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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-03-31 16:38:55 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-03-31 16:38:55 +0200
commit8aeb86c75c525887119655f72a5f2ef5d68b0940 (patch)
treed9e3c3e26244e5a597e0a34a9ae3ad73bb2c1b57
parent07531dcf8fce5ffc2401794e65c3813e86090228 (diff)
downloadmma-8aeb86c75c525887119655f72a5f2ef5d68b0940.tar.gz
mma-8aeb86c75c525887119655f72a5f2ef5d68b0940.tar.bz2
mma-8aeb86c75c525887119655f72a5f2ef5d68b0940.zip
Old work
Diffstat
-rw-r--r--n10.wl10
-rw-r--r--new_schofield.nb10888
-rw-r--r--s11-2.wl10
-rw-r--r--schofield.py23
4 files changed, 892 insertions, 10039 deletions
diff --git a/n10.wl b/n10.wl
new file mode 100644
index 0000000..247fc42
--- /dev/null
+++ b/n10.wl
@@ -0,0 +1,10 @@
+(* Created with the Wolfram Language : www.wolfram.com *)
+{41.5274892840305, {\[Theta]c -> 1.3815995225475306,
+ \[Theta]0 -> 0.19651193079603455, AH -> -2.5551253172888564,
+ A[1] -> 1.737677593541619, A[2] -> 0.6073072088307674,
+ gC[1] -> -0.3667051267605768, gC[2] -> -0.006993124776468467,
+ A[3] -> -0.2932002003072459, gC[3] -> 0.05281453358067984,
+ gC[4] -> -0.01981435048670272, A[4] -> 0.07310324475817341,
+ gC[5] -> 0.003490414297911533, gC[6] -> -0.0003499436527837343,
+ A[5] -> -0.007264248876828084, gC[7] -> 0.00001808613660184903,
+ gC[8] -> -9.089351672518404*^-7}}
diff --git a/new_schofield.nb b/new_schofield.nb
index 1c49fd2..a6d4c36 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
-NotebookDataLength[ 2421482, 43638]
-NotebookOptionsPosition[ 2397461, 43263]
-NotebookOutlinePosition[ 2397856, 43279]
-CellTagsIndexPosition[ 2397813, 43276]
+NotebookDataLength[ 1861428, 34460]
+NotebookOptionsPosition[ 1837886, 34089]
+NotebookOutlinePosition[ 1838285, 34105]
+CellTagsIndexPosition[ 1838242, 34102]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -168,9 +168,9 @@ Cell[BoxData[
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0, (Schofield`\[Theta] + Complex[0, -1] Schofield`\[Theta]0)^
Rational[-5, 6] (Complex[0, 1] Schofield`\[Theta] + Schofield`\[Theta]0)^
- Rational[5, 6], Complex[0,
- Rational[-5, 6]] 2^Rational[-1, 6] Schofield`\[Theta]0^Rational[-1, 6]},
- 0, 7, 6],
+ Rational[5, 6], (Complex[0,
+ Rational[-5, 6]] 2^Rational[-1, 6])
+ Schofield`\[Theta]0^Rational[-1, 6]}, 0, 7, 6],
Editable->False]], "Output",
CellChangeTimes->{3.844248465933242*^9},
CellLabel->
@@ -385,8 +385,7 @@ Cell[BoxData[
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CellChangeTimes->{{3.844239881151924*^9, 3.844239931615017*^9}, {
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- CellLabel->
- "In[259]:=",ExpressionUUID->"df2605ac-c626-43db-8973-5f33b1e02d11"],
+ CellLabel->"In[6]:=",ExpressionUUID->"df2605ac-c626-43db-8973-5f33b1e02d11"],
Cell[BoxData[
RowBox[{
@@ -401,10 +400,8 @@ Cell[BoxData[
RowBox[{"-", "1"}], "+", "n"}], ",",
RowBox[{"-", "1"}], ",",
FractionBox["b", "y"]}], "]"}]}]], "Output",
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- CellLabel->
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+ CellLabel->"Out[6]=",ExpressionUUID->"019710ab-1acc-4ad8-835e-5765095cc75f"]
}, Open ]],
Cell[CellGroupData[{
@@ -429,8 +426,7 @@ Cell[BoxData[
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RowBox[{"0", ",", "14"}], "]"}]}], "]"}]], "Input",
CellChangeTimes->{{3.8442403692161427`*^9, 3.8442404562087917`*^9}},
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Axes->{True, True},
AxesLabel->{None, None},
- AxesOrigin->{1.729166666666667, -4.74840999293991},
+ AxesOrigin->{1.7291666666666707`, -4.750204121772249},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{
- Charting`ScaledTicks[{Log, Exp}],
- Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, Automatic}},
+ Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision ->
+ 15.954589770191003`, RotateLabel -> 0],
+ Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
@@ -2335,8 +2431,8 @@ Cell[BoxData[
Part[#, 1]],
Exp[
Part[#, 2]]}& )}},
- PlotRange->{{1.729166666666667, 15.}, {-4.74840999293991,
- 15.929466900915301`}},
+ PlotRange->{{1.7291666666666707`, 15.}, {-4.750204121772249,
+ 15.952393130257192`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
@@ -2344,12 +2440,14 @@ Cell[BoxData[
Scaled[0.02],
Scaled[0.05]}},
Ticks->FrontEndValueCache[{Automatic,
- Charting`ScaledTicks[{Log, Exp}]}, {Automatic, {{-4.605170185988091,
+ Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision ->
+ 15.954589770191003`, RotateLabel -> 0]}, {
+ Automatic, {{-4.605170185988091,
FormBox[
TagBox[
InterpretationBox[
- StyleBox["\"0.01\"", ShowStringCharacters -> False], 0.01,
- AutoDelete -> True], NumberForm[#, {
+ StyleBox["\"0.01\"", ShowStringCharacters -> False],
+ 0.01`15.954589770191003, AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01, 0.}}, {
2.302585092994046,
FormBox["10", TraditionalForm], {0.01, 0.}}, {9.210340371976184,
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TraditionalForm], {0.01, 0.}}, {16.11809565095832,
FormBox[
TemplateBox[{"10", "7"}, "Superscript", SyntaxForm -> SuperscriptBox],
- TraditionalForm], {0.01, 0.}}, {-2.3025850929940455`,
+ TraditionalForm], {0.01, 0.}}, {-6.907755278982137,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {0.,
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005,
+ 0.}}, {-2.3025850929940455`,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {0.,
+ FormBox[
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
4.605170185988092,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
6.907755278982137,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
11.512925464970229`,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
13.815510557964274`,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
18.420680743952367`,
FormBox[
- TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
+ TemplateBox[{0, 0}, "Spacer2"], TraditionalForm], {0.005,
0.}}}}]]], "Output",
CellChangeTimes->{
3.844241760283173*^9, {3.844241804810651*^9, 3.844241808028558*^9}, {
@@ -2393,8 +2494,10 @@ Cell[BoxData[
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3.8443330336110764`*^9, {3.8443337285330963`*^9, 3.844333746273281*^9},
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- 3.8443387030590553`*^9, 3.844338757726609*^9, 3.8443388535234613`*^9},
- CellLabel->"Out[81]=",ExpressionUUID->"beb77853-1aea-4997-812b-4048f495a74a"]
+ 3.8443387030590553`*^9, 3.844338757726609*^9, 3.8443388535234613`*^9,
+ 3.850288746680285*^9, 3.850289372132516*^9},
+ CellLabel->
+ "Out[135]=",ExpressionUUID->"bb1f2185-bb32-4656-8e0e-93868523c2e4"]
}, Open ]],
Cell[CellGroupData[{
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3.844341267028554*^9}, {3.844341306485671*^9, 3.844341459432242*^9}},
CellLabel->
- "In[210]:=",ExpressionUUID->"97c0c584-c9c8-45c7-829e-72878de217a8"],
+ "In[136]:=",ExpressionUUID->"97c0c584-c9c8-45c7-829e-72878de217a8"],
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PointSize[0.011000000000000001`],
RGBColor[0.560181, 0.691569, 0.194885],
AbsoluteThickness[1.6]],
- LineBox[{{1.7288126225260636`, 0.6}, {2., 0.8232568721441744}, {3.,
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@@ -2900,8 +3003,8 @@ Cell[BoxData[
"\"|\\!\\(\\*SuperscriptBox[SubscriptBox[\\(\[ScriptCapitalF]\\), \\(-\
\\)], \\((m)\\)]\\)| / [(\\!\\(\\*SubscriptBox[\\(A\\), \\(0\\)]\\) / \[Pi]) \
\\!\\(\\*SuperscriptBox[\\(b\\), \\(m\\\\ - \\\\ 1\\)]\\) \[CapitalGamma](m \
-- 1)]\"", TraditionalForm]}, AxesOrigin -> {0., 0.6}, DisplayFunction :>
- Identity, Frame -> {{False, False}, {False, False}},
+- 1)]\"", TraditionalForm]}, AxesOrigin -> {0., 0.6000000000000013},
+ DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}},
FrameLabel -> {{None, None}, {None, None}},
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
GridLines -> {None, None}, GridLinesStyle -> Directive[
@@ -2916,7 +3019,7 @@ Cell[BoxData[
Identity[
Part[#, 1]],
Identity[
- Part[#, 2]]}& )}}, PlotRange -> {{0., 14.}, {0.6, 2}},
+ Part[#, 2]]}& )}}, PlotRange -> {{0., 14.}, {0.6, 2.}},
PlotRangeClipping -> True, PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {0, 0}}, Ticks -> {Automatic, Automatic}}],
@@ -3105,356 +3208,74 @@ Cell[BoxData[
RowBox[{
RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}],
",",
- InterpretationBox[
- ButtonBox[
- TooltipBox[
- GraphicsBox[{{
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- RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
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- FrameStyle ->
- RGBColor[
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- 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
- None, ImageSize ->
- Dynamic[{
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- StyleBox[
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- RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
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- BaseStyle -> {}, BaselinePosition -> Baseline,
- DefaultBaseStyle -> {}, ButtonFunction :>
- With[{Typeset`box$ = EvaluationBox[]},
- If[
- Not[
- AbsoluteCurrentValue["Deployed"]],
- SelectionMove[Typeset`box$, All, Expression];
- FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
- FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.368417, 0.506779, 0.709798];
- FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
- MathLink`CallFrontEnd[
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- FrontEndResource["RGBColorValueSelector"], {
- 0, {Left, Bottom}}, {Left, Top},
- "ClosingActions" -> {
- "SelectionDeparture", "ParentChanged",
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- Automatic, Method -> "Preemptive"],
- RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
- Selectable -> False], ",",
+
+ TemplateBox[<|
+ "color" -> RGBColor[0.368417, 0.506779, 0.709798]|>,
+ "RGBColorSwatchTemplate"], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
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RowBox[{
RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}],
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- FrameStyle ->
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- StyleBox[
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- DefaultBaseStyle -> {}, ButtonFunction :>
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- SelectionMove[Typeset`box$, All, Expression];
- FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
- FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.880722, 0.611041, 0.142051];
- FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
- MathLink`CallFrontEnd[
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- "ClosingActions" -> {
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- Automatic, Method -> "Preemptive"],
- RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
- Selectable -> False], ",",
+
+ TemplateBox[<|
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RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
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RowBox[{
RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}],
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- FrameStyle ->
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- FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
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- StyleBox[
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- BaseStyle -> {}, BaselinePosition -> Baseline,
- DefaultBaseStyle -> {}, ButtonFunction :>
- With[{Typeset`box$ = EvaluationBox[]},
- If[
- Not[
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- SelectionMove[Typeset`box$, All, Expression];
- FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
- FrontEnd`Private`$ColorSelectorInitialColor =
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- FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
- MathLink`CallFrontEnd[
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- FrontEndResource["RGBColorValueSelector"], {
- 0, {Left, Bottom}}, {Left, Top},
- "ClosingActions" -> {
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- Automatic, Method -> "Preemptive"],
- RGBColor[0.560181, 0.691569, 0.194885], Editable -> False,
- Selectable -> False], ",",
+
+ TemplateBox[<|
+ "color" -> RGBColor[0.560181, 0.691569, 0.194885]|>,
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RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
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RowBox[{
RowBox[{"PointSize", "[", "0.011000000000000001`", "]"}],
",",
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- RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
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- FrameStyle ->
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- PlotRangePadding -> None, ImageSize ->
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- StyleBox[
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- BaseStyle -> {}, BaselinePosition -> Baseline,
- DefaultBaseStyle -> {}, ButtonFunction :>
- With[{Typeset`box$ = EvaluationBox[]},
- If[
- Not[
- AbsoluteCurrentValue["Deployed"]],
- SelectionMove[Typeset`box$, All, Expression];
- FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
- FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.922526, 0.385626, 0.209179];
- FrontEnd`Private`$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[0.922526, 0.385626, 0.209179], Editable -> False,
- Selectable -> False], ",",
+
+ TemplateBox[<|
+ "color" -> RGBColor[0.922526, 0.385626, 0.209179]|>,
+ "RGBColorSwatchTemplate"], ",",
RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
",",
RowBox[{"Directive", "[",
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diff --git a/s11-2.wl b/s11-2.wl
new file mode 100644
index 0000000..c597446
--- /dev/null
+++ b/s11-2.wl
@@ -0,0 +1,10 @@
+(* Created with the Wolfram Language : www.wolfram.com *)
+{1370.3010684561127, {\[Theta]c -> 1.3910372586447357,
+ \[Theta]0 -> 0.19656274355982506, AH -> -2.5430070509937934,
+ A[1] -> 1.72003157406972, A[2] -> 0.5919956154568292,
+ gC[1] -> -0.3581984134361347, gC[2] -> -0.0008279978792175252,
+ A[3] -> -0.28645050025521357, gC[3] -> 0.052775222902559024,
+ gC[4] -> -0.020203799501789483, A[4] -> 0.07392503484513055,
+ gC[5] -> 0.003410853564504481, gC[6] -> -0.00021113319124048676,
+ A[5] -> -0.0072554264252400035, gC[7] -> -0.00002625143929826904,
+ gC[8] -> 3.719711744852983*^-6, A[6] -> -0.00002209555890920773}}
diff --git a/schofield.py b/schofield.py
index 96fe68a..0894a42 100644
--- a/schofield.py
+++ b/schofield.py
@@ -1,5 +1,5 @@
-from sympy import *
-from mpmath import glaisher, pi
+from sympy import Rational, Symbol, Ei, diff
+from mpmath import glaisher, pi, exp, factorial
β = Rational(1/8)
δ = 15
@@ -9,19 +9,29 @@ from mpmath import glaisher, pi
s = 2**Rational(1, 12) * exp(-β) * glaisher**Rational(3, 2)
+
def f(B, θc, θ):
- return (θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc)) + (θ - θc) * Ei(1/(B * (θ - θc))) * exp(-1/(B * (θ - θc)))) / pi
+ return (θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc))
+ + (θ - θc) * Ei(1/(B * (θ - θc))) * exp(-1/(B * (θ - θc)))) / pi
+
def FH(θ0, θ):
return (θ**2 + θ0**2)**σ - (θ0**2)**σ
+
+def FA(As, θ):
+ return sum([A * θ**(2 * i + 2) for i, A in enumerate(As)])
+
+
def FR(AL, AH, As, B, θc, θ0, θ):
- return AL * f(B, θc, -θ) + AH * FH(θ0, θ) + sum([A * θ**(2 * i + 2) for i,A in enumerate(As)])
+ return AL * f(B, θc, -θ) + AH * FH(θ0, θ) + FA(As, θ)
+
def F(AL, AH, As, B, θc, θ0, θ):
return FR(AL, AH, As, B, θc, θ0, θ) + AL * f(B, θc, θ)
-def dfc(AL, B, m):
+
+def dfc(AL, B, θc, m):
if m == 0:
return AL * θc * Ei(-1 / (B * θc)) * exp(1 / (B * θc)) / pi
elif m == 1:
@@ -29,6 +39,7 @@ def dfc(AL, B, m):
else:
return AL * factorial(m) * factorial(m - 2) * B**(m-1) / pi
+
def dFc(AL, AH, As, B, θc, θ0, m):
θ = Symbol['θ']
- return dfc(AL, B, m) + diff(FR(AL, AH, As, B, θc, θ0, θ), θ).subs(θ, θc)
+ return dfc(AL, B, m) + diff(FR(AL, AH, As, B, θc, θ0, θ), θ).subs(θ, θc)