RowBox[{"{", 
          RowBox[{"x", ",", "t"}], "}"}]}], "]"}], "]"}]}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"Manipulate", "[", 
     RowBox[{
      RowBox[{"Plot", "[", 
       RowBox[{
        RowBox[{"UMigration", "/.", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"c", "\[Rule]", "speed"}], ",", 
           RowBox[{"t", "\[Rule]", "time"}]}], "}"}]}], ",", 
        RowBox[{"{", 
         RowBox[{"x", ",", "0", ",", "100"}], "}"}], ",", 
        RowBox[{"AxesLabel", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{"x", ",", "u"}], "}"}]}], ",", 
        RowBox[{"Ticks", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{"25", ",", " ", "\"\< \>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"50", ",", " ", "\"\< \>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"75", ",", " ", "\"\< \>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"100", ",", "\"\< \>\""}], "}"}]}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{".02", ",", "\"\< \>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{".04", ",", " ", "\"\< \>\""}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{".06", ",", " ", "\"\< \>\""}], "}"}]}], "}"}]}], 
          "}"}]}], ",", 
        RowBox[{"PlotLabel", "\[Rule]", 
         RowBox[{"Row", "[", 
          RowBox[{"{", 
           RowBox[{"\"\<Migrating Population\\n\>\"", ",", 
            RowBox[{"HoldForm", "[", 
             RowBox[{
              RowBox[{"D", "[", 
               RowBox[{"u", ",", "t"}], "]"}], "\[Equal]", 
              RowBox[{
               RowBox[{"-", "c"}], " ", 
               RowBox[{"D", "[", 
                RowBox[{"u", ",", "x"}], "]"}]}]}], "]"}]}], "}"}], "]"}]}]}],
        "]"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"speed", ",", "10", ",", "\"\<speed c\>\""}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"10", ",", "50"}], "}"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"time", ",", "0", ",", "\"\<time t\>\""}], "}"}], ",", "0", 
        ",", "1"}], "}"}], ",", 
      RowBox[{"ControlType", "\[Rule]", 
       RowBox[{"{", 
        RowBox[{"SetterBar", ",", "Trigger"}], "}"}]}], ",", 
      RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}]}], 
  "]"}]], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.760367146011127*^9, 3.7603673544782553`*^9}, {
  3.761045948854948*^9, 3.761045986382255*^9}, {3.7610465904403276`*^9, 
  3.761046663735731*^9}, {3.761046702933066*^9, 3.7610467151163063`*^9}, {
  3.76104674783392*^9, 3.761046785397669*^9}},
 CellTags->"Migration",
 CellLabel->"In[14]:=",ExpressionUUID->"b5696fba-670f-44ea-b59d-74e0f4d83174"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Button", "[", 
   RowBox[{"\"\<Click to start\>\"", ",", 
    RowBox[{
     RowBox[{"nb", "=", 
      RowBox[{"EvaluationNotebook", "[", "]"}]}], ";", "\[IndentingNewLine]", 
     
     RowBox[{
      RowBox[{"NotebookFind", "[", 
       RowBox[{"nb", ",", "\"\<Migration\>\"", ",", "All", ",", "CellTags"}], 
       "]"}], "\[IndentingNewLine]", 
      RowBox[{"SelectionEvaluate", "[", "nb", "]"}]}]}]}], "]"}]}]], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.761297915595083*^9, 3.76129792576759*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"44f0436a-2bfb-40c1-937d-963f0658761e"],

Cell[BoxData[
 ButtonBox["\<\"Click to start\"\>",
  Appearance->Automatic,
  ButtonFunction:>($CellContext`nb = EvaluationNotebook[]; 
   NotebookFind[$CellContext`nb, "Migration", All, CellTags] 
    SelectionEvaluate[$CellContext`nb]),
  Evaluator->Automatic,
  Method->"Preemptive"]], "Output",
 CellChangeTimes->{3.761297934129669*^9},
 CellLabel->"Out[13]=",ExpressionUUID->"83e8d6c3-4f42-4a45-a933-18f33123f655"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1158, 1243},
WindowMargins->{{114, Automatic}, {Automatic, 6}},
FrontEndVersion->"11.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2018)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "Migration"->{
  Cell[1264, 38, 4476, 119, 19, "Input",ExpressionUUID->"b5696fba-670f-44ea-b59d-74e0f4d83174",
   CellOpen->False,
   CellTags->"Migration"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"Migration", 7167, 202}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 484, 9, 116, "Section",ExpressionUUID->"55693a20-c381-4b7f-a6a5-454b39e3d16b",
 Evaluatable->False],
Cell[1067, 33, 194, 3, 30, "Input",ExpressionUUID->"95d36ad6-be1a-41b5-b01f-be49482aeb05"],
Cell[1264, 38, 4476, 119, 19, "Input",ExpressionUUID->"b5696fba-670f-44ea-b59d-74e0f4d83174",
 CellOpen->False,
 CellTags->"Migration"],
Cell[CellGroupData[{
Cell[5765, 161, 645, 15, 19, "Input",ExpressionUUID->"44f0436a-2bfb-40c1-937d-963f0658761e",
 CellOpen->False],
Cell[6413, 178, 419, 9, 45, "Output",ExpressionUUID->"83e8d6c3-4f42-4a45-a933-18f33123f655"]
}, Open  ]]
}, Open  ]]
}
]
*)