Homec4science
Diffusion COSOlver (improved_sugama) Browse

cosolver/matlab_scripts/Speedfunctions.nb
b3f94e22e87cimproved_sugama

Last Change
Raw File

Speedfunctions.nb
View Options

(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 11.1' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 69751, 1701]
NotebookOptionsPosition[ 64691, 1571]
NotebookOutlinePosition[ 65027, 1586]
CellTagsIndexPosition[ 64984, 1583]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.791297263459988*^9,
3.791297264815939*^9}},ExpressionUUID->"45457ac5-fc1c-4c63-84a9-\
453647157b71"],
Cell[CellGroupData[{
Cell[TextData[{
"Test and Back-Reaction Speed Functions \n",
StyleBox["We compute here the closed analytical expressions of the speed \
functions of test and back-reaction operators [see Ji & Held, 2006 for \
details]", "Text"]
}], "Title",
CellChangeTimes->{{3.7831627498134527`*^9, 3.78316282626906*^9}, {
3.7838348269063063`*^9, 3.78383483374611*^9}, {3.7850461299935713`*^9,
3.785046141649485*^9}},ExpressionUUID->"32487dfa-0b15-4223-aa2c-\
568b14b50d70"],
Cell[BoxData[
RowBox[{"ClearAll", ";"}]], "Input",
CellChangeTimes->{{3.783165885296481*^9, 3.7831658878465157`*^9},
3.785211749784758*^9},ExpressionUUID->"ff3a317a-4cdd-4e0a-ab84-\
75ae6620fef1"],
Cell[CellGroupData[{
Cell["Physical parameters: \[Sigma], \[Tau], \[Chi]", "Chapter",
CellChangeTimes->{{3.783835321502646*^9, 3.783835331801469*^9},
3.78383577771546*^9, {3.785779210129293*^9,
3.785779235943714*^9}},ExpressionUUID->"46e4fc55-f689-420e-8ebb-\
43c6317e4213"],
Cell[BoxData[{
RowBox[{
RowBox[{"\[Sigma]", " ", "=", " ", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Tau]", " ", "=", "1"}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"\[Chi]", " ", "=", " ",
RowBox[{"Sqrt", "[",
FractionBox["\[Tau]", "\[Sigma]"], "]"}]}], ";"}],
"\n"}], "\[IndentingNewLine]"}], "Input",
CellChangeTimes->{{3.7838386271913443`*^9, 3.783838681513032*^9}, {
3.783838737903454*^9, 3.783838777885253*^9}, {3.783840034319172*^9,
3.783840037217824*^9}, {3.7838404761166058`*^9, 3.783840479011627*^9}, {
3.783840586754912*^9, 3.783840587314732*^9}, {3.783849270958695*^9,
3.783849271035843*^9}, {3.783854630378265*^9, 3.783854641830275*^9}, {
3.7838546743140697`*^9, 3.783854684967579*^9}, {3.7838573022143927`*^9,
3.7838573048687553`*^9}, {3.784954855108571*^9, 3.784954871389327*^9}, {
3.784956171579228*^9, 3.784956191514943*^9}, {3.784956835303032*^9,
3.784956839350119*^9}, {3.784957113706499*^9, 3.7849571266526413`*^9}, {
3.784957198725687*^9, 3.78495721569265*^9}, {3.784960781877899*^9,
3.784960805313635*^9}, {3.78496391250171*^9, 3.784963925890826*^9}, {
3.7849678053626747`*^9, 3.7849678092315817`*^9}, {3.784967856682729*^9,
3.784967859222958*^9}, {3.784968519941201*^9, 3.784968526529997*^9}, {
3.784968765715962*^9, 3.784968769128914*^9}, {3.784968825275635*^9,
3.784968826216567*^9}, {3.784981633498375*^9, 3.784981636215417*^9}, {
3.785043309554091*^9, 3.785043311765821*^9}, {3.7850439560140944`*^9,
3.78504397928918*^9}, {3.785044362130726*^9, 3.785044369926791*^9}, {
3.785045147580247*^9, 3.785045150089452*^9}, {3.785045189358987*^9,
3.785045190496707*^9}, {3.785045745112938*^9, 3.785045748739983*^9}, {
3.785048458591638*^9, 3.785048460919135*^9}, {3.785049669837163*^9,
3.785049672296723*^9}, {3.785211756612822*^9, 3.785211764084845*^9},
3.811128784339435*^9},ExpressionUUID->"64c6dc69-0b79-4b63-afd3-\
c3339329aa8d"],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.783835337046235*^9, 3.7838353402875023`*^9}, {
3.783835928226749*^9, 3.783835928298624*^9},
3.783838596328367*^9},ExpressionUUID->"4e16b959-78c1-4e1d-bdd8-\
4fabeb19a910"]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
"Closed Analytical Formulas for Speed integrals of ",
Cell[BoxData[
FormBox[
RowBox[{
RowBox[{"Error", " ", "functions", " ",
RowBox[{"(",
RowBox[{"and", " ", "derivative"}], ")"}]}], ":",
SuperscriptBox[
SubscriptBox["e", "ab"], "k"]}], TraditionalForm]],ExpressionUUID->
"9c6d33a3-5e72-433f-a47e-f8ab4ec7036f"],
" and ",
Cell[BoxData[
FormBox[
SubscriptBox[
SuperscriptBox["E", "k"], "ab"], TraditionalForm]],ExpressionUUID->
"3afd57b0-a572-4a9c-baf0-56db420e4cbd"]
}], "Chapter",
CellChangeTimes->{{3.783835375918396*^9, 3.783835411918047*^9}, {
3.783835463669812*^9, 3.783835564933565*^9}, {3.785779248791895*^9,
3.78577927393405*^9}},ExpressionUUID->"95727edf-4af9-46c6-848c-\
b2294b3e2ec2"],
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["e",
RowBox[{"ab", ",", "k_"}]], ":=", " ",
FractionBox[
RowBox[{"Factorial", "[",
RowBox[{"k", "-",
RowBox[{"1", "/", "2"}]}], "]"}],
RowBox[{
RowBox[{"Factorial", "[",
RowBox[{
RowBox[{"-", "1"}], "/", "2"}], "]"}], "*",
SuperscriptBox[
RowBox[{"(",
RowBox[{"1", " ", "+", " ",
SuperscriptBox["\[Chi]", "2"]}], ")"}],
RowBox[{"k", "+",
RowBox[{"1", "/", "2"}]}]]}]]}], "\[IndentingNewLine]",
RowBox[{
SubscriptBox["E",
RowBox[{"ab", ",", "k_"}]], ":=", " ",
RowBox[{
FractionBox["\[Chi]", "2"], "*",
RowBox[{
SubsuperscriptBox["\[Sum]",
RowBox[{"j", "=", "0"}], "k"],
RowBox[{
FractionBox[
RowBox[{"Factorial", "[", "k", "]"}],
RowBox[{"Factorial", "[", "j", "]"}]], "*",
SubscriptBox["e",
RowBox[{"ab", ",", "j"}]]}]}]}]}], "\n"}]}]], "Input",
CellChangeTimes->{{3.7838355755556726`*^9, 3.7838355761281843`*^9}, {
3.783838984469953*^9, 3.783838992701725*^9}, {3.784950250517385*^9,
3.784950253596424*^9}, {3.7849508052333307`*^9, 3.784950806632309*^9}, {
3.784957179781451*^9, 3.784957192420298*^9}, {3.784981639967022*^9,
3.784981641023785*^9}, {3.785043350639456*^9, 3.785043351645976*^9}, {
3.785043981970006*^9,
3.785043984130218*^9}},ExpressionUUID->"3c8121a4-1359-4d54-995a-\
f7e8538eca38"]
}, Open ]],
Cell[CellGroupData[{
Cell["Laguerre coefficient", "Chapter",
CellChangeTimes->{{3.783835636820557*^9,
3.7838356414523773`*^9}},ExpressionUUID->"44240ef5-784d-4db2-baa4-\
62f2de21386c"],
Cell[BoxData[
RowBox[{
SubscriptBox["L",
RowBox[{"p_", ",", "j_", ",", "l_", " "}]], ":=", " ",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "l"],
RowBox[{
RowBox[{
RowBox[{
RowBox[{"Factorial", "[",
RowBox[{"p", " ", "+", " ", "j", " ", "+", " ",
RowBox[{"1", "/", "2"}]}], "]"}], "/",
RowBox[{"Factorial", "[",
RowBox[{"j", "-", "l"}], "]"}]}], "/",
RowBox[{"Factorial", "[",
RowBox[{"l", "+", "p", " ", "+",
RowBox[{"1", "/", "2"}]}], "]"}]}], "/",
RowBox[{"Factorial", "[", "l", "]"}]}]}]}]], "Input",
CellChangeTimes->{{3.7838356538583593`*^9,
3.783835720196089*^9}},ExpressionUUID->"3c38910b-7396-4a07-b78a-\
90d351ae55e5"]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
"\n",
StyleBox["Test Speed Functions:", "Title"]
}], "Chapter",
CellChangeTimes->{{3.783835348870504*^9, 3.783835355214663*^9}, {
3.783835633228549*^9, 3.783835646220426*^9}, {3.783835729451866*^9,
3.78383576269156*^9}},ExpressionUUID->"6ea61762-dbe0-4a42-87e6-\
d055568cb1f9"],
Cell[BoxData[{
RowBox[{
RowBox[{
SubscriptBox["a", "ab0"], "=", " ",
RowBox[{
RowBox[{"-", " ", "4"}], "\[Sigma]", " ",
FractionBox[
RowBox[{"(",
RowBox[{"\[Tau]", "-", "1"}], ")"}], "\[Tau]"]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["a",
RowBox[{"ab1", ",", "p_", ",", "l_"}]], ":=", " ",
RowBox[{
RowBox[{"4",
FractionBox[
RowBox[{"l", " ", "\[Sigma]"}], "\[Tau]"],
RowBox[{"(",
RowBox[{"\[Tau]", " ", "-", "2"}], ")"}]}], " ", "-", " ",
RowBox[{"p",
RowBox[{"(", " ",
RowBox[{"p", " ", "-", " ",
RowBox[{"2", "\[Sigma]"}], " ", "+", " ",
RowBox[{"4", " ",
FractionBox["\[Sigma]", "\[Tau]"]}], " ", "+", " ", "1"}],
")"}]}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["a",
RowBox[{"ab2", ",", "p_", ",", "l_"}]], ":=", " ",
RowBox[{
FractionBox["\[Sigma]", "\[Tau]"],
RowBox[{"(",
RowBox[{
RowBox[{"4",
SuperscriptBox["l", "2"]}], " ", "+", " ",
RowBox[{"4", "l",
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}]}], " ", "+", " ",
RowBox[{
FractionBox["3", "2"], "p",
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}]}]}], ")"}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["a",
RowBox[{"pab0", " "}]], "=", " ",
RowBox[{"4",
RowBox[{"(",
RowBox[{"\[Tau]", "-", "1"}], ")"}],
FractionBox[
RowBox[{"(",
RowBox[{"\[Sigma]", " ", "+", " ", "\[Tau]"}], ")"}], "\[Tau]"]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["a",
RowBox[{"pab1", ",", "p_", ",", "l_"}]], ":=", " ",
RowBox[{
RowBox[{"-", "2"}],
RowBox[{"(",
RowBox[{
RowBox[{"2", "l"}], " ", "+", "p"}], ")"}],
RowBox[{"(",
RowBox[{
RowBox[{
FractionBox["\[Sigma]", "\[Tau]"],
RowBox[{"(",
RowBox[{"\[Tau]", " ", "-", "2"}], ")"}]}], " ", "-", "1"}],
")"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["a",
RowBox[{"pab2", ",", "p_", ",", "l_"}]], ":=", " ",
RowBox[{
FractionBox[
RowBox[{"-", " ", "\[Sigma]"}], "\[Tau]"],
RowBox[{"(",
RowBox[{
RowBox[{"4",
SuperscriptBox["l", "2"]}], " ", "+", " ",
RowBox[{"4", "l",
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}]}], " ", "+", " ",
RowBox[{
FractionBox["3", "2"], "p",
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}]}]}], ")"}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
SubscriptBox["\[Alpha]",
RowBox[{"Eab", ",", "d_", ",", "j_", ",", "n_", ",", "g_"}]], ":=", " ",
SubscriptBox["E",
RowBox[{"ab", ",",
RowBox[{"d", "+", "j", "-", "n", "+", "g"}]}]]}], "\[IndentingNewLine]",
RowBox[{
SubscriptBox["\[Alpha]",
RowBox[{"eab", ",", "d_", ",", "j_", ",", "n_", ",", "g_"}]], ":=",
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{
"d", "+", "j", "-", "n", " ", "+", "g", " ", "+", "1"}]}]]}], "\n",
RowBox[{" "}]}], "Input",
CellChangeTimes->{{3.78383578824758*^9, 3.783835919090938*^9}, {
3.7838359701386213`*^9, 3.783836102801579*^9}, {3.783836182617032*^9,
3.783836225192679*^9}, {3.783836421231509*^9, 3.783836511757928*^9}, {
3.78383654688647*^9, 3.78383655784647*^9}, {3.783836593118099*^9,
3.783836806303507*^9}, {3.783836915510477*^9, 3.7838371296370792`*^9}, {
3.783837171692642*^9, 3.783837293657864*^9}, {3.783837614871469*^9,
3.783837662566646*^9}, {3.783837716063058*^9, 3.783837716902781*^9}, {
3.783839537370204*^9, 3.783839541466062*^9}, {3.7838404942600193`*^9,
3.783840504379965*^9}, 3.783851675703457*^9, {3.783851758124722*^9,
3.78385175843633*^9}, {3.783852007140048*^9, 3.78385202055511*^9}, {
3.783852111643689*^9, 3.783852136987213*^9}, {3.78385234441084*^9,
3.783852351873611*^9}, 3.78385242073118*^9, {3.783852698733073*^9,
3.7838527043083572`*^9}, {3.7838528126561823`*^9, 3.783852865318777*^9}, {
3.783852985247779*^9, 3.7838530410319*^9}, {3.7838531163847637`*^9,
3.7838531228839903`*^9}, {3.783853169948185*^9, 3.7838531936194677`*^9}, {
3.783853237572598*^9, 3.783853253379936*^9}, {3.783853302196375*^9,
3.783853402841034*^9}, {3.7838535306440067`*^9, 3.78385361846215*^9}, {
3.783853850193218*^9, 3.783853856574594*^9}, {3.783853905208426*^9,
3.783853922574686*^9}, {3.783853952784111*^9, 3.783853969835998*^9}, {
3.783854191535039*^9, 3.783854191901479*^9}, {3.783854277813509*^9,
3.783854279411846*^9}, {3.783854328788238*^9, 3.7838543577407637`*^9}, {
3.7838544706689873`*^9, 3.7838545148912973`*^9}, {3.78495752929228*^9,
3.78495753194669*^9}, {3.784957700723815*^9, 3.7849577018914433`*^9}, {
3.7849579218219147`*^9, 3.7849579264319277`*^9}, {3.784957979525153*^9,
3.784957987328021*^9}, {3.784958532476543*^9, 3.784958557214192*^9}, {
3.784958934401826*^9, 3.7849589412723017`*^9}, {3.7849591050495787`*^9,
3.784959113455572*^9}, {3.784959640205521*^9, 3.784959644196735*^9}, {
3.784959778182014*^9, 3.7849598427157803`*^9}, {3.785043067396207*^9,
3.785043090762169*^9}, {3.785043937378212*^9, 3.785043942300021*^9}, {
3.785044698832774*^9, 3.785044699550734*^9}, {3.78521245883212*^9,
3.785212459478252*^9}},ExpressionUUID->"14b8cbf3-d1ce-4aec-8b6c-\
b2429862c65f"],
Cell[BoxData[
RowBox[{
SubscriptBox["\[Nu]",
RowBox[{"abT", ",", "p_", ",", "j_", ",", "g_", ",", "d_"}]], ":=",
RowBox[{"4", "*",
RowBox[{
SubsuperscriptBox["\[Sum]",
RowBox[{"i", "=", "0"}], "j"],
RowBox[{
SubscriptBox["L",
RowBox[{"p", ",", "j", ",", "i"}]],
FractionBox["1",
RowBox[{"Sqrt", "[", "Pi", "]"}]],
RowBox[{"(",
RowBox[{
RowBox[{
SubscriptBox["a", "ab0"], "*",
SubscriptBox["E",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "+", "g"}]}]]}], "+", " ",
RowBox[{"\[Chi]", "*",
SubscriptBox["a", "pab0"], "*",
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "+", "g", "+", "1"}]}]]}], " ", "+", " ",
RowBox[{
SubscriptBox["a",
RowBox[{"ab1", ",", "p", ",", "i"}]], "*",
SubscriptBox["E",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "+", "g", "-", "1", " "}]}]]}], "+", " ",
RowBox[{"\[Chi]", " ", "*",
SubscriptBox["a",
RowBox[{"pab1", ",", "p", ",", "i"}]], "*",
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "+", "g"}]}]]}], " ", "+", " ",
RowBox[{
SubscriptBox["a",
RowBox[{"ab2", ",", "p", ",", "i"}]],
SubscriptBox["E",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "-", "2", "+", "g"}]}]]}], "+", " ",
RowBox[{"\[Chi]", "*",
SubscriptBox["a",
RowBox[{"pab2", ",", "p", ",", "i"}]],
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{"d", "+", "i", "+", "g", "-", "1"}]}]]}]}],
")"}]}]}]}]}]], "Input",ExpressionUUID->"37a8c791-4b3a-4f3e-ba46-\
55a0cef5c703"],
Cell[CellGroupData[{
Cell["\<\
Coefficient Sampling (for COSolver benchmarking):
\
\>", "Section",
CellChangeTimes->{{3.783840507579067*^9, 3.783840537922998*^9},
3.783841059407319*^9,
3.783866927350333*^9},ExpressionUUID->"164807f6-0ca8-4015-9f35-\
fcd37522d514"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"FullSimplify", "[",
SubscriptBox["\[Nu]",
RowBox[{"abT", ",", "0", ",", "0", ",", "0", ",", "422"}]], "]"}], " ",
"\[IndentingNewLine]"}]], "Input",
CellChangeTimes->{{3.7838405394341583`*^9, 3.783840564546983*^9}, {
3.7838406093865137`*^9, 3.783840919328677*^9}, {3.7838410410893583`*^9,
3.7838410417608433`*^9}, {3.783848919083385*^9, 3.783848919166016*^9}, {
3.783851096893433*^9, 3.783851124192197*^9}, {3.783851467442251*^9,
3.783851479245625*^9}, {3.78385185263964*^9, 3.783851859490856*^9}, {
3.78385197178281*^9, 3.7838519772036943`*^9}, {3.783852079518056*^9,
3.783852091028455*^9}, {3.783852398307971*^9, 3.7838523998793583`*^9}, {
3.783852725905615*^9, 3.7838527310769167`*^9}, {3.7838529545183773`*^9,
3.7838529749554873`*^9}, {3.7838530779495277`*^9,
3.7838531026484327`*^9}, {3.7838531515026217`*^9, 3.7838531655184*^9}, {
3.78385321914228*^9, 3.783853226625616*^9}, {3.783853259345742*^9,
3.783853283892913*^9}, {3.7838533426806107`*^9, 3.783853343233018*^9}, {
3.783853377356881*^9, 3.7838533811143217`*^9}, {3.783853699786817*^9,
3.783853706686242*^9}, {3.783853885167326*^9, 3.7838538900618362`*^9}, {
3.783854384562807*^9, 3.783854416548634*^9}, {3.783854657785034*^9,
3.7838546621438713`*^9}, {3.784950934705945*^9, 3.784950934999604*^9}, {
3.78495116601637*^9, 3.784951199909017*^9}, 3.784951267589201*^9, {
3.784951300338834*^9, 3.7849513097821083`*^9}, {3.7849515298271713`*^9,
3.784951555307135*^9}, {3.784951622226893*^9, 3.784951658394166*^9}, {
3.784951706891206*^9, 3.784951711657736*^9}, {3.7849517550910177`*^9,
3.7849517574976587`*^9}, {3.7849518532173433`*^9, 3.784951856129006*^9}, {
3.7849518919280033`*^9, 3.784951998727642*^9}, {3.784954840925675*^9,
3.784954850500033*^9}, {3.784956329813095*^9, 3.7849563470818653`*^9}, {
3.784956395321764*^9, 3.784956426497177*^9}, {3.784957029605341*^9,
3.784957032878133*^9}, {3.784957341645163*^9, 3.784957344994823*^9}, {
3.784957476721178*^9, 3.7849574808498573`*^9}, {3.784958140472238*^9,
3.784958162516982*^9}, {3.7849598703632708`*^9, 3.7849598744001827`*^9}, {
3.78496346275313*^9, 3.784963464894527*^9}, {3.78496359851924*^9,
3.784963598819585*^9}, {3.784981610059235*^9, 3.784981674599133*^9}, {
3.784981884441558*^9, 3.784981900268909*^9}, {3.7850431659876137`*^9,
3.785043177749847*^9}, {3.785043998501429*^9, 3.785044014277265*^9}, {
3.78504416008447*^9, 3.7850441868312397`*^9}, {3.7850484520886917`*^9,
3.785048486583008*^9}, {3.7850496624375896`*^9, 3.7850497220234013`*^9},
3.7850522169589787`*^9, {3.811128522388628*^9, 3.811128529589903*^9}, {
3.8111288004272223`*^9,
3.8111288180505533`*^9}},ExpressionUUID->"3ae804b3-c801-45a3-9385-\
e6e38a82896d"],
Cell[BoxData["0"], "Output",
CellChangeTimes->{
3.784968041631065*^9, {3.784981612962173*^9, 3.7849816754129667`*^9}, {
3.784981890297721*^9, 3.784981900721231*^9}, {3.785043155040094*^9,
3.785043178171588*^9}, 3.785043278307719*^9, {3.785044008674719*^9,
3.785044014821705*^9}, {3.7850441611572523`*^9, 3.785044187153529*^9},
3.785044381949978*^9, {3.785044450616289*^9, 3.785044457342846*^9},
3.785044714294635*^9, {3.785048452659004*^9, 3.7850484881481667`*^9}, {
3.78504966582329*^9, 3.785049722485187*^9}, {3.811128525242923*^9,
3.811128530408267*^9}, {3.8111287969327297`*^9,
3.811128818485845*^9}},ExpressionUUID->"2aee4149-81bd-4933-bf1d-\
d8acc4d37c47"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Cancel", "[",
RowBox[{"-",
FractionBox[
RowBox[{"8", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "1"}], "+", "\[Tau]"}], ")"}], " ",
SqrtBox[
FractionBox["\[Tau]", "\[Sigma]"]]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{"\[Sigma]", "+", "\[Tau]"}], "\[Sigma]"], ")"}],
RowBox[{"3", "/", "2"}]]}]]}], "]"}]], "Input",
NumberMarks->False,ExpressionUUID->"f8b6fdd4-b291-4150-8cbf-d0939f91711e"],
Cell[BoxData[
RowBox[{"-",
FractionBox[
RowBox[{"8", " ", "\[Sigma]", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "1"}], "+", "\[Tau]"}], ")"}], " ",
SqrtBox[
FractionBox["\[Tau]", "\[Sigma]"]]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
RowBox[{"(",
RowBox[{"\[Sigma]", "+", "\[Tau]"}], ")"}], " ",
SqrtBox[
FractionBox[
RowBox[{"\[Sigma]", "+", "\[Tau]"}], "\[Sigma]"]]}]]}]], "Output",
CellChangeTimes->{
3.811128534729795*^9},ExpressionUUID->"3aac2e2b-93f1-4bbf-ae6d-\
9999000bca75"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Back-Reaction Speed Functions:", "Title"]], "Chapter",
CellChangeTimes->{{3.783165476266239*^9, 3.783165487706551*^9},
3.783835774387526*^9},ExpressionUUID->"47ab2a6d-f761-41d5-a332-\
bcd47e5bd9fe"],
Cell[BoxData[{
RowBox[{
RowBox[{
SubscriptBox["b", "ab0"], "=", " ",
RowBox[{"4", "*",
FractionBox[
SuperscriptBox["\[Tau]", "2"], "\[Sigma]"]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
SubscriptBox["b",
RowBox[{"ab01", ",", "p_"}]], ":=", " ",
RowBox[{
RowBox[{"-", "8"}], "*",
FractionBox[
RowBox[{"(",
RowBox[{
SuperscriptBox["p", "2"], " ", "+", " ", "p", " ", "-", "1"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "-", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "3"}],
")"}]}]]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"+", "ab0"}], ",", "p_", ",", "l_"}]], ":=", " ",
RowBox[{
RowBox[{
RowBox[{"-", "8"}], "*", "p", "*",
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}], "*",
FractionBox[
RowBox[{"(",
RowBox[{"l", "+", "1"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], "-", "1"}], ")"}]}]]}], " ", "-", " ",
RowBox[{"\[Tau]", "*", "8", "*",
FractionBox[
RowBox[{"(",
RowBox[{"1", " ", "+", "p", " ", "-", " ",
RowBox[{"\[Sigma]", "*", "p"}]}], ")"}],
RowBox[{"\[Sigma]", "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "1"}], ")"}]}]]}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"+", "ab1"}], ",", "p_"}]], ":=", " ",
RowBox[{"8", "*",
RowBox[{"(",
RowBox[{"p", "+", "1"}], ")"}], "*",
FractionBox[
RowBox[{"(",
RowBox[{"p", "+", "2"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], "+", "3"}], ")"}]}]]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"-", "ab0"}], ",", "p_", ",", "l_"}]], ":=",
RowBox[{
RowBox[{"4", "*",
RowBox[{"(",
RowBox[{"p", "+", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{"p", "+", "2"}], ")"}], "*",
FractionBox[
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], "+",
RowBox[{"2", "*", "l"}], "+", "3"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], "+", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "3"}], ")"}]}]]}], " ", "+", " ",
RowBox[{"8", "*",
SuperscriptBox["\[Chi]", "2"], "*",
FractionBox[
RowBox[{"(",
RowBox[{"p", "-", " ",
RowBox[{"\[Sigma]", "*", "p"}], "-", "\[Sigma]"}], ")"}],
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "1"}], ")"}]]}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"-", "ab1"}], ",", "p_"}]], ":=", " ",
RowBox[{
RowBox[{"-", " ", "8"}], "*", "p", "*",
FractionBox[
RowBox[{"(",
RowBox[{"p", "-", "1"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "+", "1"}], ")"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"2", "*", "p"}], " ", "-", "1"}], ")"}]}]]}]}],
";"}]}], "Input",
CellChangeTimes->{{3.783162849130638*^9, 3.783162935724229*^9}, {
3.783163953293124*^9, 3.783164021229011*^9}, {3.783164243250895*^9,
3.783164523154057*^9}, {3.783164621129231*^9, 3.783164745159897*^9}, {
3.783164842656008*^9, 3.7831650111659117`*^9}, {3.783165070745102*^9,
3.783165438105013*^9}, {3.7831655978463507`*^9, 3.783165604137204*^9}, {
3.78316567857146*^9, 3.783165689830372*^9}, {3.783165774172901*^9,
3.783165774442171*^9}, 3.7831659730535383`*^9, {3.783166134390232*^9,
3.7831661362749357`*^9}, 3.783166270903467*^9, {3.783166794707615*^9,
3.7831667959715014`*^9}, {3.7831680376816807`*^9, 3.78316804484888*^9}, {
3.783835585486446*^9, 3.7838355916774883`*^9}, {3.783836500735998*^9,
3.7838365076230288`*^9}, {3.783837688207013*^9, 3.7838377677023077`*^9}, {
3.783837900741445*^9, 3.783837941405252*^9}, {3.783838030052445*^9,
3.783838110788252*^9}, {3.7838383142186747`*^9, 3.783838363450362*^9}, {
3.783838466914262*^9, 3.78383846808955*^9}, {3.783854859434825*^9,
3.783854864815896*^9}, {3.783855296363172*^9, 3.783855304573185*^9}, {
3.7838553680025377`*^9, 3.7838554223326693`*^9}, {3.7838557459941263`*^9,
3.7838558283056498`*^9}, {3.783855863667*^9, 3.783855895673208*^9}, {
3.783855960002249*^9, 3.7838559994744377`*^9}, 3.7838560692770243`*^9, {
3.783856158576486*^9, 3.783856163871543*^9}, 3.7838565400137997`*^9,
3.7838566960764112`*^9, {3.78385681285964*^9, 3.783856822259541*^9}, {
3.783856922210801*^9, 3.783856969514193*^9}, {3.783857005442675*^9,
3.7838570104191*^9}, {3.784963885374926*^9, 3.784963902077915*^9}, {
3.7850431065158978`*^9, 3.78504314079982*^9}, {3.78504564662465*^9,
3.785045662329577*^9}, {3.785211923251569*^9, 3.785211925263183*^9}, {
3.785212116824469*^9, 3.7852122212531157`*^9}, {3.785212289713776*^9,
3.785212292943623*^9}, {3.7852123674153852`*^9, 3.785212424091625*^9}, {
3.785212478472756*^9, 3.785212479095694*^9}, {3.785212549280568*^9,
3.785212557262308*^9}, 3.785212595023697*^9, {3.7852127630907917`*^9,
3.7852127637842207`*^9}},ExpressionUUID->"6992090f-f457-4931-bbf1-\
83d05cf41736"],
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["\[Beta]",
RowBox[{"eab", ",", "g_", ",", "p_", ",", "d_", ",", "n_", ",", "j_"}]],
":=",
RowBox[{
SuperscriptBox["\[Chi]",
RowBox[{"p", "+",
RowBox[{"2", "*", "j"}], "+",
RowBox[{"2", "*", "n"}], " ", "-", "1"}]], "*",
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{
"g", " ", "+", " ", "1", " ", "+", " ", "d", "+", "j", "+",
"n"}]}]]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"+", "ab"}], ",", "g_", ",", "p_", ",", "d_", ",", "n_", ",",
"j_"}]], ":=", " ",
RowBox[{
SuperscriptBox["\[Chi]",
RowBox[{"p", "+",
RowBox[{"2", "*", "n"}], " ", "-", "1"}]],
RowBox[{
SubsuperscriptBox["\[Sum]",
RowBox[{"i", "=", "0"}], "j"],
FractionBox[
RowBox[{
RowBox[{"Factorial", "[", "j", "]"}], "*",
SuperscriptBox["\[Chi]",
RowBox[{"2", "*", "i"}]], "*",
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{"p", " ", "+", "n", "+", "1", "+", "d", "+", "i"}]}]]}],
RowBox[{"2", "*",
RowBox[{"Factorial", "[", "i", "]"}]}]]}]}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"-", "Eeab"}], ",", "p_", ",", "d_", ",", "n_", ",", "j_"}]], ":=",
" ",
RowBox[{
SuperscriptBox["\[Chi]",
RowBox[{
RowBox[{"2", "*", "n"}], "-", "p", "-", "2"}]], "*",
RowBox[{"(", " ",
RowBox[{
RowBox[{
FractionBox[
RowBox[{"Factorial", "[",
RowBox[{"p", "+", "j", " ", "+",
RowBox[{"1", "/", "2"}]}], "]"}],
RowBox[{"Factorial", "[",
RowBox[{"1", "/", "2"}], "]"}]], "*",
FractionBox[
SubscriptBox["E",
RowBox[{"ab", ",",
RowBox[{"d", "+", "n"}]}]], "2"]}], " ", "-", " ",
RowBox[{
SubsuperscriptBox["\[Sum]",
RowBox[{"i", "=", "0"}],
RowBox[{"p", "+", "j"}]],
RowBox[{
FractionBox[
SuperscriptBox["\[Chi]",
RowBox[{
RowBox[{"2", "*", "i"}], "+", "1"}]],
RowBox[{"Factorial", "[",
RowBox[{"i", " ", "+",
RowBox[{"1", "/", "2"}]}], "]"}]], "*",
RowBox[{"Factorial", "[",
RowBox[{"p", "+", "j", "+",
RowBox[{"1", "/", "2"}]}], "]"}], "*",
FractionBox[
SubscriptBox["e",
RowBox[{"ab", ",",
RowBox[{"d", "+", "n", "+", "i", "+", "1"}]}]], "2"]}]}]}],
")"}]}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input",
CellChangeTimes->{{3.7852127593763237`*^9, 3.785212759882465*^9}, {
3.7856080195808783`*^9, 3.785608021779014*^9}, {3.785608052236628*^9,
3.785608053282958*^9}, {3.785608604600526*^9, 3.785608637704782*^9}, {
3.7856086707478952`*^9,
3.7856086713921223`*^9}},ExpressionUUID->"c56433d1-3ccc-4253-8698-\
7b2549ed1ded"],
Cell[BoxData[
RowBox[{
SubscriptBox["\[Nu]",
RowBox[{"abF", ",", "p_", ",", "j_", ",", "g_", ",", "d_"}]], ":=",
RowBox[{"4",
RowBox[{
SubsuperscriptBox["\[Sum]",
RowBox[{"i", "=", "0"}], "j"],
RowBox[{
SubscriptBox["L",
RowBox[{"p", ",", "j", ",", "i"}]],
FractionBox["1",
RowBox[{"Sqrt", "[", "Pi", "]"}]],
RowBox[{"(",
RowBox[{
RowBox[{
SubscriptBox["b", "ab0"],
SubscriptBox["\[Beta]",
RowBox[{"eab", ",", "g", ",", "p", ",", "d", ",", "0", ",", "i"}]]}],
" ", "+", " ",
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"+", "ab0"}], ",", "p", ",", "i"}]],
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"+", "ab"}], ",", "g", ",", "p", ",", "d", ",", "0", ",",
"i"}]]}], "+",
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"-", "ab0"}], ",", "p", ",", "i"}]],
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"-", "Eeab"}], ",", "p", ",", "d", ",", "0", ",", "i"}]]}],
" ", "+", " ",
RowBox[{
SubscriptBox["b",
RowBox[{"ab01", ",", "p"}]], "*",
SubscriptBox["\[Beta]",
RowBox[{
"eab", ",", "g", ",", "p", ",", "d", ",", "1", ",", "i", " "}]]}],
" ", " ", "+", " ",
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"+", "ab1"}], ",", "p"}]],
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"+", "ab"}], ",", "g", ",", "p", ",", "d", ",", "1", ",",
"i"}]]}], " ", "+",
RowBox[{
SubscriptBox["b",
RowBox[{
RowBox[{"-", "ab1"}], ",", "p"}]],
SubscriptBox["\[Beta]",
RowBox[{
RowBox[{"-", "Eeab"}], ",", "p", ",", "d", ",", "1", ",",
"i"}]]}]}], ")"}]}]}]}]}]], "Input",
CellChangeTimes->{{3.78521253676797*^9, 3.785212541991909*^9}, {
3.785212580558896*^9,
3.785212590964575*^9}},ExpressionUUID->"5773ea11-fef8-435b-ade0-\
de4f24954aaa"],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.783855987466969*^9, 3.783855993493289*^9},
3.78385606719067*^9, {3.78385611335681*^9, 3.783856117316914*^9},
3.783857277266204*^9},ExpressionUUID->"54906d8c-0547-4e30-9b82-\
76ecbcb6401e"],
Cell[CellGroupData[{
Cell["\<\
Coefficient Sampling (for COSolver benchmarking):
\
\>", "Section",
CellChangeTimes->{
3.783841114647036*^9, {3.7838412718620234`*^9, 3.783841275141946*^9}, {
3.7851489989486237`*^9, 3.7851489998205433`*^9},
3.811128671851016*^9},ExpressionUUID->"0d4f0793-56d1-4151-ba9e-\
f2ce92a09932"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"Simplify", "[",
RowBox[{
SubscriptBox["\[Nu]",
RowBox[{"abF", ",", "0", ",", "0", ",", "0", ",", "5"}]], " ", "+",
SubscriptBox["\[Nu]",
RowBox[{"abT", ",", "0", ",", "0", ",", "0", ",", "5", " "}]]}], " ",
"]"}], "\[IndentingNewLine]"}]], "Input",
CellChangeTimes->{{3.81112867483428*^9,
3.811128771196521*^9}},ExpressionUUID->"7ce5d460-68b1-48f9-a7b0-\
689450556307"],
Cell[BoxData["0"], "Output",
CellChangeTimes->{{3.811128688800838*^9, 3.811128771708021*^9}, {
3.811128828678925*^9,
3.811128870497471*^9}},ExpressionUUID->"7aedc2ad-30ab-4d1f-9ceb-\
50b9fbbb87d5"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Cancel", "[",
RowBox[{"-",
FractionBox[
RowBox[{"16", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "1"}], "+", "\[Tau]"}], ")"}], " ",
SqrtBox[
FractionBox["\[Tau]", "\[Sigma]"]]}],
RowBox[{
SqrtBox["\[Pi]"], " ",
SuperscriptBox[
RowBox[{"(",
FractionBox[
RowBox[{"\[Sigma]", "+", "\[Tau]"}], "\[Sigma]"], ")"}],
RowBox[{"3", "/", "2"}]]}]]}], "]"}]], "Input",
NumberMarks->False,ExpressionUUID->"d6330e0a-517f-4795-8dc1-ce6b8e71b154"],
Cell[BoxData["0"], "Output",
CellChangeTimes->{3.811128733045418*^9,
3.811128872851248*^9},ExpressionUUID->"854daa58-4eb2-41ef-8a0f-\
65c486e65a72"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Sampling Speed functions: only p =g contributes in \
the Lin. Coll. Op.", "Title"]], "Chapter",
CellChangeTimes->{{3.783165449737569*^9, 3.783165469011043*^9}, {
3.7838385009367733`*^9,
3.7838385530562973`*^9}},ExpressionUUID->"1278c08e-842f-4211-8544-\
2b73be67ca03"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"TeXForm", "[",
RowBox[{"FullSimplify", "[",
RowBox[{"Cancel", "[",
SubscriptBox["\[Nu]",
RowBox[{"abF", ",", "2", ",", "2", ",", "2", ",", "2"}]], "]"}], "]"}],
"]"}], "\n", "\[IndentingNewLine]", "\[IndentingNewLine]", "\n"}]], "Input",
CellChangeTimes->CompressedData["
1:eJwdzl9IEwEAx/Gzh6BIAoukK7a54BoOlpmJbWPsNnqQmszACcIaSltJphK4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"],ExpressionUUID->"41413a09-0daf-453f-b9ac-2d1fbb80236a"],
Cell["\<\
\\frac{945 \\sigma ^4 \\sqrt{\\frac{\\tau }{\\sigma +\\tau }} \\left(\\sigma \
^2 (7 \\tau -1)+2 \\sigma (8-11 \\tau ) \\tau +4 (\\tau -4) \\tau \
^2\\right)}{8
\\sqrt{\\pi } (\\sigma +\\tau )^6}\
\>", "Output",
CellChangeTimes->{
3.78504342111108*^9, 3.785045766090019*^9, {3.785045797928685*^9,
3.785045806910033*^9}, {3.78504584501159*^9, 3.78504588181184*^9}, {
3.7850459195083227`*^9, 3.785045939154125*^9}, {3.785045978352549*^9,
3.785046000173078*^9}, {3.785476757055067*^9,
3.785476897305562*^9}},ExpressionUUID->"c746e0ae-d455-4421-a73e-\
7619c8deca11"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
"Test and Back-reaction Speed Collisional Coefficients: ",
Cell[BoxData[
FormBox[
RowBox[{
SubsuperscriptBox["A", "abmp", "Tlkj"], ",",
SubsuperscriptBox["B", "abmp", "Flkj"]}], TraditionalForm]],
ExpressionUUID->"d8a7e3d2-750b-4ddb-b810-e85b317ff9d6"],
" "
}], "Title",
CellChangeTimes->{{3.785778816896193*^9, 3.785778848830338*^9}, {
3.785778905216839*^9,
3.785778964399984*^9}},ExpressionUUID->"00b4d26f-5ef9-43f6-865c-\
155b27722294"],
Cell[BoxData[
RowBox[{
SubscriptBox["A",
RowBox[{"m_", ",", "p_", ",", "l_", ",", "k_", ",", "j_"}]], ":=",
"\[IndentingNewLine]",
RowBox[{
SubscriptBox["B",
RowBox[{"m_", ",", "p_", ",", " ", "l_", ",", "k_", ",", "l_", " "}]], ":=",
" "}]}]], "Input",
CellChangeTimes->{{3.7857789716185226`*^9, 3.785778989639922*^9}, {
3.7857790902576942`*^9,
3.785779107951961*^9}},ExpressionUUID->"e42a4d16-d173-4c54-ae2c-\
a31b513924c5"]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
"Deflection and Energy Diffusion Frequencies: ",
Cell[BoxData[
FormBox[
RowBox[{
SubsuperscriptBox["\[Nu]", "ab", "D"], ",", " ",
SubsuperscriptBox["\[Nu]", "ab",
RowBox[{"\[DoubleVerticalBar]", " "}]]}], TraditionalForm]],
ExpressionUUID->"2a66d5cc-eab3-46ca-ba99-fd9ae0e294e1"]
}], "Title",
CellChangeTimes->{{3.785512410295312*^9, 3.7855124640840063`*^9}, {
3.785518212084159*^9, 3.785518214542944*^9}, {3.785779133519412*^9,
3.7857791712396593`*^9}},ExpressionUUID->"b8fe643f-a51c-48d6-9bf5-\
d9f4a21e73c1"],
Cell[BoxData[{
RowBox[{
RowBox[{
SubscriptBox["\[Nu]", "abD"], "[", "x_", "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"Erf", "[", "x", "]"}], " ", "-", " ",
RowBox[{
FractionBox["1",
RowBox[{"2",
RowBox[{"x", "^", "2"}]}]],
RowBox[{"(", " ",
RowBox[{
RowBox[{"Erf", "[", "x", "]"}], " ", "-", " ",
RowBox[{
FractionBox[
RowBox[{"2", "*", "x"}],
RowBox[{"Sqrt", "[", "Pi", "]"}]],
RowBox[{"Exp", "[",
RowBox[{"-",
RowBox[{"x", "^", "2"}]}], "]"}]}]}],
")"}]}]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
SubscriptBox["\[Nu]", "abE"], "[", "x_", "]"}], " ", ":=", " ",
RowBox[{
FractionBox["1",
RowBox[{"2",
RowBox[{"x", "^", "2"}]}]],
RowBox[{"(", " ",
RowBox[{
RowBox[{"Erf", "[", "x", "]"}], " ", "-", " ",
RowBox[{
FractionBox[
RowBox[{"2", "*", "x"}],
RowBox[{"Sqrt", "[", "Pi", "]"}]],
RowBox[{"Exp", "[",
RowBox[{"-",
RowBox[{"x", "^", "2"}]}], "]"}]}]}], ")"}]}]}]}], "Input",
CellChangeTimes->{{3.785512466795322*^9, 3.7855124795325203`*^9}, {
3.785512516900545*^9, 3.7855126192985973`*^9}, {3.785512649729583*^9,
3.7855127110071774`*^9}, {3.7855127576313133`*^9, 3.785512819397114*^9}, {
3.785513094398336*^9,
3.7855131200912123`*^9}},ExpressionUUID->"8d389202-f6b7-421d-aeda-\
1943ae3a6fe9"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"p1", " ", "=", " ",
RowBox[{"LogPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
SubscriptBox["\[Nu]", "abD"], "[", "x", "]"}], ",",
RowBox[{
SubscriptBox["\[Nu]", "abE"], "[", "x", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "10"}], "}"}], ",",
RowBox[{"PlotLegends", "\[Rule]",
RowBox[{"{",
RowBox[{
"\"\<\!\(\*FractionBox[\(\*OverscriptBox[SubscriptBox[\(\[Nu]\), \
\(ab\)], \(D\)] \((v)\) \*OverscriptBox[SubscriptBox[\(s\), \(a\)], \(3\)]\), \
SubscriptBox[\(\[Nu]\), \(ab\)]]\)\>\"", ",",
"\"\<\!\(\*FractionBox[\(\*SubsuperscriptBox[\(\[Nu]\), \(ab\), \(\
\[DoubleVerticalBar]\)] \((v)\) \*OverscriptBox[SubscriptBox[\(s\), \(a\)], \
\(3\)]\), SubscriptBox[\(\[Nu]\), \(ab\)]]\)\>\""}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"{",
RowBox[{"Blue", ",", "Red"}], "}"}]}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{
"\"\<\[Chi] \!\(\*SubscriptBox[\(s\), \(a\)]\)\>\"", ",",
"\"\<Arb. Unit\>\""}], "}"}]}]}], "]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Export", "[",
RowBox[{"\"\<DeflectionEnergyCollfreq.pdf\>\"", ",", "p1"}], "]"}],
"$"}]}], "Input",
CellChangeTimes->{{3.783166391470845*^9, 3.7831663914777527`*^9}, {
3.785512858646717*^9, 3.7855128903828773`*^9}, {3.785512938111417*^9,
3.785512938408408*^9}, {3.785512975273191*^9, 3.785512980727449*^9}, {
3.785513012247184*^9, 3.785513044336856*^9}, {3.7855131274289083`*^9,
3.785513130859223*^9}, {3.7855132092357264`*^9, 3.785513388595798*^9}, {
3.785513420455347*^9, 3.785513433999155*^9}, {3.78551348862395*^9,
3.785513541940905*^9}, {3.785513572511495*^9, 3.78551359451779*^9}, {
3.785513981865*^9, 3.7855139829499063`*^9}, {3.7855142567382593`*^9,
3.785514264352097*^9}, {3.785514387486477*^9,
3.785514453109432*^9}},ExpressionUUID->"71c90a67-4bdb-4300-9ac0-\
3bb7c38bc159"],
Cell[BoxData[
TemplateBox[{GraphicsBox[{{{{}, {}, {
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]],
LineBox[CompressedData["
1:eJwV1ucj1f0fgPEzIrsQqYQ6hRC6m0ifTwlRWSFJKrfVUurIHiGjkpGkhMzK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"]]}, {
Directive[
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]],
LineBox[CompressedData["
1:eJwV1Wk8lF8bB3CMPTtDIktjKVsplSVdd9FCqCwt0kIkKdE/UhRCUSqppIVK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"]]}}}, {}}, {Ticks -> {Automatic,
Charting`ScaledTicks[{Log, Exp}]}, GridLines -> {None, None},
FrameTicks -> {{
Charting`ScaledTicks[{Log, Exp}],
Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}},
AxesOrigin -> {0, -11.114195132429554`},
PlotRange -> {{0, 10}, {-11.114195132429554`, 0.5554591295200452}},
DisplayFunction -> Identity,
Method -> {
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None}, DisplayFunction ->
Identity, DisplayFunction -> Identity, PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All,
DisplayFunction -> Identity,
Method -> {
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"ClippingRange" -> {{{2.0408163265306121`*^-7,
9.999999795918367}, {-16.376632753053585`, -0.005012542028651463}}, {{
2.0408163265306121`*^-7,
9.999999795918367}, {-11.114195132429554`, -0.005012542028651463}}}},
DisplayFunction -> Identity, AspectRatio ->
NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True},
AxesLabel -> {
FormBox[
"\"\[Chi] \\!\\(\\*SubscriptBox[\\(s\\), \\(a\\)]\\)\"",
TraditionalForm],
FormBox["\"Arb. Unit\"", TraditionalForm]}, AxesOrigin -> {0, 0},
CoordinatesToolOptions -> {"DisplayFunction" -> ({
Part[#, 1],
Exp[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
Part[#, 1],
Exp[
Part[#, 2]]}& )}, DisplayFunction :> Identity,
Frame -> {{False, False}, {False, False}},
FrameLabel -> {{None, None}, {None, None}},
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
GridLines -> {None, None}, GridLinesStyle -> Directive[
GrayLevel[0.5, 0.4]],
Method -> {
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange -> {{0, 10}, {-11.114195132429554`, 0.}}, PlotRangeClipping ->
True, PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.02],
Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
FormBox[
TemplateBox[{
"\"\\!\\(\\*FractionBox[\\(\\*OverscriptBox[SubscriptBox[\\(\[Nu]\\), \
\\(ab\\)], \\(D\\)] \\((v)\\) \\*OverscriptBox[SubscriptBox[\\(s\\), \
\\(a\\)], \\(3\\)]\\), SubscriptBox[\\(\[Nu]\\), \\(ab\\)]]\\)\"",
"\"\\!\\(\\*FractionBox[\\(\\*SubsuperscriptBox[\\(\[Nu]\\), \\(ab\\), \
\\(\[DoubleVerticalBar]\\)] \\((v)\\) \\*OverscriptBox[SubscriptBox[\\(s\\), \
\\(a\\)], \\(3\\)]\\), SubscriptBox[\\(\[Nu]\\), \\(ab\\)]]\\)\""},
"LineLegend", DisplayFunction -> (FormBox[
StyleBox[
StyleBox[
PaneBox[
TagBox[
GridBox[{{
TagBox[
GridBox[{{
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]], {
LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full,
ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]], {
LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
Opacity[1.],
AbsoluteThickness[1.6],
RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full,
ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}},
GridBoxAlignment -> {
"Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
AutoDelete -> False,
GridBoxDividers -> {
"Columns" -> {{False}}, "Rows" -> {{False}}},
GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
GridBoxSpacings -> {
"Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
AutoDelete -> False,
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
"Grid"], Alignment -> Left, AppearanceElements -> None,
ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
"ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
False], TraditionalForm]& ),
InterpretationFunction :> (RowBox[{"LineLegend", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[0, 0, 1],
RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame ->
True, FrameStyle -> RGBColor[0., 0., 0.6666666666666666],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]], "RGBColor[0, 0, 1]"], Appearance ->
None, BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0, 0, 1];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[0, 0, 1], Editable -> False, Selectable ->
False]}], "]"}], ",",
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
GrayLevel[0],
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
RGBColor[1, 0, 0],
RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame ->
True, FrameStyle -> RGBColor[0.6666666666666666, 0., 0.],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}]], "RGBColor[1, 0, 0]"], Appearance ->
None, BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[1, 0, 0];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
RGBColor[1, 0, 0], Editable -> False, Selectable ->
False]}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{#, ",", #2}], "}"}], ",",
RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"{", "}"}]}], ",",
RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
Editable -> True], TraditionalForm], TraditionalForm]},
"Legended",
DisplayFunction->(GridBox[{{
TagBox[
ItemBox[
PaneBox[
TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline},
BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"],
"SkipImageSizeLevel"],
ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}},
GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}},
AutoDelete -> False, GridBoxItemSize -> Automatic,
BaselinePosition -> {1, 1}]& ),
Editable->True,
InterpretationFunction->(RowBox[{"Legended", "[",
RowBox[{#, ",",
RowBox[{"Placed", "[",
RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
CellChangeTimes->{{3.785513516851136*^9, 3.785513542649312*^9},
3.785513595346929*^9, 3.7855139833320417`*^9, 3.785514264711059*^9,
3.7855144533973703`*^9,
3.785779176041235*^9},ExpressionUUID->"894b4e15-1ec2-48cb-96ac-\
0c1980f270ef"],
Cell[BoxData[
RowBox[{"\<\"DeflectionEnergyCollfreq.pdf\"\>", " ", "$"}]], "Output",
CellChangeTimes->{{3.785513516851136*^9, 3.785513542649312*^9},
3.785513595346929*^9, 3.7855139833320417`*^9, 3.785514264711059*^9,
3.7855144533973703`*^9,
3.7857791766763363`*^9},ExpressionUUID->"e2dba31d-eb60-4c6b-94ff-\
ff8d0332a7b0"]
}, Open ]],
Cell[BoxData[
RowBox[{"SystemOpen", "[",
RowBox[{"DirectoryName", "[",
RowBox[{
"AbsoluteFileName", "[", "\"\<DeflectionEnergyCollfreq.pdf\>\"", "]"}],
"]"}], "]"}]], "Input",
NumberMarks->False,ExpressionUUID->"ad991559-874a-483d-aa68-6699adfa18f9"],
Cell[BoxData[
RowBox[{"SystemOpen", "[", "\"\<DeflectionEnergyCollfreq.pdf\>\"",
"]"}]], "Input",
NumberMarks->False,ExpressionUUID->"bf36a46f-9510-4b16-a535-dcc56bb503c5"],
Cell[BoxData[
RowBox[{"SystemOpen", "[", "\"\<DeflectionEnergyCollfreq.png\>\"",
"]"}]], "Input",
NumberMarks->False,ExpressionUUID->"b49ff5b1-f543-4605-bc57-052c5efa8801"],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.7831662541191893`*^9,
3.783166258659399*^9}},ExpressionUUID->"6b049220-0c0a-48e4-bb84-\
4ca401a8bb81"]
}, Open ]]
},
WindowSize->{Full, Full},
WindowMargins->{{87, Automatic}, {Automatic, 3}},
FrontEndVersion->"11.1 for Linux x86 (64-bit) (April 18, 2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 152, 3, 33, "Input", "ExpressionUUID" -> \
"45457ac5-fc1c-4c63-84a9-453647157b71"],
Cell[CellGroupData[{
Cell[735, 27, 467, 9, 115, "Title", "ExpressionUUID" -> \
"32487dfa-0b15-4223-aa2c-568b14b50d70"],
Cell[1205, 38, 202, 4, 35, "Input", "ExpressionUUID" -> \
"ff3a317a-4cdd-4e0a-ab84-75ae6620fef1"],
Cell[CellGroupData[{
Cell[1432, 46, 262, 4, 67, "Chapter", "ExpressionUUID" -> \
"46e4fc55-f689-420e-8ebb-43c6317e4213"],
Cell[1697, 52, 1969, 33, 141, "Input", "ExpressionUUID" -> \
"64c6dc69-0b79-4b63-afd3-c3339329aa8d"],
Cell[3669, 87, 227, 4, 33, "Input", "ExpressionUUID" -> \
"4e16b959-78c1-4e1d-bdd8-4fabeb19a910"]
}, Open ]],
Cell[CellGroupData[{
Cell[3933, 96, 767, 21, 68, "Chapter", "ExpressionUUID" -> \
"95727edf-4af9-46c6-848c-b2294b3e2ec2"],
Cell[4703, 119, 1503, 41, 155, "Input", "ExpressionUUID" -> \
"3c8121a4-1359-4d54-995a-f7e8538eca38"]
}, Open ]],
Cell[CellGroupData[{
Cell[6243, 165, 167, 3, 66, "Chapter", "ExpressionUUID" -> \
"44240ef5-784d-4db2-baa4-62f2de21386c"],
Cell[6413, 170, 753, 22, 37, "Input", "ExpressionUUID" -> \
"3c38910b-7396-4a07-b78a-90d351ae55e5"]
}, Open ]],
Cell[CellGroupData[{
Cell[7203, 197, 301, 7, 123, "Chapter", "ExpressionUUID" -> \
"6ea61762-dbe0-4a42-87e6-d055568cb1f9"],
Cell[7507, 206, 5425, 136, 328, "Input", "ExpressionUUID" -> \
"14b8cbf3-d1ce-4aec-8b6c-b2429862c65f"],
Cell[12935, 344, 1778, 50, 53, "Input", "ExpressionUUID" -> \
"37a8c791-4b3a-4f3e-ba46-55a0cef5c703"],
Cell[CellGroupData[{
Cell[14738, 398, 252, 7, 101, "Section", "ExpressionUUID" -> \
"164807f6-0ca8-4015-9f35-fcd37522d514"],
Cell[CellGroupData[{
Cell[15015, 409, 2815, 42, 60, "Input", "ExpressionUUID" -> \
"3ae804b3-c801-45a3-9385-e6e38a82896d"],
Cell[17833, 453, 695, 11, 33, "Output", "ExpressionUUID" -> \
"2aee4149-81bd-4933-bf1d-d8acc4d37c47"]
}, Open ]],
Cell[CellGroupData[{
Cell[18565, 469, 542, 17, 77, "Input", "ExpressionUUID" -> \
"f8b6fdd4-b291-4150-8cbf-d0939f91711e"],
Cell[19110, 488, 546, 18, 108, "Output", "ExpressionUUID" -> \
"3aac2e2b-93f1-4bbf-ae6d-9999000bca75"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[19717, 513, 227, 3, 78, "Chapter", "ExpressionUUID" -> \
"47ab2a6d-f761-41d5-a332-bcd47e5bd9fe"],
Cell[19947, 518, 5703, 154, 283, "Input", "ExpressionUUID" -> \
"6992090f-f457-4931-bbf1-83d05cf41736"],
Cell[25653, 674, 3157, 89, 185, "Input", "ExpressionUUID" -> \
"c56433d1-3ccc-4253-8698-7b2549ed1ded"],
Cell[28813, 765, 2085, 62, 53, "Input", "ExpressionUUID" -> \
"5773ea11-fef8-435b-ade0-de4f24954aaa"],
Cell[30901, 829, 245, 4, 33, "Input", "ExpressionUUID" -> \
"54906d8c-0547-4e30-9b82-76ecbcb6401e"],
Cell[CellGroupData[{
Cell[31171, 837, 307, 8, 101, "Section", "ExpressionUUID" -> \
"0d4f0793-56d1-4151-ba9e-f2ce92a09932"],
Cell[CellGroupData[{
Cell[31503, 849, 437, 11, 60, "Input", "ExpressionUUID" -> \
"7ce5d460-68b1-48f9-a7b0-689450556307"],
Cell[31943, 862, 203, 4, 33, "Output", "ExpressionUUID" -> \
"7aedc2ad-30ab-4d1f-9ceb-50b9fbbb87d5"]
}, Open ]],
Cell[CellGroupData[{
Cell[32183, 871, 543, 17, 77, "Input", "ExpressionUUID" -> \
"d6330e0a-517f-4795-8dc1-ce6b8e71b154"],
Cell[32729, 890, 152, 3, 65, "Output", "ExpressionUUID" -> \
"854daa58-4eb2-41ef-8a0f-65c486e65a72"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[32942, 900, 298, 5, 78, "Chapter", "ExpressionUUID" -> \
"1278c08e-842f-4211-8544-2b73be67ca03"],
Cell[CellGroupData[{
Cell[33265, 909, 1023, 20, 129, "Input", "ExpressionUUID" -> \
"41413a09-0daf-453f-b9ac-2d1fbb80236a"],
Cell[34291, 931, 594, 12, 52, "Output", "ExpressionUUID" -> \
"c746e0ae-d455-4421-a73e-7619c8deca11"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[34946, 950, 480, 13, 109, "Title", "ExpressionUUID" -> \
"00b4d26f-5ef9-43f6-865c-155b27722294"],
Cell[35429, 965, 457, 12, 64, "Input", "ExpressionUUID" -> \
"e42a4d16-d173-4c54-ae2c-a31b513924c5"]
}, Open ]],
Cell[CellGroupData[{
Cell[35923, 982, 557, 13, 104, "Title", "ExpressionUUID" -> \
"b8fe643f-a51c-48d6-9bf5-d9f4a21e73c1"],
Cell[36483, 997, 1413, 43, 96, "Input", "ExpressionUUID" -> \
"8d389202-f6b7-421d-aeda-1943ae3a6fe9"],
Cell[CellGroupData[{
Cell[37921, 1044, 1996, 43, 88, "Input", "ExpressionUUID" -> \
"71c90a67-4bdb-4300-9ac0-3bb7c38bc159"],
Cell[39920, 1089, 23618, 447, 233, "Output", "ExpressionUUID" -> \
"894b4e15-1ec2-48cb-96ac-0c1980f270ef"],
Cell[63541, 1538, 336, 6, 33, "Output", "ExpressionUUID" -> \
"e2dba31d-eb60-4c6b-94ff-ff8d0332a7b0"]
}, Open ]],
Cell[63892, 1547, 266, 6, 33, "Input", "ExpressionUUID" -> \
"ad991559-874a-483d-aa68-6699adfa18f9"],
Cell[64161, 1555, 177, 3, 33, "Input", "ExpressionUUID" -> \
"bf36a46f-9510-4b16-a535-dcc56bb503c5"],
Cell[64341, 1560, 177, 3, 33, "Input", "ExpressionUUID" -> \
"b49ff5b1-f543-4605-bc57-052c5efa8801"],
Cell[64521, 1565, 154, 3, 33, "Input", "ExpressionUUID" -> \
"6b049220-0c0a-48e4-bb84-4ca401a8bb81"]
}, Open ]]
}
]
*)
c4science · Help