(* 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[ 160916, 3981] NotebookOptionsPosition[ 156139, 3903] NotebookOutlinePosition[ 156503, 3919] CellTagsIndexPosition[ 156460, 3916] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["With the explicit expressions - ideal gas", "Section", CellChangeTimes->{{3.85968594258692*^9, 3.8596859548032*^9}, { 3.85968602880628*^9, 3.859686040225389*^9}, {3.8597001728473387`*^9, 3.859700178579138*^9}, {3.859792831078507*^9, 3.859792831544446*^9}, 3.8598145828583717`*^9},ExpressionUUID->"af616f43-a4f9-4918-b6eb-\ 1c3097adaf06"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"kB", "=", RowBox[{"1.380649", " ", SuperscriptBox["10", RowBox[{"-", "23"}]]}]}], ";"}], RowBox[{"(*", RowBox[{"J", "/", "K"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"h", "=", RowBox[{"6.62607015", " ", SuperscriptBox["10", RowBox[{"-", "34"}]]}]}], ";"}], " ", RowBox[{"(*", RowBox[{"J", "/", "Hz"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Da", "=", RowBox[{"1.66053906660", " ", SuperscriptBox["10", RowBox[{"-", "27"}]]}]}], ";"}], RowBox[{"(*", "kg", "*)"}]}]}], "Input", CellChangeTimes->{{3.859004032593636*^9, 3.859004041918112*^9}, { 3.859006453100181*^9, 3.859006464095994*^9}, {3.8590064951508503`*^9, 3.859006520248178*^9}, {3.859006607326933*^9, 3.859006630071869*^9}}, CellLabel->"In[21]:=",ExpressionUUID->"672b74be-f9eb-48ef-8e80-38b97f8749ec"], Cell[BoxData[ RowBox[{ RowBox[{"\[Kappa]num", "=", "100"}], ";", RowBox[{"\[Kappa]min", "=", "0.5"}], ";", RowBox[{"\[Kappa]max", "=", "2"}], ";", RowBox[{"Ratios4\[Kappa]", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], ";"}]], "Input",\ CellChangeTimes->{{3.859527096233446*^9, 3.859527107406684*^9}, { 3.8595326227768383`*^9, 3.859532631404169*^9}, {3.859532677809911*^9, 3.859532678052629*^9}, {3.859532727468124*^9, 3.859532727693267*^9}, { 3.8596106610008802`*^9, 3.859610662580072*^9}, {3.8596109999687023`*^9, 3.8596110000351048`*^9}}, CellLabel->"In[24]:=",ExpressionUUID->"4c09e09b-b1dc-4eff-9ef2-d7eec4e53b0b"], Cell[BoxData[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "1"}], ",", RowBox[{"j", "\[LessEqual]", RowBox[{"\[Kappa]num", "+", "1"}]}], ",", RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Kappa]", "=", RowBox[{"\[Kappa]min", "+", RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], " ", RowBox[{ RowBox[{"(", RowBox[{"\[Kappa]max", "-", "\[Kappa]min"}], ")"}], "/", "\[Kappa]num"}]}]}]}], ";", " ", RowBox[{"(*", RowBox[{"=", RowBox[{"m2", "/", "m1"}]}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"u", "=", "0"}], ";", "\[IndentingNewLine]", RowBox[{"m2", "=", RowBox[{"10", " ", "Da"}]}], ";", RowBox[{"(*", RowBox[{"mass", " ", "of", " ", "a", " ", "molecule"}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mixture", " ", "state", " ", "variables"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", "1"}], ";", " ", RowBox[{"(*", RowBox[{"kg", "/", SuperscriptBox["m", "3"]}], "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"0", " ", SuperscriptBox["10", "3"]}]}], ";", " ", RowBox[{"(*", RowBox[{"kg", " ", RowBox[{"m", "/", "s"}]}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "set", " ", "either", " ", "energy", " ", "or", " ", "temperature"}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", " ", RowBox[{ RowBox[{ FractionBox["3", "2"], " ", "kB", " ", "300", RowBox[{"(", FractionBox["\[Rho]", "m2"], ")"}]}], "+", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u", "2"], "\[Rho]"]}]}]}], ";", " ", RowBox[{"(*", RowBox[{"J", "/", SuperscriptBox["m", "3"]}], "*)"}], RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{ "some", " ", "reasonable", " ", "estimate", " ", "of", " ", "total", " ", "mixture", " ", "energy"}], ";", " ", RowBox[{ RowBox[{"Note", " ", "that", " ", "with", " ", "u"}], "=", RowBox[{ RowBox[{"0", " ", "we", " ", "have", " ", "e"}], "=", "\[Epsilon]"}]}]}], ",", " ", RowBox[{ "that", " ", "is", " ", "total", " ", "mixture", " ", "energy", " ", "is", " ", "equal", " ", "to", " ", "internal", " ", "mixture", " ", "energy"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"T", "=", "300"}], ";"}], RowBox[{"(*", "K", "*)"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"rel26", "=", RowBox[{ SuperscriptBox[ RowBox[{"\[Kappa]", " "}], RowBox[{ RowBox[{"5", "/", "2"}], " ", "\[Kappa]"}]], SuperscriptBox["m2", RowBox[{"4", " ", RowBox[{"(", RowBox[{"1", "-", "\[Kappa]"}], ")"}]}]], " ", SuperscriptBox["\[Rho]1", "\[Kappa]"], SuperscriptBox[ RowBox[{"(", RowBox[{"4", " ", FractionBox["\[Pi]", "3"], " ", FractionBox[ RowBox[{"e", "-", FractionBox[ SuperscriptBox["u", "2"], RowBox[{"2", " ", "\[Rho]"}]]}], RowBox[{ SuperscriptBox["h", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[Kappa]", " ", "\[Rho]1"}], "+", "\[Rho]", "-", "\[Rho]1"}], ")"}]}]]}], ")"}], RowBox[{ RowBox[{"3", "/", "2"}], " ", RowBox[{"(", RowBox[{"1", "-", "\[Kappa]"}], ")"}]}]]}]}], ";", "\[IndentingNewLine]", RowBox[{"rel24", "=", RowBox[{ FractionBox[ RowBox[{ RowBox[{"2", " ", "e", " ", SuperscriptBox["\[Rho]", "2"]}], "+", RowBox[{ SuperscriptBox["u", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "-", "1"}], ")"}], RowBox[{"(", RowBox[{"\[Rho]", "-", "\[Rho]1"}], ")"}]}]}], RowBox[{"2", " ", "\[Rho]", " ", RowBox[{"(", RowBox[{"\[Rho]1", "+", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], RowBox[{"(", RowBox[{"\[Rho]", "-", "\[Rho]1"}], ")"}]}]}], ")"}]}]], FractionBox["\[Rho]1", "\[Rho]"]}]}], ";", "\[IndentingNewLine]", RowBox[{"rel23", "=", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], " ", "u"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]1sol", "=", RowBox[{ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"\[Rho]", "-", "\[Rho]1"}], "\[Equal]", "rel26"}], ",", RowBox[{"{", RowBox[{"\[Rho]1", ",", RowBox[{"0.5", " ", "\[Rho]"}]}], "}"}]}], "]"}], "//", "Flatten"}]}], ";", "\[IndentingNewLine]", RowBox[{"e1sol", "=", RowBox[{ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"e1", "\[Equal]", "rel24"}], "/.", "\[Rho]1sol"}], ",", RowBox[{"{", RowBox[{"e1", ",", RowBox[{"0.5", " ", "e"}]}], "}"}]}], "]"}], "//", "Flatten"}]}], ";", "\[IndentingNewLine]", RowBox[{"u1sol", "=", RowBox[{ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"u1", "\[Equal]", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "u"}]}], "/.", "\[Rho]1sol"}], ",", RowBox[{"{", RowBox[{"u1", ",", RowBox[{"0.5", " ", "u"}]}], "}"}]}], "]"}], "//", "Flatten"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]2sol", "=", RowBox[{"{", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"\[Rho]", "-", "\[Rho]1"}], ")"}], "/.", "\[Rho]1sol"}], ")"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"e2sol", "=", RowBox[{"{", RowBox[{"e2", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"e", "-", "e1"}], "/.", "e1sol"}], ")"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"u2sol", "=", RowBox[{"{", RowBox[{"u2", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], " ", "u"}], "/.", "\[Rho]2sol"}], ")"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"s1sol", "=", RowBox[{"{", RowBox[{"s1", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"kB", " ", FractionBox["\[Rho]1", "m1"], RowBox[{"(", RowBox[{ FractionBox["5", "2"], "+", RowBox[{"Log", "[", RowBox[{ FractionBox["m1", "\[Rho]1"], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m1"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], " ", FractionBox[ RowBox[{"e1", "-", FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}], RowBox[{"\[Rho]1", "/", "m1"}]]}], ")"}], RowBox[{"3", "/", "2"}]]}], "]"}]}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", " ", SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]]}]}]}], "/.", "\[Rho]1sol"}], "/.", "u1sol"}], "/.", "e1sol"}], ")"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"s2sol", "=", RowBox[{"{", RowBox[{"s2", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"kB", " ", FractionBox["\[Rho]2", "m2"], RowBox[{"(", RowBox[{ FractionBox["5", "2"], "+", RowBox[{"Log", "[", RowBox[{ FractionBox["m2", "\[Rho]2"], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m2"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], " ", FractionBox[ RowBox[{"e2", "-", FractionBox[ SuperscriptBox["u2", "2"], RowBox[{"2", " ", "\[Rho]2"}]]}], RowBox[{"\[Rho]2", "/", "m2"}]]}], ")"}], RowBox[{"3", "/", "2"}]]}], "]"}]}], ")"}]}], "/.", "\[Rho]2sol"}], "/.", "u2sol"}], "/.", "e2sol"}], ")"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Rho]star", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", FractionBox["kB", "m1"]}], RowBox[{"Log", "[", FractionBox["\[Rho]1", "m1"], "]"}]}], "+", RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m1"], RowBox[{"Log", "[", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m1"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], " ", FractionBox["m1", "\[Rho]1"], RowBox[{"(", RowBox[{"e1", "-", FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}], ")"}]}], "]"}]}], "+", RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m1"], " ", FractionBox["1", RowBox[{"e1", "-", FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}]], FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", " ", SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]]}]}]}], "/.", "\[Rho]1sol"}], "/.", "u1sol"}], "/.", "e1sol"}]}], ";", "\[IndentingNewLine]", RowBox[{"estar", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"(", RowBox[{"kB", " ", FractionBox["\[Rho]1", "m1"], RowBox[{"(", RowBox[{ FractionBox["5", "2"], "+", RowBox[{"Log", "[", RowBox[{ FractionBox["m1", "\[Rho]1"], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m1"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], " ", FractionBox[ RowBox[{"e1", "-", FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}], RowBox[{"\[Rho]1", "/", "m1"}]]}], ")"}], RowBox[{"3", "/", "2"}]]}], "]"}]}], ")"}]}], ")"}], ",", "e1"}], "]"}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", " ", SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]]}]}]}], "/.", "\[Rho]1sol"}], "/.", "u1sol"}], "/.", "e1sol"}]}], ";", "\[IndentingNewLine]", RowBox[{"p", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "e"}], "+", RowBox[{"\[Rho]", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s"}]}], ")"}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", RowBox[{"s", "\[Rule]", RowBox[{"s1", "+", "s2"}]}]}], "/.", "\[Rho]1sol"}], "/.", "e1sol"}], "/.", "s1sol"}], "/.", "s2sol"}]}], ";", "\[IndentingNewLine]", RowBox[{"p1", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e1"}], "+", RowBox[{"\[Rho]1", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s1"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", "e1sol"}], "/.", "\[Rho]1sol"}], "/.", "s1sol"}]}], ";", "\[IndentingNewLine]", RowBox[{"p2", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e2"}], "+", RowBox[{"\[Rho]2", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s2"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", "e2sol"}], "/.", "\[Rho]2sol"}], "/.", "s2sol"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", "j", "]"}], "]"}], "=", RowBox[{"{", RowBox[{"\[Kappa]", ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"\[Rho]1", "/", "\[Rho]"}], "/.", "\[Rho]1sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"e", "/", "e1"}]}], ")"}], "/.", "\[Rho]1sol"}], "/.", "e1sol"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"s", "/", "s1"}]}], ")"}], "/.", RowBox[{"s", "\[Rule]", RowBox[{"s1", "+", "s2"}]}]}], "/.", "\[Rho]1sol"}], "/.", "s1sol"}], "/.", "s2sol"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "e"}], "-", "e1"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "s"}], "-", "s1"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "p"}], ")"}]}], "/.", RowBox[{"s", "\[Rule]", RowBox[{"s1", "+", "s2"}]}]}], "/.", "\[Rho]1sol"}], "/.", "e1sol"}], "/.", "s1sol"}], "/.", "s2sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "\[Rho]1", ")"}], "/.", "\[Rho]1sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "\[Rho]2", ")"}], "/.", "\[Rho]2sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "e1", ")"}], "/.", "e1sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "e2", ")"}], "/.", "e2sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "s1", ")"}], "/.", "s1sol"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{"(", "s2", ")"}], "/.", "s2sol"}], "]"}], ",", RowBox[{"Chop", "[", "p", "]"}], ",", RowBox[{"Chop", "[", "p1", "]"}], ",", RowBox[{"Chop", "[", "p2", "]"}], ",", RowBox[{"Chop", "[", "estar", "]"}]}], "}"}]}]}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.859003684163105*^9, 3.859003745959848*^9}, { 3.8590038322325*^9, 3.859003848442205*^9}, {3.859003884000902*^9, 3.859004020468811*^9}, {3.859006604112194*^9, 3.8590066046528378`*^9}, { 3.85900665573822*^9, 3.8590066835617447`*^9}, {3.8590073292796783`*^9, 3.8590073304610863`*^9}, {3.859023404317885*^9, 3.859023663627729*^9}, { 3.859023738481776*^9, 3.859023780408155*^9}, {3.8590238394739103`*^9, 3.859023844981728*^9}, {3.859023941592525*^9, 3.859023953089074*^9}, { 3.8590240543670197`*^9, 3.85902406442233*^9}, {3.859024252666738*^9, 3.859024280881693*^9}, 3.859037100153151*^9, {3.8590380490801477`*^9, 3.859038068524189*^9}, {3.859038405652028*^9, 3.8590384574387617`*^9}, { 3.8593427722437763`*^9, 3.859342781424169*^9}, {3.8593436404583282`*^9, 3.8593436655903177`*^9}, {3.859343987204646*^9, 3.859343987525599*^9}, 3.8593440274099073`*^9, 3.8593441074498043`*^9, {3.859346582991984*^9, 3.859346625574361*^9}, {3.859368213800564*^9, 3.859368235554236*^9}, { 3.8593682808908997`*^9, 3.859368303332468*^9}, {3.859368953999317*^9, 3.859368955909123*^9}, {3.859369386858694*^9, 3.859369391311701*^9}, { 3.859369859383062*^9, 3.85936987637763*^9}, {3.859370557220182*^9, 3.859370646221528*^9}, {3.85937068982584*^9, 3.859370697362488*^9}, { 3.859370863588719*^9, 3.859370876316638*^9}, {3.859526501949636*^9, 3.859526502729855*^9}, {3.859527111302061*^9, 3.8595271165928307`*^9}, { 3.8595272117756033`*^9, 3.859527212040094*^9}, {3.859527251340817*^9, 3.859527260462924*^9}, {3.859527367888115*^9, 3.859527370901854*^9}, { 3.8595326367401333`*^9, 3.859532647197557*^9}, {3.8595340027213163`*^9, 3.859534010415688*^9}, {3.859607000362165*^9, 3.859607138478568*^9}, { 3.8596082694304028`*^9, 3.859608278676107*^9}, {3.859793003661746*^9, 3.859793028508874*^9}, {3.859793080585743*^9, 3.859793083620883*^9}, { 3.859793117954851*^9, 3.8597931276703176`*^9}, {3.859793243804906*^9, 3.859793249056563*^9}, {3.8597933948809*^9, 3.859793403447342*^9}, { 3.859814671922962*^9, 3.8598147229474688`*^9}, 3.859815483727086*^9, 3.859816276041547*^9, {3.890319345978245*^9, 3.89031938535981*^9}},ExpressionUUID->"ca4f6923-c1ae-4710-b6e5-\ a71811d566ff"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{ "\[Kappa]", ",", "j", ",", "p", ",", "p1", ",", "p2", ",", "estar"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.859793412909254*^9, 3.85979341447532*^9}, { 3.85981488961779*^9, 3.859814909117222*^9}}, CellLabel->"In[26]:=",ExpressionUUID->"f2ee71cb-b939-4841-bfc6-1df9b62859b9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e1"}], ")"}], "-", RowBox[{ FractionBox["1", "estar"], RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"(", RowBox[{"s1", "+", "s2"}], ")"}]}], "-", "s1"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "p"}], ")"}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"s1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}], "/.", RowBox[{"s2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "12"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "13"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "14"}], "]"}], "]"}]}]}], "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "15"}], "]"}], "]"}]}]}], ",", SuperscriptBox["10", RowBox[{"-", "8"}]]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", "j", "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e2"}], ")"}], "-", RowBox[{ FractionBox["1", "estar"], RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], RowBox[{"(", RowBox[{"s1", "+", "s2"}], ")"}]}], "-", "s2"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], "p"}], ")"}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"s1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}], "/.", RowBox[{"s2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "12"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "13"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "14"}], "]"}], "]"}]}]}], "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "15"}], "]"}], "]"}]}]}], ",", SuperscriptBox["10", RowBox[{"-", "8"}]]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"AxesStyle", " ", "\[Rule]", " ", RowBox[{"Thickness", "[", "0.0025", "]"}]}], ",", RowBox[{"PlotTheme", "\[Rule]", RowBox[{"{", "\"\\"", "}"}]}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontSize", "\[Rule]", "16"}], ",", "Black"}], "}"}]}], ",", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"Style", "[", RowBox[{"\"\<\[Kappa]\>\"", RowBox[{"(*", "\"\<\\kappa\>\"", "*)"}], ",", " ", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", " ", "\[Rule]", " ", "20"}]}], "]"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.859534638665761*^9, 3.859534640985155*^9}, { 3.859534707586021*^9, 3.859534718802548*^9}, {3.859534787685721*^9, 3.859535058453478*^9}, {3.8596106558200397`*^9, 3.8596107119598093`*^9}, { 3.859793430549447*^9, 3.859793446022356*^9}, {3.859814797279438*^9, 3.859814883777583*^9}, {3.859814919534582*^9, 3.859815051090249*^9}}, CellLabel->"In[27]:=",ExpressionUUID->"27db8a35-fa9d-42cd-bcf7-65dd74369ab7"], Cell[BoxData[ GraphicsBox[{{}, {{ {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[DiskBox[{0, 0}, Offset[{2.75, 2.75}, {0., 0.}]]], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJwt031MU1cYBvBKExGyqQhDcIg4YMCUqajZkMGjoiIRGVSUj4ATqeAQxI5M ojhxKgM/AIUVkEyR4cDpYLplDMPmGR1BpvgxUEFGtXwUEaq0pbRQoF17z3mT 88fNTZ77nvf33sW70wR7+DweT2g6M0zHwnQy7WqDeg7LEDV0MuZ96xdE6xlb IBmTQbnkj9uhds+JyN+6o/JADy6qXX2TnKVEEV7vnD3cg8BwrUOiZzdJ5KoX 3/3u4u3v8x/pOWwO7MXRyrydnX5dxJzmGdsH3ySdm9PGZ8QUZkrsg6VapOzb 2kkE5rjwfuiK9//M29FB7reaqx9/Np65+lHcU7KZC5RDYTs0si7hCTGnFUjk COltf9ia9JgEmNvzH0C7vd/pzOR2wsXVD0DSbJQNJbeRlVy9xHODbVvd3n+J +bZ2tS9xsj9CfjzhEfHiGhxExTrHPOu6B+SKub3KQZCsv8K9LrUSLs75FQ7N e7FElHWXlF0w1ys0GZ5WHoxpIdz47IYgc1nRlbG8mXDXLRiCJKqP/xW/iXDt WQ+j22Fo2YGnjYSLyx5Gru2T0K0xhPC4UiBScLTlJ4cGQj0UeNxZcWdAXcc8 FGhqk6YOaH4hXHsHXqM6LtjYt72WebxGhFvECsm6aubxBruXtlXlSS4zjzco URfeu94mZh4jsC9vFiVb5jCPEcyWNXovWriHzUMJZUaXl8w3HTRPieLUjLmu t7NB56PEtcTgeb9uLgDNVyL4SkFQr18R6LxUsBZGaS1bxKDfU8HLuqFTlFoC Oj8VrLylKwfDSkG/r4LKcufIZXEp6DzVqHsSVfhWbCnofpieA/bFvdtYAjpf NZYLKvJfSovBrUurGiHFsZk1d8Sg8x7Fmr9vResLvgXdn1H0lOemT28oAp3/ KJYcnzo7rDoPuk+jGEu1P7a3/ByohwbtKTZXpdX5oPulgeBawo5dnmdBfTTY cyV8f0fzKdB900BOmt9Jz8kB9dLgYM28I+KUbND9G4NPkt/MgIwToH5jEDz7 RBhf/TXoPo5BdKOkNX48C9RzDOkB0a+rBo+Aemhhs0lqcHM6zDy0GJ+ZdXEi P4N5aBFqoSqz8P+SeWihcyhbNfO9dOahQ2GyY8MjXxHz0OGmRtxYxEtjHjpc l+p5ln37mIcO8cHbar6x/Zx5jCNBqW2wOZPIPMaxfpZPtkugkHmMY7b7YHTV 6t2g/+84Dsav0s2J28U8JjD4tjwna28c85iA+McSJ5vUGOYxgSS+9GooiWQe E0h7Pot/KHI789ADD3d2nfpwG7jx+etRWv99jXtAOPPQo5YfZ+8041Pmoccr 2W9Vnj1bmIce94dzNy6wDWYekwi+91ibm7+JeUzCfkGeSL5lA/OYxD+Pnv0g 3LAe9HedxPFbeqlCtJZ5TKHmXlj3rEv+zGMK9WHFTSdq1jCPKXyRJvbKtPqY eUyhK2/bMqtrq5nHNEQuwhuOuSuZxzQWys/fjbi4AhzHhWl0HDHw57csYx7T eOGqLQupXco8DCizmCv5oN+LeRgQk+PjlB3vwTwMSI/c52G1yJ15GCDc6pzh Ye/KPIxQzN4VZFy7GNx1g4xw3zgSW7pqEfMwQjDnQcr1NU7Mw/T+5rGYxjOO zIO39hw+Mwa6zMf/+5QbzQ== "]]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[{ {GrayLevel[1], PolygonBox[{ Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}]}]}, {AbsoluteThickness[1], Dashing[{}], JoinedCurveBox[ Line[{Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}], Offset[{0., 2.975}]}], CurveClosed->True]}}], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJw103lQU1cYBXBA0RRRpFJFBqFa7JBBHS2Og7IcFYVWwQVsq5axVVlGqzV2 0BGwbsjWoiDQ4Fa1FSu24lKoWqNei8oooBAgBsKSBFEkEFmSkJCQpOTd2zvz /j33u+f3velbdkXFjbKzs4sb+exHPge7/48Co6ssH++bIQ1JcbsWrkxWoIM3 a5Fp25uQQd+YnHKdAiU+KfmHxNqQ3cFO0osCJXzv/X7s0ikH9Ky945XWrcTj hdeERbyJiOdOO5bqPc8p7ntAmWwLbEdNweFs+fmZsKX5xrzC1ISyp8PmuRgJ G0l8Befwk+4x1oWIssWt7cAifubES7GheF5tOx1I8euaPH5JBD7lAl+jc29Y tch7HWxpOeWv4RcUeMbJJQYhtvGC32B5sTGrnb8VXNydNxBO2JKrurIN/tzp RIAmrE/QLIDttW7XOhEk/0udI9oDPjfgWyin7RJXHUpBkW28i2+RrjFUFnxw GFycVxfcv1S/nys5itOnbKcLDePm+4veZYKrz02Fm4mVkx6HHgP33BwVxJHp Mm9JLrjxnLqhTFQ28HR54OLSujHL6HFd31YA6tGDxRkPzBe2C0E9elCxs+bR 428LQT168GPoxvMnywrBjSdQQzwoE5S7FzIPNST9RZ6nBT8zj3fgrxM6rz6b xzzeITiq9xZv/DHm0Yvap99FjYk4wjx6Ud4wKdxvYCvrow8bp5cqqo7uITSv D1LnyKQZ97MJ7acPo1vqXD5cf5LQ/D6MG5Uw/qf8Xwntqx+fzfs7bc7ay4Te 14+8sut5qWtKCO2vH8fD949zJTcJvb8fu7MbW+d2lBHa5wDulcTz2l3uELof AxgIntefGygitN8BbIpbd7th8wPCrUv1APKFps455CGhfWuQE709UB1WTuj+ aDCx1sGxu+IRof1r8Oz49ayVIU8I3ScNGhxVyw5erSDUQ4tzqirVfNenhO6X Fkv8NsyN2PGMUB8tvrCfllJ5v5LQfdPixhrfnWLHakK9tDjqfcC3cNlzQvdP h9ebm6d8k/yCUD8ddJGrxyRfriF0H3VY7cfz9YyvJdRTh6gX6T/s09YS6jGI ioSry80HxMxjEJaVtQskjnXMYxBPhIZuflYd8xjE1nuLUj96r5556HErf/vX b9PqmYcehwsOjv7FWs889Filax4bu7eBeejhtmGKyyZVA/MwwOeud9OVryTM wwA5P2lVbKWEeRiweyVfWLzgJaH/rwGi0r2zcy+8ZB5DqPH2svfnSZnHEHQe lvTLO6XMYwiu8iNSB7GUeQyBb4yuWP9JI/MwIutJ75DoRCPh6gs2YnKYnUNI byPzMCK7ImJH74om5mHE8sSgRnlRE/MwwuOsiudlbmIeJljSJLrb0TLmYcIm /QLZ3WIZ8zAhMN891H9YRujvasKj0gDP2auamccw+idIRKXnmpnHMKJ7BGqx upl5DCM140/TicAW5jEMn9jAf8wZLczDjIDvp2d51bcwDzM0hpnxZs9WwnGc MsNp1o2u3+JamYcZ0qSxUVNKWpmHBXUa58wtmlbmYcG2h0k+2QFtzMOCzJsl iWf2tzEPCxSpUw8WkjbmYUW8LHJshr2ccM8NtyKp+PYJwVI587BC+4drwsYj cuZhRdCE/MIV/8qZh93iz8cozGFWOfkPYQ5JOA== "]]}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{ FormBox[ StyleBox[ "\"\[Kappa]\"", FontFamily -> "Times", FontSize -> 20, StripOnInput -> False], TraditionalForm], None}, AxesOrigin->{0.4687500000000003, 0}, AxesStyle->Thickness[0.0025], BaseStyle->GrayLevel[0], DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->GrayLevel[0], FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, FrameTicksStyle->GrayLevel[0], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], ImageSize->{679., Automatic}, LabelStyle->{FontSize -> 16, GrayLevel[0]}, Method->{ "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange->{{0.4687500000000003, 2.}, {-0.4999558905838957, 0.024008288011380278`}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}, TicksStyle->GrayLevel[0]]], "Output", CellChangeTimes->{ 3.859534852083694*^9, {3.859534884945137*^9, 3.859535059208827*^9}, { 3.859610669716248*^9, 3.859610712503234*^9}, 3.859611004622802*^9, 3.859793446883456*^9, 3.859815052151017*^9, 3.8598154989558887`*^9}, CellLabel->"Out[27]=",ExpressionUUID->"23a497be-7f2e-4e41-9b56-b327f42e2b51"] }, Open ]], Cell["\<\ index 1 is denoted with circles, index 2 with triangles \ \>", "Text", CellChangeTimes->{{3.859385141537698*^9, 3.859385142262722*^9}, { 3.859545615547648*^9, 3.8595456401233807`*^9}, {3.859611005701091*^9, 3.859611007892489*^9}, {3.859815060021441*^9, 3.8598150801889553`*^9}, 3.859816282739657*^9},ExpressionUUID->"aa16e227-6fbf-466b-9625-\ 1d609252e717"], Cell[TextData[{ "Testing Dalton\[CloseCurlyQuote]s law of partial pressures, distribution \ according to ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["p", "\[Alpha]"], "-", SubscriptBox["x", "\[Alpha]"]}]}], TraditionalForm]],ExpressionUUID-> "05d6d305-ccbd-43f4-bdfb-41376cb22403"], " ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"p", ")"}], "/", RowBox[{"(", SubscriptBox["x", "\[Alpha]"]}]}], TraditionalForm]],ExpressionUUID-> "500353b7-90f8-47aa-8749-9c8b5bcf127f"], " p)" }], "Text", CellChangeTimes->{{3.859546937559267*^9, 3.859546975898838*^9}, { 3.8596071561270447`*^9, 3.859607157103159*^9}, {3.859607263655648*^9, 3.859607337823737*^9}, {3.8598150870118647`*^9, 3.859815097332143*^9}},ExpressionUUID->"a1bb8dc1-513a-481b-b788-\ 367283c3081d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p1", "-", RowBox[{ FractionBox["\[Rho]1", RowBox[{"\[Rho]1", "+", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}]}]], " ", "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", RowBox[{"\[Rho]1", "+", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}]}]], "p"}], ")"}]}], "/.", RowBox[{"\[Kappa]", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"s1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}], "/.", RowBox[{"s2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "12"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "13"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "14"}], "]"}], "]"}]}]}], "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "15"}], "]"}], "]"}]}]}], ",", SuperscriptBox["10", RowBox[{"-", "8"}]]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p2", "-", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}], RowBox[{"\[Rho]1", "+", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}]}]], " ", "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}], RowBox[{"\[Rho]1", "+", RowBox[{ SuperscriptBox["\[Kappa]", RowBox[{"-", "1"}]], "\[Rho]2"}]}]], "p"}], ")"}]}], "/.", RowBox[{"\[Kappa]", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"s1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}], "/.", RowBox[{"s2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "12"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "13"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "14"}], "]"}], "]"}]}]}], "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "15"}], "]"}], "]"}]}]}], ",", SuperscriptBox["10", RowBox[{"-", "8"}]]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"AxesStyle", " ", "\[Rule]", " ", RowBox[{"Thickness", "[", "0.0025", "]"}]}], ",", RowBox[{"PlotTheme", "\[Rule]", RowBox[{"{", "\"\\"", "}"}]}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontSize", "\[Rule]", "16"}], ",", "Black"}], "}"}]}], ",", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"Style", "[", RowBox[{"\"\<\[Kappa]\>\"", RowBox[{"(*", "\"\<\\kappa\>\"", "*)"}], ",", " ", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", " ", "\[Rule]", " ", "20"}]}], "]"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "0.01"}], ",", "0.01"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.859534638665761*^9, 3.859534640985155*^9}, { 3.859534707586021*^9, 3.859534718802548*^9}, {3.859534787685721*^9, 3.859535058453478*^9}, {3.859547014300929*^9, 3.8595470670593557`*^9}, { 3.8595471391308813`*^9, 3.859547146406279*^9}, {3.859547178121149*^9, 3.859547192976644*^9}, {3.859607390127355*^9, 3.859607413109771*^9}, { 3.859607571814349*^9, 3.859607699825883*^9}, {3.859607738523419*^9, 3.859607758892765*^9}, {3.859607825089344*^9, 3.859607829383259*^9}, { 3.8596084515507517`*^9, 3.859608513134482*^9}, {3.859608627403636*^9, 3.859608628136135*^9}, {3.859609105498066*^9, 3.8596091141461906`*^9}, { 3.859609219879084*^9, 3.85960922027428*^9}, 3.859610628497617*^9, { 3.8598151183690033`*^9, 3.859815245601603*^9}, {3.8598155166339293`*^9, 3.859815531446415*^9}}, CellLabel->"In[30]:=",ExpressionUUID->"7d7ba42f-a5cb-407e-a133-bc1a71973b51"], Cell[BoxData[ GraphicsBox[{{}, {{ {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[DiskBox[{0, 0}, Offset[{2.75, 2.75}, {0., 0.}]]], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJxdkz1MwlAURqtuzMwkbjg7o264wsxkgqu44szMjCvOzMzMOLuK/8pfC7Sl pbT2vRfeTc5NmvQsX9/7zu3pzV29eeI4TjN/jvLn2DnM6+Xh7aE4qE7awkG5 0R35wveVwku/NbE8qw1LnanwrZ43y5O2ChRWaeXGu+U8LE8Urqu42ofl57Ea 4Wsd+GlZpXVHwhfqeJUvyzpuKHyu59uyum1xIHymD/hj+Ukdry+s40q/lh97 aoR1fcU/y/q6XWF9vMLUso7rCJuZwccMPoT18Vpz+JjDxwI+FvCxhI8l+nCR 56IfF/ku+vLwPQ/9efi+hz5X2I8V+hXW6zJeoe819meN/oXNPq3hY4P92sCP sNm3DXwJm/3z4U/Y7KMPnz58BPARwEcAHwF8hPARwkcIHyF8bOFjCx/C5v/d wkcEHxF8RPARwUdsWddXieEjho8YPmL42MHHDj6Eze+6g48EPhL4SOAjgY89 fAhrHb09fOzhI4WPFD5S+EjhI7Osr1vN4CODjww+nKvDyz/fo5pj "]]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[{ {GrayLevel[1], PolygonBox[{ Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}]}]}, {AbsoluteThickness[1], Dashing[{}], JoinedCurveBox[ Line[{Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}], Offset[{0., 2.975}]}], CurveClosed->True]}}], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJxdkz1MwlAURqtuzMwkbjg7o264wsxkgqu44szMjCvOzMzMOLuK/8pfC7Sl pbT2vRfeTc5NmvQsX9/7zu3pzV29eeI4TjN/jvLn2DnM6+Xh7aE4qE7awkG5 0R35wveVwku/NbE8qw1LnanwrZ43y5O2ChRWaeXGu+U8LE8Urqu42ofl57Ea 4Wsd+GlZpXVHwhfqeJUvyzpuKHyu59uyum1xIHymD/hj+Ukdry+s40q/lh97 aoR1fcU/y/q6XWF9vMLUso7rCJuZwccMPoT18Vpz+JjDxwI+FvCxhI8l+nCR 56IfF/ku+vLwPQ/9efi+hz5X2I8V+hXW6zJeoe819meN/oXNPq3hY4P92sCP sNm3DXwJm/3z4U/Y7KMPnz58BPARwEcAHwF8hPARwkcIHyF8bOFjCx/C5v/d wkcEHxF8RPARwUdsWddXieEjho8YPmL42MHHDj6Eze+6g48EPhL4SOAjgY89 fAhrHb09fOzhI4WPFD5S+EjhI7Osr1vN4CODjww+nKvDyz/fo5pj "]]}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{ FormBox[ StyleBox[ "\"\[Kappa]\"", FontFamily -> "Times", FontSize -> 20, StripOnInput -> False], TraditionalForm], None}, AxesOrigin->{0.4687500000000003, 0}, AxesStyle->Thickness[0.0025], BaseStyle->GrayLevel[0], DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->GrayLevel[0], FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, FrameTicksStyle->GrayLevel[0], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], ImageSize->{630.9090909090908, Automatic}, LabelStyle->{FontSize -> 16, GrayLevel[0]}, Method->{ "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange->{{0.4687500000000003, 2.}, {-0.01, 0.01}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}, TicksStyle->GrayLevel[0]]], "Output", CellChangeTimes->{3.859815531802802*^9}, CellLabel->"Out[30]=",ExpressionUUID->"d64f7b91-f22b-466c-bf16-34137a7d5b4b"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["(numerically) Without the explicit expressions - ideal gas", "Section", CellChangeTimes->{{3.85968594258692*^9, 3.8596859548032*^9}, { 3.85968602880628*^9, 3.859686040225389*^9}, {3.8597001728473387`*^9, 3.859700178579138*^9}, {3.859815256105233*^9, 3.859815268475994*^9}},ExpressionUUID->"a7e55685-9f27-417e-a4e2-\ 8cb1525483d6"], Cell[BoxData[{ RowBox[{ RowBox[{"s1", "=", RowBox[{"kB", " ", FractionBox["\[Rho]1", "m1"], " ", RowBox[{"(", RowBox[{ FractionBox["5", "2"], "+", RowBox[{"Log", "[", RowBox[{ FractionBox["m1", "\[Rho]1"], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m1"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], FractionBox[ RowBox[{"e1", "-", FractionBox[ SuperscriptBox["u1", "2"], RowBox[{"2", " ", "\[Rho]1"}]]}], RowBox[{"\[Rho]1", "/", "m1"}]]}], ")"}], RowBox[{"3", "/", "2"}]]}], "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"s2", "=", RowBox[{"kB", " ", FractionBox["\[Rho]2", "m2"], " ", RowBox[{"(", RowBox[{ FractionBox["5", "2"], "+", RowBox[{"Log", "[", RowBox[{ FractionBox["m2", "\[Rho]2"], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"4", " ", "\[Pi]", " ", "m2"}], RowBox[{"3", " ", SuperscriptBox["h", "2"]}]], FractionBox[ RowBox[{"e2", "-", FractionBox[ SuperscriptBox["u2", "2"], RowBox[{"2", " ", "\[Rho]2"}]]}], RowBox[{"\[Rho]2", "/", "m2"}]]}], ")"}], RowBox[{"3", "/", "2"}]]}], "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"s", "=", RowBox[{"s1", "+", "s2"}]}], ";"}]}], "Input", CellChangeTimes->{{3.859688131053954*^9, 3.8596881452240667`*^9}, { 3.859688500397032*^9, 3.859688540662909*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"c82495e6-8b96-45a5-a53c-4c346b338f28"], Cell[BoxData[ RowBox[{ RowBox[{"FirstMEstep", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "\[Rho]1"}], "]"}], "\[Equal]", "\[Rho]star"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "\[Rho]2"}], "]"}], "\[Equal]", "\[Rho]star"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "u1"}], "]"}], "\[Equal]", "ustar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "u2"}], "]"}], "\[Equal]", "ustar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "e1"}], "]"}], "\[Equal]", "estar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "e2"}], "]"}], "\[Equal]", "estar"}]}], "}"}], "//", "Simplify"}]}], ";"}]], "Input", CellChangeTimes->{{3.859688114706395*^9, 3.859688179113668*^9}, { 3.8596882130918007`*^9, 3.859688213919829*^9}, {3.859688547629517*^9, 3.8596885771977053`*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"eb8d189a-e53b-4443-b0c8-1bc3b7b4c751"], Cell["instead of the second step, we use the upscaling mapping", "Text", CellChangeTimes->{{3.85968841256456*^9, 3.859688420410017*^9}, { 3.8598152801330357`*^9, 3.859815294713951*^9}, {3.859815733044631*^9, 3.859815734013857*^9}},ExpressionUUID->"cab53a8f-aefd-4254-907f-\ 7d1030123ba5"], Cell[BoxData[ RowBox[{ RowBox[{"Projections", "=", RowBox[{"{", RowBox[{ RowBox[{"\[Rho]", "\[Equal]", RowBox[{"\[Rho]1", "+", "\[Rho]2"}]}], ",", RowBox[{"u", "\[Equal]", RowBox[{"u1", "+", "u2"}]}], ",", RowBox[{"e", "\[Equal]", RowBox[{"e1", "+", "e2"}]}]}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.859688231152259*^9, 3.859688233764982*^9}, { 3.859688406426537*^9, 3.859688438052717*^9}, {3.85968848182981*^9, 3.859688495827775*^9}, {3.859688586298517*^9, 3.859688587655958*^9}}, CellLabel->"In[5]:=",ExpressionUUID->"9fd46310-fefd-4fe1-aaa0-1c359e11da6d"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"kB", "=", RowBox[{"1.380649", " ", SuperscriptBox["10", RowBox[{"-", "23"}]]}]}], ";"}], RowBox[{"(*", RowBox[{"J", "/", "K"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"h", "=", RowBox[{"6.62607015", " ", SuperscriptBox["10", RowBox[{"-", "34"}]]}]}], ";"}], " ", RowBox[{"(*", RowBox[{"J", "/", "Hz"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Da", "=", RowBox[{"1.66053906660", " ", SuperscriptBox["10", RowBox[{"-", "27"}]]}]}], ";"}], RowBox[{"(*", "kg", "*)"}]}]}], "Input", CellChangeTimes->{{3.859004032593636*^9, 3.859004041918112*^9}, { 3.859006453100181*^9, 3.859006464095994*^9}, {3.8590064951508503`*^9, 3.859006520248178*^9}, {3.859006607326933*^9, 3.859006630071869*^9}}, CellLabel->"In[6]:=",ExpressionUUID->"ab9544ab-c336-46bc-b9f9-737e735f5cca"], Cell[CellGroupData[{ Cell["With a prescribed energy:", "Subsubsection", CellChangeTimes->{{3.859692481906189*^9, 3.8596924858769007`*^9}, { 3.859815689257913*^9, 3.859815716526265*^9}},ExpressionUUID->"0f9ac615-1162-4456-8ca3-\ ea1f4c076fbd"], Cell[BoxData[{ RowBox[{ RowBox[{"\[Kappa]num", "=", "100"}], ";", RowBox[{"\[Kappa]min", "=", "0.5"}], ";", RowBox[{"\[Kappa]max", "=", "2"}], ";", RowBox[{"Ratios4\[Kappa]", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], ";", RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "e", ",", "T", ",", "estar", ",", "\[Kappa]", ",", "m1", ",", "m2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "1"}], ",", RowBox[{"j", "\[LessEqual]", RowBox[{"\[Kappa]num", "+", "1"}]}], ",", RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Kappa]", "=", RowBox[{"\[Kappa]min", "+", RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], " ", RowBox[{ RowBox[{"(", RowBox[{"\[Kappa]max", "-", "\[Kappa]min"}], ")"}], "/", "\[Kappa]num"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"m2", "=", RowBox[{"10", " ", "Da"}]}], ";", RowBox[{"(*", RowBox[{"mass", " ", "of", " ", "a", " ", "molecule"}], "*)"}], "\[IndentingNewLine]", RowBox[{"m1", "=", RowBox[{"m2", "/", "\[Kappa]"}]}], ";", " ", RowBox[{"(*", RowBox[{"\[Kappa]", "=", RowBox[{"m2", "/", "m1"}]}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mixture", " ", "state", " ", "variables"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", "1"}], ";", " ", RowBox[{"(*", RowBox[{"kg", "/", SuperscriptBox["m", "3"]}], "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"0", " ", SuperscriptBox["10", "3"]}]}], ";", " ", RowBox[{"(*", RowBox[{"kg", " ", RowBox[{"m", "/", "s"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"e", "=", " ", RowBox[{ RowBox[{ FractionBox["3", "2"], " ", "kB", " ", "300", RowBox[{"(", FractionBox["\[Rho]", "m2"], ")"}]}], "+", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u", "2"], "\[Rho]"]}]}]}], ";", " ", RowBox[{"(*", RowBox[{"J", "/", SuperscriptBox["m", "3"]}], "*)"}], RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{ "some", " ", "reasonable", " ", "estimate", " ", "of", " ", "total", " ", "mixture", " ", "energy", " ", "from", " ", "a", " ", "prescribed", " ", "temperature"}], ";", " ", "again"}], ",", " ", RowBox[{ "internal", " ", "and", " ", "total", " ", "are", " ", "equal"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"numEstimate", "=", RowBox[{"Chop", "[", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"FirstMEstep", "\[Union]", "Projections"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Rho]1", ",", RowBox[{"\[Rho]", RowBox[{"(", RowBox[{"1.5", " ", RowBox[{"(", RowBox[{"\[Kappa]", "-", "0.45"}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]2", ",", RowBox[{"\[Rho]", RowBox[{"(", RowBox[{"1", "-", RowBox[{"(", RowBox[{"1.5", " ", RowBox[{"(", RowBox[{"\[Kappa]", "-", "0.45"}], ")"}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"u1", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u2", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e1", ",", RowBox[{"e", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", RowBox[{"e", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]star", ",", SuperscriptBox["10", "3"]}], "}"}], ",", RowBox[{"{", RowBox[{"ustar", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"estar", ",", RowBox[{"1", "/", "300"}]}], "}"}]}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"p", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "e"}], "+", RowBox[{"\[Rho]", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s"}]}], ")"}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p1", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e1"}], "+", RowBox[{"\[Rho]1", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s1"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p2", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e2"}], "+", RowBox[{"\[Rho]2", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s2"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", "j", "]"}], "]"}], "=", RowBox[{"{", RowBox[{"\[Kappa]", ",", RowBox[{"\[Rho]1", "/.", "numEstimate"}], ",", RowBox[{"\[Rho]2", "/.", "numEstimate"}], ",", RowBox[{"u1", "/.", "numEstimate"}], ",", RowBox[{"u2", "/.", "numEstimate"}], ",", RowBox[{"e1", "/.", "numEstimate"}], ",", RowBox[{"e2", "/.", "numEstimate"}], ",", "p", ",", "p1", ",", "p2", ",", RowBox[{ RowBox[{"1", "/", "estar"}], "/.", "numEstimate"}]}], "}"}]}]}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.859003684163105*^9, 3.859003745959848*^9}, { 3.8590038322325*^9, 3.859003848442205*^9}, {3.859003884000902*^9, 3.859004020468811*^9}, {3.859006604112194*^9, 3.8590066046528378`*^9}, { 3.85900665573822*^9, 3.8590066835617447`*^9}, {3.8590073292796783`*^9, 3.8590073304610863`*^9}, {3.859023404317885*^9, 3.859023663627729*^9}, { 3.859023738481776*^9, 3.859023780408155*^9}, {3.8590238394739103`*^9, 3.859023844981728*^9}, {3.859023941592525*^9, 3.859023953089074*^9}, { 3.8590240543670197`*^9, 3.85902406442233*^9}, {3.859024252666738*^9, 3.859024280881693*^9}, 3.859037100153151*^9, {3.8590380490801477`*^9, 3.859038068524189*^9}, {3.859038405652028*^9, 3.8590384574387617`*^9}, { 3.8593427722437763`*^9, 3.859342781424169*^9}, {3.8593436404583282`*^9, 3.8593436655903177`*^9}, {3.859343987204646*^9, 3.859343987525599*^9}, 3.8593440274099073`*^9, 3.8593441074498043`*^9, {3.859346582991984*^9, 3.859346625574361*^9}, {3.859368213800564*^9, 3.859368235554236*^9}, { 3.8593682808908997`*^9, 3.859368303332468*^9}, {3.859368953999317*^9, 3.859368955909123*^9}, {3.859369386858694*^9, 3.859369391311701*^9}, { 3.859369859383062*^9, 3.85936987637763*^9}, {3.859370557220182*^9, 3.859370646221528*^9}, {3.85937068982584*^9, 3.859370697362488*^9}, { 3.859370863588719*^9, 3.859370876316638*^9}, {3.859526501949636*^9, 3.859526502729855*^9}, {3.859527111302061*^9, 3.8595271165928307`*^9}, { 3.8595272117756033`*^9, 3.859527212040094*^9}, {3.859527251340817*^9, 3.859527260462924*^9}, {3.859527367888115*^9, 3.859527370901854*^9}, { 3.8595326367401333`*^9, 3.859532647197557*^9}, {3.8595340027213163`*^9, 3.859534010415688*^9}, {3.859607000362165*^9, 3.859607138478568*^9}, { 3.8596082694304028`*^9, 3.859608278676107*^9}, {3.859692536454299*^9, 3.859692646987258*^9}, {3.859692710035172*^9, 3.859692742831143*^9}, { 3.859692849999578*^9, 3.859692915414981*^9}, 3.859692951637721*^9, 3.859693355774358*^9, {3.859695667208379*^9, 3.859695698321272*^9}, { 3.859695734248781*^9, 3.859695743369685*^9}, {3.859695874327547*^9, 3.859695902169895*^9}, 3.859695953113415*^9, {3.859696012159186*^9, 3.859696017795232*^9}, {3.859815363685677*^9, 3.859815398203207*^9}, { 3.859815561701169*^9, 3.859815578881032*^9}, {3.859815939536191*^9, 3.859815995286625*^9}, {3.859816040107761*^9, 3.859816040795529*^9}, { 3.85981608634718*^9, 3.859816203542982*^9}, {3.890319442002409*^9, 3.8903194525359917`*^9}},ExpressionUUID->"1a9912d9-1277-4567-ae79-\ a2c33a985929"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "m1", ",", "\[Kappa]", ",", "estar"}], "]"}]], "Input", CellChangeTimes->{{3.859693864888701*^9, 3.859693886122714*^9}, { 3.859696113559352*^9, 3.85969612159828*^9}, 3.859696176589321*^9}, CellLabel->"In[71]:=",ExpressionUUID->"97aa4eb9-ae3c-43d0-80f8-4d4db0d79fe0"], Cell[BoxData[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e1"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "s"}], "-", "s1"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], " ", "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<((\!\(\*FractionBox[\(\[Rho]1\), \ \(\[Rho]\)]\)e-e1)-T(\!\(\*FractionBox[\(\[Rho]1\), \(\[Rho]\)]\)s-s1))/(\!\(\ \*FractionBox[\(\[Rho]1\), \(\[Rho]\)]\)p) ratio\>\""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e2"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], "s"}], "-", "s2"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"T", "\[Rule]", RowBox[{"1", "/", "estar"}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], " ", "/.", RowBox[{"estar", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "11"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<((\!\(\*FractionBox[\(\[Rho]2\), \ \(\[Rho]\)]\)e-e2)-T(\!\(\*FractionBox[\(\[Rho]2\), \(\[Rho]\)]\)s-s2))/(\!\(\ \*FractionBox[\(\[Rho]2\), \(\[Rho]\)]\)p) ratio\>\""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p1", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(1\)] - \ \*SubscriptBox[\(x\), \(1\)]\\\ p)\)/\((\*SubscriptBox[\(x\), \(1\)] p)\)\)\>\ \""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p2", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(2\)] - \ \*SubscriptBox[\(x\), \(2\)]\\\ p)\)/\((\*SubscriptBox[\(x\), \(2\)] p)\)\)\>\ \""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGAQA2IQfVKO8UzZwTeO/wpmXQHRIive3QPRcVfTnoHopDt2 r0D0twMrP4Bohe7qPZVA+lZ54HEQLXrC6CyIjj647iqIFrlw+CaIvuG19haI 1oi//ABET7vn8RBEy6d3PQXRXHuNX4Hom+ylH0C0iUHAXxCt1/eNowpIC3yp EAXRfO76UiB61+SfSiD6kKjQq+NAOneCIfMJkLs5A4VANM+nVBUQzZLvrwWi T/RKGYHoD5U/HED0uoQGJxDN53vQDURfejDDHUQXRG/1BdHnOBSiQXRDp2g8 iN4etCQRRJtLNbqcBNKVilvB9JGbe71ANA/bczD9rT9vLvOhN44h85rA9NIF pTtAdJBn0V4QDQAQnsZV "], CellLabel->"In[73]:=",ExpressionUUID->"463f7049-9a34-40f8-9251-464595228901"] }, Closed]], Cell[CellGroupData[{ Cell["With a prescribed temperature:", "Subsubsection", CellChangeTimes->{{3.859692481906189*^9, 3.8596924858769007`*^9}, { 3.859815689257913*^9, 3.859815695248618*^9}},ExpressionUUID->"2229137f-127d-43fc-9c9e-\ 3781280f8daa"], Cell[BoxData[{ RowBox[{ RowBox[{"\[Kappa]num", "=", "100"}], ";", RowBox[{"\[Kappa]min", "=", "0.5"}], ";", RowBox[{"\[Kappa]max", "=", "2"}], ";", RowBox[{"Ratios4\[Kappa]", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], ";", RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "e", ",", "T", ",", "estar", ",", "\[Kappa]", ",", "m1", ",", "m2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "1"}], ",", RowBox[{"j", "\[LessEqual]", RowBox[{"\[Kappa]num", "+", "1"}]}], ",", RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Kappa]", "=", RowBox[{"\[Kappa]min", "+", RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], " ", RowBox[{ RowBox[{"(", RowBox[{"\[Kappa]max", "-", "\[Kappa]min"}], ")"}], "/", "\[Kappa]num"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"m2", "=", RowBox[{"10", " ", "Da"}]}], ";", RowBox[{"(*", RowBox[{"mol", " ", "mass"}], "*)"}], "\[IndentingNewLine]", RowBox[{"m1", "=", RowBox[{"m2", "/", "\[Kappa]"}]}], ";", " ", RowBox[{"(*", RowBox[{"\[Kappa]", "=", RowBox[{"m2", "/", "m1"}]}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mixture", " ", "state", " ", "variables"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", "1"}], ";", " ", RowBox[{"(*", RowBox[{"kg", "/", SuperscriptBox["m", "3"]}], "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"0", " ", SuperscriptBox["10", "3"]}]}], ";", " ", RowBox[{"(*", RowBox[{"kg", " ", RowBox[{"m", "/", "s"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"T", "=", "300"}], ";", " ", RowBox[{"(*", "K", "*)"}], "\[IndentingNewLine]", RowBox[{"estar", "=", RowBox[{"1", "/", "T"}]}], ";", "\[IndentingNewLine]", RowBox[{"eestimate", "=", RowBox[{ RowBox[{ FractionBox["3", "2"], RowBox[{"kB", "/", "estar"}], RowBox[{"(", FractionBox["\[Rho]", RowBox[{ RowBox[{"(", RowBox[{"m1", "+", "m2"}], ")"}], "/", "2"}]], ")"}]}], "+", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u", "2"], "\[Rho]"]}]}]}], ";", " ", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"with", " ", "u"}], "=", "0"}], ",", " ", RowBox[{"total", "=", "internal"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"numEstimate", "=", RowBox[{"Chop", "[", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"FirstMEstep", "\[Union]", "Projections"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Rho]1", ",", RowBox[{"\[Rho]", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]2", ",", RowBox[{"\[Rho]", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u1", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u2", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e1", ",", RowBox[{"eestimate", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", RowBox[{"eestimate", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]star", ",", SuperscriptBox["10", "3"]}], "}"}], ",", RowBox[{"{", RowBox[{"ustar", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"e", ",", "eestimate"}], "}"}]}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"p", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "e"}], "+", RowBox[{"\[Rho]", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s"}]}], ")"}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p1", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e1"}], "+", RowBox[{"\[Rho]1", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s1"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p2", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e2"}], "+", RowBox[{"\[Rho]2", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s2"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", "j", "]"}], "]"}], "=", RowBox[{"{", RowBox[{"\[Kappa]", ",", RowBox[{"\[Rho]1", "/.", "numEstimate"}], ",", RowBox[{"\[Rho]2", "/.", "numEstimate"}], ",", RowBox[{"u1", "/.", "numEstimate"}], ",", RowBox[{"u2", "/.", "numEstimate"}], ",", RowBox[{"e1", "/.", "numEstimate"}], ",", RowBox[{"e2", "/.", "numEstimate"}], ",", "p", ",", "p1", ",", "p2"}], "}"}]}]}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.859003684163105*^9, 3.859003745959848*^9}, { 3.8590038322325*^9, 3.859003848442205*^9}, {3.859003884000902*^9, 3.859004020468811*^9}, {3.859006604112194*^9, 3.8590066046528378`*^9}, { 3.85900665573822*^9, 3.8590066835617447`*^9}, {3.8590073292796783`*^9, 3.8590073304610863`*^9}, {3.859023404317885*^9, 3.859023663627729*^9}, { 3.859023738481776*^9, 3.859023780408155*^9}, {3.8590238394739103`*^9, 3.859023844981728*^9}, {3.859023941592525*^9, 3.859023953089074*^9}, { 3.8590240543670197`*^9, 3.85902406442233*^9}, {3.859024252666738*^9, 3.859024280881693*^9}, 3.859037100153151*^9, {3.8590380490801477`*^9, 3.859038068524189*^9}, {3.859038405652028*^9, 3.8590384574387617`*^9}, { 3.8593427722437763`*^9, 3.859342781424169*^9}, {3.8593436404583282`*^9, 3.8593436655903177`*^9}, {3.859343987204646*^9, 3.859343987525599*^9}, 3.8593440274099073`*^9, 3.8593441074498043`*^9, {3.859346582991984*^9, 3.859346625574361*^9}, {3.859368213800564*^9, 3.859368235554236*^9}, { 3.8593682808908997`*^9, 3.859368303332468*^9}, {3.859368953999317*^9, 3.859368955909123*^9}, {3.859369386858694*^9, 3.859369391311701*^9}, { 3.859369859383062*^9, 3.85936987637763*^9}, {3.859370557220182*^9, 3.859370646221528*^9}, {3.85937068982584*^9, 3.859370697362488*^9}, { 3.859370863588719*^9, 3.859370876316638*^9}, {3.859526501949636*^9, 3.859526502729855*^9}, {3.859527111302061*^9, 3.8595271165928307`*^9}, { 3.8595272117756033`*^9, 3.859527212040094*^9}, {3.859527251340817*^9, 3.859527260462924*^9}, {3.859527367888115*^9, 3.859527370901854*^9}, { 3.8595326367401333`*^9, 3.859532647197557*^9}, {3.8595340027213163`*^9, 3.859534010415688*^9}, {3.859607000362165*^9, 3.859607138478568*^9}, { 3.8596082694304028`*^9, 3.859608278676107*^9}, {3.859692536454299*^9, 3.859692646987258*^9}, {3.859692710035172*^9, 3.859692742831143*^9}, { 3.859692849999578*^9, 3.859692915414981*^9}, 3.859692951637721*^9, 3.859693355774358*^9, {3.859695922688858*^9, 3.859695944999322*^9}, 3.859816248447702*^9, {3.8903194826586027`*^9, 3.8903194996155*^9}},ExpressionUUID->"af052ee7-a730-4fbc-a943-\ 248604d6ccc6"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "m1", ",", "\[Kappa]", ",", "estar"}], "]"}]], "Input", CellChangeTimes->{{3.859693864888701*^9, 3.859693886122714*^9}, { 3.859696113559352*^9, 3.85969612159828*^9}, 3.859696176589321*^9}, CellLabel->"In[11]:=",ExpressionUUID->"fb2e256a-b859-4e88-a414-4d63b3734ba1"], Cell[BoxData[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e1"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "s"}], "-", "s1"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<((\!\(\*FractionBox[\(\[Rho]1\), \ \(\[Rho]\)]\)e-e1)-T(\!\(\*FractionBox[\(\[Rho]1\), \(\[Rho]\)]\)s-s1))/(\!\(\ \*FractionBox[\(\[Rho]1\), \(\[Rho]\)]\)p) ratio\>\""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e2"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], "s"}], "-", "s2"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<((\!\(\*FractionBox[\(\[Rho]2\), \ \(\[Rho]\)]\)e-e2)-T(\!\(\*FractionBox[\(\[Rho]2\), \(\[Rho]\)]\)s-s2))/(\!\(\ \*FractionBox[\(\[Rho]2\), \(\[Rho]\)]\)p) ratio\>\""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p1", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(1\)] - \ \*SubscriptBox[\(x\), \(1\)]\\\ p)\)/\((\*SubscriptBox[\(x\), \(1\)] p)\)\)\>\ \""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"p2", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\<\[Kappa]\>\"", ",", "\"\<\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(2\)] - \ \*SubscriptBox[\(x\), \(2\)]\\\ p)\)/\((\*SubscriptBox[\(x\), \(2\)] p)\)\)\>\ \""}], "}"}]}]}], RowBox[{"(*", RowBox[{",", RowBox[{"MaxPlotPoints", "\[Rule]", "60"}]}], "*)"}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGAQBWIQfVKO8UzZwTeO/wpmXQHRIive3QPRcVfTnoHopDt2 r0D0twMrP4Bohe7qPZVA+lZ54HEQLXrC6CyIjj647iqIFrlw+CaIvuG19haI 1oi//ABET7vn8RBEy6d3PQXRXHuNX4Hom+ylH0C0iUHAXxCt1/eNowpIC3yp EAXRfO76UiB61+SfSiD6kKjQq+NAOneCIfMJkLs5A4VANM+nVBUQzZLvrwWi T/RKGYHoD5U/HED0uoQGJxDN53vQDURfejDDHUQXRG/1BdHnOBSiQXRDp2g8 iN4etCQRRJtLNbqcBNKVilvB9JGbe71ANA/bczD9rT9vLvOhN44h85rANADk c740 "], CellLabel->"In[12]:=",ExpressionUUID->"070c747d-f3b2-437d-8cc1-bf06de2c5462"], Cell["matches the explicit results", "Text", CellChangeTimes->{{3.8596962623712997`*^9, 3.8596962733758*^9}, { 3.859815666801489*^9, 3.859815675953641*^9}},ExpressionUUID->"9b8978ba-4830-4bd4-9db9-\ 2a4ea3eb286d"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Without the explicit expressions - vdW gas", "Section", CellChangeTimes->{{3.85968594258692*^9, 3.8596859548032*^9}, { 3.85968602880628*^9, 3.859686040225389*^9}, {3.8597001728473387`*^9, 3.859700193111833*^9}, {3.890319538000763*^9, 3.890319538594637*^9}},ExpressionUUID->"3e892c92-2849-4c1e-b599-\ d77fa44acf61"], Cell[BoxData[{ RowBox[{ RowBox[{"s1", "=", RowBox[{ RowBox[{ RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m1"], " ", "\[Rho]1", " ", RowBox[{"Log", "[", FractionBox["T1", "Tref"], "]"}]}], "-", RowBox[{ FractionBox["kB", "m1"], " ", "\[Rho]1", " ", RowBox[{"Log", "[", RowBox[{"C1", " ", FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{"1", "-", RowBox[{"\[Nu]1", " ", RowBox[{"\[Rho]1", "/", "m1"}]}]}]]}], "]"}]}]}], "/.", RowBox[{"T1", "\[Rule]", RowBox[{ RowBox[{"(", RowBox[{"e1", "-", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u1", "2"], "\[Rho]1"]}], "-", RowBox[{"a1", " ", SuperscriptBox["\[Rho]1", "2"]}]}], ")"}], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m1"], "\[Rho]1"}], ")"}], RowBox[{"-", "1"}]]}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"s2", "=", RowBox[{ RowBox[{ RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m2"], " ", "\[Rho]2", " ", RowBox[{"Log", "[", FractionBox["T2", "Tref"], "]"}]}], "-", RowBox[{ FractionBox["kB", "m2"], " ", "\[Rho]2", " ", RowBox[{"Log", "[", RowBox[{"C2", " ", FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{"1", "-", RowBox[{"\[Nu]2", " ", RowBox[{"\[Rho]2", "/", "m2"}]}]}]]}], "]"}]}]}], "/.", RowBox[{"T2", "\[Rule]", RowBox[{ RowBox[{"(", RowBox[{"e2", "-", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u2", "2"], "\[Rho]2"]}], "-", RowBox[{"a2", " ", SuperscriptBox["\[Rho]2", "2"]}]}], ")"}], SuperscriptBox[ RowBox[{"(", RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m2"], "\[Rho]2"}], ")"}], RowBox[{"-", "1"}]]}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"s", "=", RowBox[{"s1", "+", "s2"}]}], ";"}]}], "Input", CellChangeTimes->{{3.859688131053954*^9, 3.8596881452240667`*^9}, { 3.859688500397032*^9, 3.859688540662909*^9}, {3.859700346441039*^9, 3.859700359926921*^9}, {3.859700404821456*^9, 3.859700501121632*^9}, { 3.859702851802215*^9, 3.859702908048374*^9}, {3.859777983784473*^9, 3.859778011218926*^9}, {3.859778042473023*^9, 3.8597780448681393`*^9}, { 3.859782405070703*^9, 3.859782410530209*^9}, {3.859782467048685*^9, 3.8597824707370653`*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"b4283d6b-730a-45c2-be54-f24f471dd6c6"], Cell[BoxData[ RowBox[{ RowBox[{"FirstMEstep", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "\[Rho]1"}], "]"}], "\[Equal]", "\[Rho]star"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "\[Rho]2"}], "]"}], "\[Equal]", "\[Rho]star"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "u1"}], "]"}], "\[Equal]", "ustar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "u2"}], "]"}], "\[Equal]", "ustar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "e1"}], "]"}], "\[Equal]", "estar"}], ",", RowBox[{ RowBox[{"D", "[", RowBox[{"s", ",", "e2"}], "]"}], "\[Equal]", "estar"}]}], "}"}], "//", "Simplify"}]}], ";"}]], "Input", CellChangeTimes->{{3.859688114706395*^9, 3.859688179113668*^9}, { 3.8596882130918007`*^9, 3.859688213919829*^9}, {3.859688547629517*^9, 3.8596885771977053`*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"d0129655-0cc8-45de-b0bc-ee156ce9ab17"], Cell["instead of the second step, we use projections", "Text", CellChangeTimes->{{3.85968841256456*^9, 3.859688420410017*^9}, 3.859793497254418*^9, 3.859816303141656*^9},ExpressionUUID->"47265026-52aa-49bc-b916-\ 019947875e4a"], Cell[BoxData[ RowBox[{ RowBox[{"Projections", "=", RowBox[{"{", RowBox[{ RowBox[{"\[Rho]", "\[Equal]", RowBox[{"\[Rho]1", "+", "\[Rho]2"}]}], ",", RowBox[{"u", "\[Equal]", RowBox[{"u1", "+", "u2"}]}], ",", RowBox[{"e", "\[Equal]", RowBox[{"e1", "+", "e2"}]}]}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.859688231152259*^9, 3.859688233764982*^9}, { 3.859688406426537*^9, 3.859688438052717*^9}, {3.85968848182981*^9, 3.859688495827775*^9}, {3.859688586298517*^9, 3.859688587655958*^9}}, CellLabel->"In[5]:=",ExpressionUUID->"55dcb87d-1787-4f75-a6dd-86f8716368e6"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"free", " ", "ene", " ", "fE"}], "=", RowBox[{"e", "-", "Ts"}]}], ";", " ", RowBox[{ RowBox[{"pressure", " ", "p"}], "=", RowBox[{ RowBox[{"\[Rho]", " ", RowBox[{ SubscriptBox["\[PartialD]", "\[Rho]"], "fE"}]}], "-", "fE"}]}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fE", "=", RowBox[{ RowBox[{ RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m"], "\[Rho]", " ", "T"}], "+", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u", "2"], "\[Rho]"]}], "-", RowBox[{"a", " ", SuperscriptBox["\[Rho]", "2"]}], "-", RowBox[{"T", " ", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["3", "2"], FractionBox["kB", "m"], " ", "\[Rho]", " ", RowBox[{"Log", "[", FractionBox["T", "Tref"], "]"}]}], "-", RowBox[{ FractionBox["kB", "m"], " ", "\[Rho]", " ", RowBox[{"Log", "[", RowBox[{"C", " ", FractionBox[ RowBox[{"\[Rho]", "/", "m"}], RowBox[{"1", "-", RowBox[{"\[Nu]", " ", RowBox[{"\[Rho]", "/", "m"}]}]}]]}], "]"}]}]}], ")"}]}]}], "//", "Simplify"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Rho]", " ", RowBox[{"D", "[", RowBox[{"fE", ",", "\[Rho]"}], "]"}]}], "-", "fE"}], "//", "Simplify"}]}]}]], "Input", CellChangeTimes->{{3.859778548401408*^9, 3.859778567097253*^9}, { 3.8597791800917187`*^9, 3.859779294120717*^9}, {3.859779334578948*^9, 3.8597793355034246`*^9}, {3.859779754061535*^9, 3.859779793343299*^9}, 3.859816316553659*^9},ExpressionUUID->"958c2569-903f-4ddb-a41d-\ 6750cd8134b1"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"m", " ", SuperscriptBox["u", "2"]}], "+", RowBox[{"3", " ", "kB", " ", "T", " ", SuperscriptBox["\[Rho]", "2"]}], "-", RowBox[{"2", " ", "a", " ", "m", " ", SuperscriptBox["\[Rho]", "3"]}], "-", RowBox[{"3", " ", "kB", " ", "T", " ", SuperscriptBox["\[Rho]", "2"], " ", RowBox[{"Log", "[", FractionBox["T", "Tref"], "]"}]}], "+", RowBox[{"2", " ", "kB", " ", "T", " ", SuperscriptBox["\[Rho]", "2"], " ", RowBox[{"Log", "[", FractionBox[ RowBox[{"C", " ", "\[Rho]"}], RowBox[{"m", "-", RowBox[{"\[Nu]", " ", "\[Rho]"}]}]], "]"}]}]}], RowBox[{"2", " ", "m", " ", "\[Rho]"}]]], "Output", CellChangeTimes->{3.859779239506428*^9, 3.859779295283445*^9, 3.859779342237113*^9, 3.859779794346888*^9, 3.8597798265429087`*^9, 3.859782419931398*^9, 3.859782484985157*^9, 3.859793500102372*^9, 3.859793889148848*^9}, CellLabel->"Out[8]=",ExpressionUUID->"24a16a3e-6c70-4309-9265-f4437406b055"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"m", " ", RowBox[{"(", RowBox[{ SuperscriptBox["u", "2"], "+", RowBox[{"a", " ", SuperscriptBox["\[Rho]", "3"]}]}], ")"}]}], "-", RowBox[{"\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["u", "2"], " ", "\[Nu]"}], "+", RowBox[{"kB", " ", "T", " ", "\[Rho]"}], "+", RowBox[{"a", " ", "\[Nu]", " ", SuperscriptBox["\[Rho]", "3"]}]}], ")"}]}]}], RowBox[{"\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "m"}], "+", RowBox[{"\[Nu]", " ", "\[Rho]"}]}], ")"}]}]]], "Output", CellChangeTimes->{3.859779239506428*^9, 3.859779295283445*^9, 3.859779342237113*^9, 3.859779794346888*^9, 3.8597798265429087`*^9, 3.859782419931398*^9, 3.859782484985157*^9, 3.859793500102372*^9, 3.859793889175832*^9}, CellLabel->"Out[9]=",ExpressionUUID->"d3a3c0af-e1b6-45aa-abcf-10631c3477c8"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"%", "/.", RowBox[{"u", "\[Rule]", "0"}]}], "//", "Simplify"}]], "Input", CellChangeTimes->{{3.8597798160629597`*^9, 3.8597798246673603`*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"ae9991c1-1b6a-4100-ae9e-cde9df315f84"], Cell[BoxData[ RowBox[{"\[Rho]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", "\[Rho]"}], "+", FractionBox[ RowBox[{"kB", " ", "T"}], RowBox[{"m", "-", RowBox[{"\[Nu]", " ", "\[Rho]"}]}]]}], ")"}]}]], "Output", CellChangeTimes->{3.859779827428121*^9, 3.859782421403487*^9, 3.859782508333261*^9, 3.859793503733646*^9, 3.859793889469368*^9}, CellLabel->"Out[10]=",ExpressionUUID->"5a0d95ad-44a3-4e54-89bf-3cf29fc84141"] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"kB", "=", RowBox[{"1.380649", " ", SuperscriptBox["10", RowBox[{"-", "23"}]]}]}], ";"}], RowBox[{"(*", RowBox[{"J", "/", "K"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"h", "=", RowBox[{"6.62607015", " ", SuperscriptBox["10", RowBox[{"-", "34"}]]}]}], ";"}], " ", RowBox[{"(*", RowBox[{"J", "/", "Hz"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Da", "=", RowBox[{"1.66053906660", " ", SuperscriptBox["10", RowBox[{"-", "27"}]]}]}], ";"}], RowBox[{"(*", "kg", "*)"}]}]}], "Input", CellChangeTimes->{{3.859004032593636*^9, 3.859004041918112*^9}, { 3.859006453100181*^9, 3.859006464095994*^9}, {3.8590064951508503`*^9, 3.859006520248178*^9}, {3.859006607326933*^9, 3.859006630071869*^9}}, CellLabel->"In[6]:=",ExpressionUUID->"b4d8769a-dbd3-4b2c-a060-320f92f56865"], Cell[BoxData[{ RowBox[{ RowBox[{"\[Kappa]num", "=", "100"}], ";", RowBox[{"\[Kappa]min", "=", "0.1"}], ";", RowBox[{"\[Kappa]max", "=", "5"}], ";", RowBox[{"Ratios4\[Kappa]", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], ";", RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "e", ",", "T", ",", "estar", ",", "\[Kappa]", ",", "m1", ",", "m2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "1"}], ",", RowBox[{"j", "\[LessEqual]", RowBox[{"\[Kappa]num", "+", "1"}]}], ",", RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Kappa]", "=", RowBox[{"\[Kappa]min", "+", RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], " ", RowBox[{ RowBox[{"(", RowBox[{"\[Kappa]max", "-", "\[Kappa]min"}], ")"}], "/", "\[Kappa]num"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"m2", "=", RowBox[{"10", " ", "Da"}]}], ";", RowBox[{"(*", RowBox[{"mol", " ", "mass"}], "*)"}], "\[IndentingNewLine]", RowBox[{"m1", "=", RowBox[{"m2", "/", "\[Kappa]"}]}], ";", " ", RowBox[{"(*", RowBox[{"\[Kappa]", "=", RowBox[{"m2", "/", "m1"}]}], "*)"}], " ", "\[IndentingNewLine]", RowBox[{"Tref", "=", "300"}], ";", " ", RowBox[{"(*", "K", "*)"}], "\[IndentingNewLine]", RowBox[{"C1", "=", RowBox[{ FractionBox["1", "10"], FractionBox["m1", "\[Rho]"]}]}], ";", "\[IndentingNewLine]", RowBox[{"C2", "=", RowBox[{ FractionBox["1", "10"], FractionBox["m2", "\[Rho]"]}]}], ";", "\[IndentingNewLine]", RowBox[{"a1", "=", RowBox[{"3", " ", RowBox[{ SuperscriptBox["10", RowBox[{"-", "49"}]], "/", SuperscriptBox["m1", "2"]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"a2", "=", RowBox[{"3", " ", RowBox[{ SuperscriptBox["10", RowBox[{"-", "49"}]], "/", SuperscriptBox["m2", "2"]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"\[Nu]1", "=", SuperscriptBox["10", RowBox[{"-", "28"}]]}], ";", "\[IndentingNewLine]", RowBox[{"\[Nu]2", "=", RowBox[{"0.5", " ", SuperscriptBox["10", RowBox[{"-", "28"}]]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"mixture", " ", "state", " ", "variables"}], "*)"}], "\[IndentingNewLine]", RowBox[{"\[Rho]", "=", "1"}], ";", " ", RowBox[{"(*", RowBox[{"kg", "/", SuperscriptBox["m", "3"]}], "*)"}], "\[IndentingNewLine]", RowBox[{"u", "=", RowBox[{"0", " ", SuperscriptBox["10", "3"]}]}], ";", " ", RowBox[{"(*", RowBox[{"kg", " ", RowBox[{"m", "/", "s"}]}], "*)"}], " ", RowBox[{"(*", RowBox[{ "and", " ", "hence", " ", "total", " ", "and", " ", "interal", " ", "energies", " ", "are", " ", "equal"}], "*)"}], "\[IndentingNewLine]", RowBox[{"T", "=", "300"}], ";", "\[IndentingNewLine]", RowBox[{"estar", "=", RowBox[{"1", "/", "T"}]}], ";", "\[IndentingNewLine]", RowBox[{"eestimate", "=", RowBox[{ RowBox[{ FractionBox["3", "2"], RowBox[{"kB", "/", "estar"}], RowBox[{"(", FractionBox["\[Rho]", RowBox[{ RowBox[{"(", RowBox[{"m1", "+", "m2"}], ")"}], "/", "2"}]], ")"}]}], "+", RowBox[{ FractionBox["1", "2"], FractionBox[ SuperscriptBox["u", "2"], "\[Rho]"]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"numEstimate", "=", RowBox[{"Chop", "[", RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"FirstMEstep", "\[Union]", "Projections"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Rho]1", ",", RowBox[{"\[Rho]", RowBox[{"(", RowBox[{"0.8", "-", RowBox[{ FractionBox["0.6", "4"], "\[Kappa]"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]2", ",", RowBox[{"\[Rho]", RowBox[{"(", RowBox[{"1", "-", RowBox[{"(", RowBox[{"0.8", "-", RowBox[{ FractionBox["0.6", "4"], "\[Kappa]"}]}], ")"}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"u1", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u2", ",", RowBox[{"u", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e1", ",", RowBox[{"eestimate", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"e2", ",", RowBox[{"eestimate", "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Rho]star", ",", SuperscriptBox["10", "3"]}], "}"}], ",", RowBox[{"{", RowBox[{"ustar", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"e", ",", "eestimate"}], "}"}]}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"p", "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "e"}], "+", RowBox[{"\[Rho]", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s"}]}], ")"}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p1", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e1"}], "+", RowBox[{"\[Rho]1", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s1"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{"p2", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "e2"}], "+", RowBox[{"\[Rho]2", " ", "\[Mu]"}], "+", RowBox[{"T", " ", "s2"}]}], "/.", RowBox[{"\[Mu]", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"-", "\[Rho]star"}], " ", "T"}], ")"}]}]}], "/.", "numEstimate"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", "j", "]"}], "]"}], "=", RowBox[{"{", RowBox[{"\[Kappa]", ",", RowBox[{"\[Rho]1", "/.", "numEstimate"}], ",", RowBox[{"\[Rho]2", "/.", "numEstimate"}], ",", RowBox[{"u1", "/.", "numEstimate"}], ",", RowBox[{"u2", "/.", "numEstimate"}], ",", RowBox[{"e1", "/.", "numEstimate"}], ",", RowBox[{"e2", "/.", "numEstimate"}], ",", "p", ",", "p1", ",", "p2"}], "}"}]}]}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.859003684163105*^9, 3.859003745959848*^9}, { 3.8590038322325*^9, 3.859003848442205*^9}, {3.859003884000902*^9, 3.859004020468811*^9}, {3.859006604112194*^9, 3.8590066046528378`*^9}, { 3.85900665573822*^9, 3.8590066835617447`*^9}, {3.8590073292796783`*^9, 3.8590073304610863`*^9}, {3.859023404317885*^9, 3.859023663627729*^9}, { 3.859023738481776*^9, 3.859023780408155*^9}, {3.8590238394739103`*^9, 3.859023844981728*^9}, {3.859023941592525*^9, 3.859023953089074*^9}, { 3.8590240543670197`*^9, 3.85902406442233*^9}, {3.859024252666738*^9, 3.859024280881693*^9}, 3.859037100153151*^9, {3.8590380490801477`*^9, 3.859038068524189*^9}, {3.859038405652028*^9, 3.8590384574387617`*^9}, { 3.8593427722437763`*^9, 3.859342781424169*^9}, {3.8593436404583282`*^9, 3.8593436655903177`*^9}, {3.859343987204646*^9, 3.859343987525599*^9}, 3.8593440274099073`*^9, 3.8593441074498043`*^9, {3.859346582991984*^9, 3.859346625574361*^9}, {3.859368213800564*^9, 3.859368235554236*^9}, { 3.8593682808908997`*^9, 3.859368303332468*^9}, {3.859368953999317*^9, 3.859368955909123*^9}, {3.859369386858694*^9, 3.859369391311701*^9}, { 3.859369859383062*^9, 3.85936987637763*^9}, {3.859370557220182*^9, 3.859370646221528*^9}, {3.85937068982584*^9, 3.859370697362488*^9}, { 3.859370863588719*^9, 3.859370876316638*^9}, {3.859526501949636*^9, 3.859526502729855*^9}, {3.859527111302061*^9, 3.8595271165928307`*^9}, { 3.8595272117756033`*^9, 3.859527212040094*^9}, {3.859527251340817*^9, 3.859527260462924*^9}, {3.859527367888115*^9, 3.859527370901854*^9}, { 3.8595326367401333`*^9, 3.859532647197557*^9}, {3.8595340027213163`*^9, 3.859534010415688*^9}, {3.859607000362165*^9, 3.859607138478568*^9}, { 3.8596082694304028`*^9, 3.859608278676107*^9}, {3.859692536454299*^9, 3.859692646987258*^9}, {3.859692710035172*^9, 3.859692742831143*^9}, { 3.859692849999578*^9, 3.859692915414981*^9}, 3.859692951637721*^9, 3.859693355774358*^9, {3.859695922688858*^9, 3.859695944999322*^9}, 3.859780496449086*^9, 3.859781424288138*^9, {3.859781483304515*^9, 3.859781513881997*^9}, {3.859781873099489*^9, 3.859781886458707*^9}, { 3.8597823207373238`*^9, 3.85978233384374*^9}, 3.859782782801992*^9, { 3.859792072209255*^9, 3.859792072455175*^9}, {3.8597921138213177`*^9, 3.859792114146385*^9}, {3.859816398271865*^9, 3.859816422295699*^9}, { 3.890319581605915*^9, 3.8903195933121*^9}},ExpressionUUID->"e00980a9-84df-45e5-b06e-\ c198867e58c0"], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{ "j", ",", "p", ",", "p1", ",", "p2", ",", "m1", ",", "\[Kappa]", ",", "estar"}], "]"}]], "Input", CellChangeTimes->{{3.859693864888701*^9, 3.859693886122714*^9}, { 3.859696113559352*^9, 3.85969612159828*^9}, 3.859696176589321*^9}, CellLabel->"In[11]:=",ExpressionUUID->"e0396e8a-553f-4adc-a804-686b79304b31"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e1"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], "s"}], "-", "s1"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]1", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], RowBox[{"(", RowBox[{"e1", "+", "e2"}], ")"}]}], "-", "e2"}], ")"}], "-", RowBox[{"T", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], "s"}], "-", "s2"}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox["\[Rho]2", "\[Rho]"], " ", "p"}], ")"}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}]}], " ", "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"AxesStyle", " ", "\[Rule]", " ", RowBox[{"Thickness", "[", "0.0025", "]"}]}], ",", RowBox[{"PlotTheme", "\[Rule]", RowBox[{"{", "\"\\"", "}"}]}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontSize", "\[Rule]", "16"}], ",", "Black"}], "}"}]}], ",", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"Style", "[", RowBox[{"\"\<\[Kappa]\>\"", RowBox[{"(*", "\"\<\\kappa\>\"", "*)"}], ",", " ", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", " ", "\[Rule]", " ", "20"}]}], "]"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.8597942049432983`*^9, 3.859794245484088*^9}, { 3.8598164531852007`*^9, 3.8598164664572983`*^9}}, CellLabel->"In[20]:=",ExpressionUUID->"9b018302-f70e-4dcb-ba2a-76e625a62395"], Cell[BoxData[ GraphicsBox[{{}, {{ {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[DiskBox[{0, 0}, Offset[{2.75, 2.75}, {0., 0.}]]], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJwtlHlUjXkYx682ddtuN0sysiXNiERxZpLvYylGiGukidRpylJUEyNjkmOL SMZW2ZNTkq1QKKMZW+qcpluc0nK73f2+trRNCZn3fd3nnN9f9z3PfZ7v9/N9 RofHSiKNBQJBJPsGsM+IfadOcnUPs5K/VcgqW8taAw5lxIgfwdizYkXIwLqy jtpF4aKgChw58HTAXFl5mWmgzcSbZ6tRHex4rDImryx1g+7j5fZaPO5fc7tA eAuDrs9TbBtUh8Txhds+zy7HubZLT/2nN2DDqhFZsXk1cPUwv/pNcDP27wwa 5/+uDgXx6468TZSD6fylJX1fE0YER3jLAxTYuUDe/ypZDrYZ21GJJ+KspCNJ CuSefjyqIF6NaydWLiz7pET0/c3HHEy0SJ48Sd4yVw13mbPZzhM6bPTvzx8R okHX5xdbGRcGP1evGmTir8Vdp72vl959hQW+Yzt22euwHV6rS358g2HXO/WC Uh1mh2mkY5re4uHR1PC1vnqwzeYc3NAG6cm015OK9dCyv35Ieo/qYrU0SsRg Pj9gOxwmStXPAxlcaecE68CdIklY7UEG1kYT9g1p6IDK4qI8uZBBrHj335UX OpHcdXxHbQWDWq5dVBdK2p66rK5j4DmVq24Eum0yv/CSQTr777qP3VhcFB6n rWHQu0yVc/rxfyhNHKaXPGKwkpPrUA9CR3o80V9j8BcnR2Avlnd6T049ymAk t67TB5z+lHXTLJ7BLm4d3QeUXa0KEi5ioM7hBO1DG9O52dOZgV9xJ6vYR1iG hVuLevW4zLqXMusTQhIiBQ4VeljWX4zzEX7Gl0WHtXcz9NjI2/8ZS/Lnl0oi 9JD2cAP2Q/gwR/KDux5TOLsjviBjc152Sa8OC6w4QQS0IC1EM/gfHf7ggRHQ kzenMpP368B97S0XUGXA4VAK0KGFs3POANqtlFbEDdbBlqWv7dIACg8ca0xN WhBnn5URZfs8i6nJ0uJXHyE7oRGpcmsnz12jRbYvt5ARLQ3Pu3RrghbPOZy/ N6aIw+n109s1+MqzMZUpx1RqijWYxrczodDtacrqRA3WruHKhKZMrXE1m6NB ZgxnoAkV9kxITbfQoGLLg/OO7qY03max0yGpGn1JUSyRpnS2g5nXlaEG5/6/ PaZUNzKx50WoGiGHH3a7rjKjg9HvKqe5qpGWwTU0I2e3656j2lUoY7vJnAdS aOy9M+klKrzn4pMykITSoUnn9qgwmg/MQJpZNG6nd4AKEh5oc0oqsjoW56jC HpYu32JzSp15rw9aJYqecQNaUF/Q8egrN5UGfi3ohgcNub1DiaHsdMtUFiTW pt0JXqQ08Cyky6XqnPPDlfidcWETK6Qbqzxku14pkM/zbUlfKnMtTEoUaP7A LWxJTyOWHBlzQGHg3ZIk+/POyIIVmMnZ4WNF3wnmO3m6KQz8W5HfuvIG5/5W ZHHrmlnTwSH69delrajh82BNC+8P9au+2ApjXkBrMlaGlu9NaDXkw4aKU6Ru Uv9WRHL4Z9iQ6YVN56+OajXkxYa8uvOjp7yRo5zDN8yW7vwW/G58ptyQH1vK FKy+7+UrN9wrEU20G31nRWcLeLz8RLQu6M+ClOwW8PhsFVHGJsfYckkLeDyu iOieERVambQggbNfJqInWx5MXl4sA2+vrR3l14bmnFkvQx6fHztKn7G1vGWE DLw9m+zovrujZOjzZvDy59hRldDcdHZKM3h5X9rRA1FUbjA1g5dPKKZltxab hPQ2YSwnzwwxxR/r655b2AR+/RgxxYmtQ2yim/ATt16WmArqt7sUjWvC1/Ms pkyfBH8vRSP4c2BqT/u87GoPnG003Gd7cm1sqyoMbgS/7np7ckp/Fpbr0Ihq Ps/25JckLYmobwDfrsqe4r2HDGfSGyDgaxC9zKmodl/RgP8BG9cVOQ== "]]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[{ {GrayLevel[1], PolygonBox[{ Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}]}]}, {AbsoluteThickness[1], Dashing[{}], JoinedCurveBox[ Line[{Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}], Offset[{0., 2.975}]}], CurveClosed->True]}}], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJw1VHk4VWkYv/Z9u1eS0UgokgpJM+J78SSJMdGoFKJU1rRMtJmytE1MatK0 EEWKJp6SpHgnPBUtRENCC+W667lIstWcczLf83x/nXN+5/1tr2nYFr9wBQ6H E05fOfrK0/fsGebcIUdLfSyUbOrIW9+007HcGmJ+wNA8WVxN+pt8wnRX1ZFt S/ZHx7WXEaUAbZsbWQ2kPv/F0KrsM+RYNH/0al8TMbeOunntRD7qX1/ybrd+ C+mvtAqytLuH2VTBg2WObWTIyWFj1J0HaGmres04sIPs5xxMjzBrwJJtmzMk e9+QlIAc/YwLzTg1cIPTG993ZKx4XbpbYivSYDRiF5lj065UadmOl8/VTivZ 9p4ML9js6HD+NUbd23HSULGHHNJIqnkoeotzO82VD5ziE8pkNCE+pgs/jr9I EMwQkLhDl7OuN3dj+fepouXlQmI0vmufu8kH3EccgiuWisnSo2HF7st70G3d h8bp7RKS2xZm8TaSjzSY++/RFBFPWjwlOKYXe+inw4kyojX51EONQAF6sgP2 EVl/telCOyEW9TGC9ZPkwfIns4eEqCVvfcigrZ947xW+tyoU4RZu8j/1uQPk aseRqeu9xdjEwEV+JMkOe/jjr8U43545gyQipCVYd70EM+m/80cHSWI6PMlp k+Bn/+78c7WfiKCw+US+uxTXMHKlDZFFLZ7RShelWMnIEfCZ+NtZd5welKIJ Q/f7YUL1Bj2yIBQmMXT4w6TxVbpV5G8Uvs9nBB0hITqH67i3KfQoG6AVGyXG WwUq93sovEq7d8R1jFRMF/qmqshQo/VSnLP6OGlM8XFwNpRhDGv/ODE7Gpj+ yEKGjUPMgF9IEnVsPGyeDO0Yuzd8JcRJWOO+UIZemowgHOAFHudmO8twDxsY DnypDV2ZCzJk3nZ6w4Gx6vqUXa4yfM3Y6S4HSSGlK3zp5zp0+qgCOUiwenzQ k/4eGPs05eFa2jKjwzT+Vmd1ekJ5uKuZljzHToYXFzOE5MEAj3SuniXDZibO PyhA1ubcyTNMZfgtzwrgurXV5G8DGS5g4RRBRVSnpqIhw00bmaMIgWlO4X+O UfhXLGOgIozttK81eEdh3c6qC0ZzlUCh07vpbg2FI4mRdCKVwOfXZ3sK8ihk 3H82pATbdzpajyZTGPRH9aDlWmVYMyz5/G8ohemnGUBlsJo0u3WFC4VIo3Wa q0C1wq6KE1MolDH1OaICNTWDVVcGpGjKFkYFPM3Q6/oTKfqxgVaFcmGuzZ08 KabQ6VpcpgqxnNVVnXukeOsRM6AaQMvhwTl+0on8qsEZ54KDVTOlOJmezr9b DcTtI5/Oj0km8qwOP3W13WhrlOAuwQy6sepQEuRtmpwnwUI23xpgG21fdjle gh3DDGENGHnJU1juJZnIuwbE83IepBlL0IWxw1kT5k39bnSTVDyRf03o+FDU LUAx5jB0lbVAO7PMcGqGGJ+zfdAC332+J9XDxKjACqgFbrfablfY/d8PbQC1 rhAHBTGGM/E/rQ2WvyzuPtAsmuiLNnz1KplWcEmED5n4rtOBxMjU1KLtoon+ 6ECacP6kU+6iiX2lCyvX6sVF8ETIxstDF8hAYZtNtxDZ+CToglpahQv/hhDZ eBTpQsOrvB/PJgkxnrG/UxfkQ7OMl/kJkbVXRw/so+LE46ZCvML2Rw/8Q0Zi y/oEyNqzXQ8yi/1mJdwXICt/vh6klBZHeGQIkJX3pR7ML1N1NQ8VICufOheW Pt19XN9WgGaMPIu4IB7aoWIkJ0CWfiwXcjYVz3R83osrGHo5XMiu7FsSm9uL 39YzF27mFWXe39qL7DpQ4kHEQJixvVvvxH7mQbLHSGUttxdZuhE8MKpvckno 5mMD22ceON167OZbykcW7ikPsh6b/rwslY8c9uhDsLbt85gAPv4H9CM/Pw== "]]}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{ FormBox[ StyleBox[ "\"\[Kappa]\"", FontFamily -> "Times", FontSize -> 20, StripOnInput -> False], TraditionalForm], None}, AxesOrigin->{0, 0}, AxesStyle->Thickness[0.0025], BaseStyle->GrayLevel[0], DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->GrayLevel[0], FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, FrameTicksStyle->GrayLevel[0], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], ImageSize->{668.1818181818179, Automatic}, LabelStyle->{FontSize -> 16, GrayLevel[0]}, Method->{ "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange->{{0, 5.}, {-1.015985029906175, 0.8076939740216271}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}, TicksStyle->GrayLevel[0]]], "Output", CellChangeTimes->{{3.8597942257180777`*^9, 3.859794246046297*^9}, { 3.8598164490055532`*^9, 3.859816467133366*^9}}, CellLabel->"Out[20]=",ExpressionUUID->"f3e8f597-9dbb-47f8-b69e-8154c0f50678"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"100", " ", RowBox[{ RowBox[{"(", RowBox[{"p1", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]1", "/", "m1"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"100", " ", RowBox[{ RowBox[{"(", RowBox[{"p2", "-", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], "p"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"\[Rho]2", "/", "m2"}], RowBox[{ RowBox[{"\[Rho]1", "/", "m1"}], "+", RowBox[{"\[Rho]2", "/", "m2"}]}]], " ", "p"}], ")"}]}]}], "/.", RowBox[{"m1", "\[Rule]", RowBox[{"m2", "/", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}]}]}], "/.", RowBox[{"\[Rho]1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}]}], "/.", RowBox[{"\[Rho]2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "3"}], "]"}], "]"}]}]}], "/.", RowBox[{"u1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "4"}], "]"}], "]"}]}]}], "/.", RowBox[{"u2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "5"}], "]"}], "]"}]}]}], "/.", RowBox[{"e1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "6"}], "]"}], "]"}]}]}], "/.", RowBox[{"e2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "7"}], "]"}], "]"}]}]}], "/.", RowBox[{"p", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "8"}], "]"}], "]"}]}]}], "/.", RowBox[{"p1", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "9"}], "]"}], "]"}]}]}], "/.", RowBox[{"p2", "\[Rule]", RowBox[{"Ratios4\[Kappa]", "[", RowBox[{"[", RowBox[{"j", ",", "10"}], "]"}], "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"\[Kappa]num", "+", "1"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"AxesStyle", " ", "\[Rule]", " ", RowBox[{"Thickness", "[", "0.0025", "]"}]}], ",", RowBox[{"PlotTheme", "\[Rule]", RowBox[{"{", "\"\\"", "}"}]}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontSize", "\[Rule]", "16"}], ",", "Black"}], "}"}]}], ",", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"Style", "[", RowBox[{"\"\<\[Kappa]\>\"", RowBox[{"(*", "\"\<\\kappa\>\"", "*)"}], ",", " ", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", " ", "\[Rule]", " ", "20"}]}], "]"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.859789640301268*^9, 3.859789648873452*^9}, { 3.859794098533031*^9, 3.8597941533951406`*^9}, {3.85981647351787*^9, 3.8598165281287203`*^9}}, CellLabel->"In[23]:=",ExpressionUUID->"66b36fc2-a33c-4a80-a803-d918646c99e4"], Cell[BoxData[ GraphicsBox[{{}, {{ {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[DiskBox[{0, 0}, Offset[{2.75, 2.75}, {0., 0.}]]], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJwtlHs0lHkYx8eYocEwxmy2mxK12orc6nR9HpXKth3R5YRYa0sXNi3VsqWz Lm0lsVFRTiXlFpHOibLpFVNuGfP+prRq3EVYSYao1L7vm+ec31/znmee5/v9 fB9zvyD3ndo8Hm8n87SYx2fexQts3YOmyjU3zR2aqRbX00n7pOXw4Gz27Yxp auod2eAn2VYF02UB5XFWDZRwq+H825fqQFK4frZmcz0VG9j1MXuAgHue09SJ 11WULG9t6x+yeojVVfbKTGnqcn/m4/WLGmBt6kvLyd61lJXthNypnmpI9MmM 0XtWSd0K3n2m70gzWKi33Bw5K6emee5Y2uzaCprSyzaClFKKacZ0bIPV570P rKu6R2WkyGfcCu6ACHqXoqDxNhVw/0Dit4JOqJ7Z5rC1IYuyabTUiTjXBYoL JQ2TSi5QmrGnod2zu0Ex1ydKowig7pod63W72wMByaf4+vZnIBwcfYpd/gP8 XNQbYZcGK31fKWe+7IOc5gXbFk/JAabZqlOB/SAQy/Nn3iqATubX0aNvIbG1 07j6rzuwjhtwAJY86YuwMb0HOQOsYO8gPbq5MtH/Poj5c49PbHgHlSMup9Vh FARJo0qrrw6CaFaTZ833D4Gw7fZqwMlDOPjpaBk42LM1BBbBPh6H/imH88y/ d30cgu1bg64I2uQwsqk9PUU+DKav+Dpumkfgxcp1+j1ozOg97YOPoYSVY+sI zPgFMyzbKmA6u67ZKFSfsO/wLa2ESHadrlGIn+SsqIqvgo50VtAP8GzW9oxQ t2pYUzjIKPYRLOwDluzXqYFsxr2TTp9gnkNs0eX8GtB/fm3/cr0xGI675tW8 4Qn8ytk/BiPtu3U+tT4B5Xt2wM8wzc4yJy+wFuxYu3d8gcXqkutpb2rhBwNW EB5qWXX0HdytgMMcMDyUNlpA8QsFsF8vbeZhgqhONuxcB02snau0UHvjscvp N+rAiKGvP1MLZ+01rr0kUAKy9hnw8UBfi9jYVgm/LddjJuSji7VdWqOnEtKc 2YX42B3kq1kQqQQVi/NibRTxK2WOmUr4yrM2+tMbv0iqlbCQayfAXPnAi9c9 Stjlz5YA1wcW2jeJaEjexxoowKowuY3kOxqqDj24MtlGiL11KiplJQ0fju5l iBRiCS+yJmU7Daz7ivdC/GDe4jHnIA3e8WVDVtt1cNL8hEKvWBriktiGOqhY pkhcl0YDxXRrtNTFheei5giKaHjLxuekLrZBj9vVahrMucDoosXawmu2jTS4 c0BPwCMrLGMevaEhmqHLuXACVqQZeQV+oeFOJTugCMvbVwQ4GJFxfkXocUJs PteMgCkz3aZ2EeYmJwu955FxnvXQwzXu6bPFBMK6ZzOJ1UO/kQcxqWsI3OD4 1sebDjEhFe4E1KPswvpoWe3kuNmHjPOuj+n9SWrXPQRWsHYsN0AXMr+rLISM 82+A1xds2XAnnEAqu66OGBPSvzllfZwAzeVBjBfdjmU5/k1AmxNQjMqxSCc6 mYznwxC9Iptida8S2Mnin2SIP4k++jVlkfG8GGLYkeFVXrcIVLD4+hphqMbH O6qIjOfHCKOlf8Z7PSDw9V5JMLvWNfi1nACH1xoJrj7M97SuIcDhEyrB+LYf vWxpAhweORL0OODpOlRP4HfW/kYJ5r8Mfx6uJsDZa2SMNe1pvopWAllcfozR 6OGR2T2dBDh7QoxxTtDJhU97CXDypxvjoZLnwfFvCXDy/muMgQZpZ82GCHDy 6UmxIOS+dfQoAQtWnmVS5M94kV82RoBbf58UJcW5O9RaKtjMrpcqxdXFLWEq oQq+nmcpZkhHx7JFKuDOgdAEhZEG7T+LVfD1Ppvg2jx/3phEBdy6e0yw/rOh LFymgjouzyY4lb9I3m6qAq5drQma6iWk2k1RAY8rGR4uSLIIMFPB/0a8DmI= "]]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"], GeometricTransformationBox[InsetBox[ FormBox[ StyleBox[ GraphicsBox[{ {GrayLevel[1], PolygonBox[{ Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}]}]}, {AbsoluteThickness[1], Dashing[{}], JoinedCurveBox[ Line[{Offset[{0., 2.975}], Offset[{-2.5764255762587047`, -1.4875}], Offset[{2.5764255762587047`, -1.4875}], Offset[{0., 2.975}]}], CurveClosed->True]}}], StripOnInput->False, GraphicsBoxOptions->{DefaultBaseStyle->Directive[ PointSize[0.009166666666666668], CapForm["Butt"], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], GrayLevel[0]]}], TraditionalForm], {0., 0.}], CompressedData[" 1:eJwtlHs0lHkYx+fqbswMpRtd1raWdrWy0Rn8fhFJ1i1aibJuaSJDscXqVGpF ujpl5doyyK3LbiS237vD7kiFrJIit9yvM65Dw77vy3PO7695zzPP8/1+vs9G 31DXADqFQgnAHxV/NPzdSSGqHOgxjXsEpTdBh9OV5OPcKqAT6fOLW20akDb+ 4Mv2eA6sqPFeuSuyAXM/65tH6fUgO6bqyulNeSAxuG/+nqQRfKn00CLNowBo lezujNJ6C/JL2IcdbxeBjLG8f/eatgAXilY6XVwM9L9TKlrn2Qpkq+tv7+ko Bg/Cg26M/NIOkiR6Bm7tRUDH05/X7tQJdLfcD1EUFwC8Gd6xC/SwIulHMvJA bmr1hgfhn0C/UuSiR2g2OFZ5MmkVoxeoL85WHLycBoza9BTO3eoDktpLe0Re 18GkvOnUwOYB0Ch443lW4Aee6F4ccnkyCEp3XXAOtk9AMeD7Q0/3DIPt/tf9 6ndmICufnoZNH0bA9I7Uq8mB+QhvZn05eAy4ssviww0fol78V9mZceAt5uo2 hpciO3JACSgMlKbn0ytRoYQQTAqURdodNsMYUqcZxq1skYK6JkGNyXQVCuXG YrV3J0Czbcwtax0xaiTa8SdB4rfliuBwLTLZRtQUeLLVxG7d01foNv7vffNT QBBlx5+/1YBm93ULU6ungbOp+ca4A43oICHXlRlw7itnWefmJvQXIcf+WTCY 5ePrIH+D1hPr6sqA/Tvn4BWtzeg8sU6fDHBKeI9SRC3ok5AQdA5sGJp2tXrw AdmWTuCKzQPJyajZ2Jw2dA93L37nZxBMkY62ZbQj1eZsgYWKHAz93SQMru9A IaT9chAnbOAwGjtRwwwx4AJQPiwMojV3IWPCbv9F0Gvkm2P2sRvZqxGCUKDZ aLd5dN8nFE0CQ4H+jrz2u9IeRHzNa6dA7X0cw7jFXvSRsNOaCp8OpkYosfqR Bk7fWB4VJg8+vsHUHUCQsE+NBtVnHqX5GA2iMAsVfEIaLOxKrJfvHEK/2xAL 0eD7E+puVe7D6D8C5x10WPcyQyeFP4KWeKZD/8Kwf4LOjqLtZDsGjB++f1Qn eQwdCSSKAYuDKsQuP46j344TBjKgpXtx7MnucfQ88lnmGiMmnOPp8EdDJWju DB8nkgkd0rUTyj5LEOF+3QwTHnv4R0RNvBR5XxNN6XspQEXTn8zWaE+gq8lE QwVIraA55uZMIIR3a9NThNvMRXcCjSfROBGfeEVoWHfNzx2bRBvJwCjCRBfe 7hDHKeRKAq0EPfPWmt1rnUIXcLpsSpVgi61pJOPYNHpcQwyoDGtedsVHyaaX +VWGCZ4vLBUvzSBtfLp93crwxXu/zNyVs8s8q0BeYNG4m3AWnR7YjCdWBSqZ OJSwTGSogORbFR6Nmfm1QSRDrTJiYVUYcmHNgWSXuWXeVaHAodrIp2MOWRJ2 WKhBO9ELoB86v8y/Gmz2NugZls+jLGJdBXV4Q/dSVmHiZ/SazIM6jCif1PJd K0d0UkB1eOhELZNVIF/OBwtWuJW5FZstoAAC/2QWLMgeWLQQLyznhQWz+702 PHNfRGICXx8NeIBi02/4aXE5PxrQj1/bYLWDgi3dKzaM8HJ663+WgpF42bJh vV4giBZTMBKfU2x4Sq/U+SKLipF4FLLhOwN7j/PuVOxnwv42NtzSoVIclkbF SHs1ONBJbF3i2k3F8sn8cOC1t/pVegY0jLTnBAdmglDPPgENI+UXcmDdme6B lDIaRsr7jgN1RpRHeQs0jJRPhQv3JlUPvNxFx74g5DHnQn78QoDDZTpGrn+c C0POeUnKX9MxN2K9LC4cWSldv2IVA1s6z1x4RDif4H2IgZHngKkJbWBaw80c BrZ0nzWh5c3MpD8HGRi57lFN6OIAokVbmVg9mWdNqPb1sHFlJBMj273ShLE1 q/l3K5kYhSwtWF6n3hRGU8D+B4t0Ilw= "]]}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}, { {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], Dashing[{}], CapForm["Butt"]}, {GrayLevel[0], PointSize[0.009166666666666668], AbsoluteThickness[1.6], AbsoluteDashing[{6, 2}], CapForm["Butt"]}, {}, {}, {}}}, {{}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{ FormBox[ StyleBox[ "\"\[Kappa]\"", FontFamily -> "Times", FontSize -> 20, StripOnInput -> False], TraditionalForm], None}, AxesOrigin->{0, 0}, AxesStyle->Thickness[0.0025], BaseStyle->GrayLevel[0], DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameStyle->GrayLevel[0], FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, FrameTicksStyle->GrayLevel[0], GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0], AbsoluteThickness[1], AbsoluteDashing[{1, 2}]], ImageSize->{701., Automatic}, LabelStyle->{FontSize -> 16, GrayLevel[0]}, Method->{ "OptimizePlotMarkers" -> True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}}, PlotRange->{{0, 5.}, {-2.751193672820446, 0.29873159862361093`}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}, TicksStyle->GrayLevel[0]]], "Output", CellChangeTimes->{ 3.859789653388701*^9, 3.859792161434154*^9, {3.859794129153832*^9, 3.859794153903432*^9}, {3.8598164875348377`*^9, 3.8598165292956057`*^9}}, CellLabel->"Out[23]=",ExpressionUUID->"d698f4fe-605f-4128-bf72-90f4eb96cc18"] }, Open ]] }, Open ]] }, WindowSize->{1536, 800}, WindowMargins->{{0, Automatic}, {Automatic, 48}}, Magnification:>1.1 Inherited, 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[CellGroupData[{ Cell[580, 22, 355, 5, 75, "Section",ExpressionUUID->"af616f43-a4f9-4918-b6eb-1c3097adaf06"], Cell[938, 29, 941, 27, 91, "Input",ExpressionUUID->"672b74be-f9eb-48ef-8e80-38b97f8749ec"], Cell[1882, 58, 791, 18, 36, "Input",ExpressionUUID->"4c09e09b-b1dc-4eff-9ef2-d7eec4e53b0b"], Cell[2676, 78, 19310, 501, 1325, "Input",ExpressionUUID->"ca4f6923-c1ae-4710-b6e5-a71811d566ff"], Cell[21989, 581, 353, 8, 36, "Input",ExpressionUUID->"f2ee71cb-b939-4841-bfc6-1df9b62859b9"], Cell[CellGroupData[{ Cell[22367, 593, 8344, 199, 520, "Input",ExpressionUUID->"27db8a35-fa9d-42cd-bcf7-65dd74369ab7"], Cell[30714, 794, 7329, 155, 454, "Output",ExpressionUUID->"23a497be-7f2e-4e41-9b56-b327f42e2b51"] }, Open ]], Cell[38058, 952, 379, 8, 67, "Text",ExpressionUUID->"aa16e227-6fbf-466b-9625-1d609252e717"], Cell[38440, 962, 827, 24, 40, "Text",ExpressionUUID->"a1bb8dc1-513a-481b-b788-367283c3081d"], Cell[CellGroupData[{ Cell[39292, 990, 9273, 214, 560, "Input",ExpressionUUID->"7d7ba42f-a5cb-407e-a133-bc1a71973b51"], Cell[48568, 1206, 4802, 111, 430, "Output",ExpressionUUID->"d64f7b91-f22b-466c-bf16-34137a7d5b4b"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[53419, 1323, 345, 5, 59, "Section",ExpressionUUID->"a7e55685-9f27-417e-a4e2-8cb1525483d6"], Cell[53767, 1330, 1850, 56, 206, "Input",ExpressionUUID->"c82495e6-8b96-45a5-a53c-4c346b338f28"], Cell[55620, 1388, 1077, 28, 36, "Input",ExpressionUUID->"eb8d189a-e53b-4443-b0c8-1bc3b7b4c751"], Cell[56700, 1418, 294, 4, 40, "Text",ExpressionUUID->"cab53a8f-aefd-4254-907f-7d1030123ba5"], Cell[56997, 1424, 624, 14, 36, "Input",ExpressionUUID->"9fd46310-fefd-4fe1-aaa0-1c359e11da6d"], Cell[57624, 1440, 940, 27, 91, "Input",ExpressionUUID->"ab9544ab-c336-46bc-b9f9-737e735f5cca"], Cell[CellGroupData[{ Cell[58589, 1471, 227, 4, 50, "Subsubsection",ExpressionUUID->"0f9ac615-1162-4456-8ca3-ea1f4c076fbd"], Cell[58819, 1477, 9304, 222, 544, "Input",ExpressionUUID->"1a9912d9-1277-4567-ae79-a2c33a985929"], Cell[68126, 1701, 368, 7, 36, "Input",ExpressionUUID->"97aa4eb9-ae3c-43d0-80f8-4d4db0d79fe0"], Cell[68497, 1710, 14485, 372, 925, "Input",ExpressionUUID->"463f7049-9a34-40f8-9251-464595228901"] }, Closed]], Cell[CellGroupData[{ Cell[83019, 2087, 232, 4, 41, "Subsubsection",ExpressionUUID->"2229137f-127d-43fc-9c9e-3781280f8daa"], Cell[83254, 2093, 8030, 191, 545, "Input",ExpressionUUID->"af052ee7-a730-4fbc-a943-248604d6ccc6"], Cell[91287, 2286, 368, 7, 36, "Input",ExpressionUUID->"fb2e256a-b859-4e88-a414-4d63b3734ba1"], Cell[91658, 2295, 13731, 356, 945, "Input",ExpressionUUID->"070c747d-f3b2-437d-8cc1-bf06de2c5462"], Cell[105392, 2653, 219, 4, 40, "Text",ExpressionUUID->"9b8978ba-4830-4bd4-9db9-2a4ea3eb286d"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[105660, 2663, 329, 5, 59, "Section",ExpressionUUID->"3e892c92-2849-4c1e-b599-d77fa44acf61"], Cell[105992, 2670, 2751, 79, 149, "Input",ExpressionUUID->"b4283d6b-730a-45c2-be54-f24f471dd6c6"], Cell[108746, 2751, 1077, 28, 36, "Input",ExpressionUUID->"d0129655-0cc8-45de-b0bc-ee156ce9ab17"], Cell[109826, 2781, 236, 4, 40, "Text",ExpressionUUID->"47265026-52aa-49bc-b916-019947875e4a"], Cell[110065, 2787, 624, 14, 36, "Input",ExpressionUUID->"55dcb87d-1787-4f75-a6dd-86f8716368e6"], Cell[CellGroupData[{ Cell[110714, 2805, 1871, 55, 116, "Input",ExpressionUUID->"958c2569-903f-4ddb-a41d-6750cd8134b1"], Cell[112588, 2862, 1030, 25, 75, "Output",ExpressionUUID->"24a16a3e-6c70-4309-9265-f4437406b055"], Cell[113621, 2889, 943, 26, 67, "Output",ExpressionUUID->"d3a3c0af-e1b6-45aa-abcf-10631c3477c8"] }, Open ]], Cell[CellGroupData[{ Cell[114601, 2920, 260, 5, 36, "Input",ExpressionUUID->"ae9991c1-1b6a-4100-ae9e-cde9df315f84"], Cell[114864, 2927, 477, 12, 59, "Output",ExpressionUUID->"5a0d95ad-44a3-4e54-89bf-3cf29fc84141"] }, Open ]], Cell[115356, 2942, 940, 27, 91, "Input",ExpressionUUID->"b4d8769a-dbd3-4b2c-a060-320f92f56865"], Cell[116299, 2971, 9799, 237, 797, "Input",ExpressionUUID->"e00980a9-84df-45e5-b06e-c198867e58c0"], Cell[126101, 3210, 368, 7, 36, "Input",ExpressionUUID->"e0396e8a-553f-4adc-a804-686b79304b31"], Cell[CellGroupData[{ Cell[126494, 3221, 6545, 163, 421, "Input",ExpressionUUID->"9b018302-f70e-4dcb-ba2a-76e625a62395"], Cell[133042, 3386, 7725, 161, 446, "Output",ExpressionUUID->"f3e8f597-9dbb-47f8-b69e-8154c0f50678"] }, Open ]], Cell[CellGroupData[{ Cell[140804, 3552, 7505, 182, 448, "Input",ExpressionUUID->"66b36fc2-a33c-4a80-a803-d918646c99e4"], Cell[148312, 3736, 7799, 163, 469, "Output",ExpressionUUID->"d698f4fe-605f-4128-bf72-90f4eb96cc18"] }, Open ]] }, Open ]] } ] *)