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authorJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-26 17:17:45 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2021-03-26 17:17:45 +0100
commitc9967adc9f7545667f747fd066ea61cbc20d8d13 (patch)
treed2553e2094075b694a8903c72b7cf891e20d8f0f
parent7648a521d9f90820ad22ae47c9a9aad481f3a2c2 (diff)
downloadmma-c9967adc9f7545667f747fd066ea61cbc20d8d13.tar.gz
mma-c9967adc9f7545667f747fd066ea61cbc20d8d13.tar.bz2
mma-c9967adc9f7545667f747fd066ea61cbc20d8d13.zip
Fixed efficiency problems, having convergence issues now.
-rw-r--r--new_schofield.nb33625
-rw-r--r--schofield.wl32
2 files changed, 18461 insertions, 15196 deletions
diff --git a/new_schofield.nb b/new_schofield.nb
index 5b6f1cb..97284a1 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
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+NotebookOptionsPosition[ 2342168, 45886]
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+CellTagsIndexPosition[ 2342523, 45899]
WindowFrame->Normal*)
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AxesLabel->{None, None},
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GridLines->{None, None},
GridLinesStyle->Directive[
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+ ImagePadding->{{0.3749999999999716, 0.375}, {0.375, 0.3749999999999858}},
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"DefaultGraphicsInteraction" -> {
@@ -988,8 +975,8 @@ WDMK0akKwomSjuArlvvCT3UUOusPfsKSPbDjpZNng8Yo1Ja+/U8TDeH//3+E
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PlotRangeClipping->True,
PlotRangePadding->{{
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AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
- AxesOrigin->{-6.452539234513867, -11.975073258008543`},
+ AxesOrigin->{-6.452539234549762, -11.975073257993463`},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
@@ -40428,7 +40451,6 @@ kB4anaBqJAM2ocgm8h4J/geFtRjL
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
- ImageSize->{365.9999999999984, Automatic},
Method->{
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diff --git a/schofield.wl b/schofield.wl
index 0d18848..646881d 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -35,28 +35,26 @@ t[θ_] := (θ)^2 - 1
h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
RFf[y_] := π^-1 y Exp[1/y] ExpIntegralEi[-1/y]
-RF[n_][θ_] := A (RFf[B(θc-θ)] + RFf[B(θc+θ)]) + Sum[FC[i] θ^(2i) , {i, 0, n}]
+RFnonsingular[n_][θ_] := A RFf[B(θc+θ)] + Sum[FC[i] θ^(2i) , {i, 0, n}]
+RF[n_][θ_] := A RFf[B(θc-θ)] + RFnonsingular[n][θ]
+
+RFfCoeff[m_] := 0 /; m < 2
+RFfCoeff[m_] := Gamma[m - 1] / π /; m > 1
ruleB[g_] := π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
-eqLow[F_, h_][m_] := SeriesCoefficient[
- F[θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
- {θ, θc, m},
- Assumptions -> Join[$Assumptions, {θ < θc, θ > 1}]
-]
+eqLow[n_, h_][m_] := -A B^m RFfCoeff[m] + D[
+ RFnonsingular[n][θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
+ {θ, m} ] / m! /. θ -> θc
-eqHigh[F_, h_][m_] := SeriesCoefficient[
- F[θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
- {θ, 0, m},
- Assumptions -> Join[$Assumptions, {θ > 0, θ < 1}]
-]
+eqHigh[n_, h_][m_] := D[
+ RF[n][θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
+ {θ, m} ] /. θ -> 0
-eqMid[F_, h_][m_] := SeriesCoefficient[
- F[θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
+eqMid[n_, h_][m_] := D[
+ RF[n][θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
/. η -> t[θ] / h[θ]^(1 / Δ[2]),
- {θ, 1, m},
- Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
-]
+ {θ, m} ] /. θ -> 1
Φs = {
-1.197733383797993,
@@ -103,7 +101,7 @@ GhRules = MapIndexed[dRule[Gh], Ghs];
rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
-eq[F_, g_][m_] := Select[Flatten[{eqLow[F, g][#], eqMid[F, g][#], eqHigh[F, g][#]} & /@ Range[0, m]] /. rules[g], !(# === 0) &]
+eq[F_, g_][m_] := Flatten[Join[{eqLow[F, g][#], eqMid[F, g][#]} & /@ Range[0, m], eqHigh[F, g] /@ Range[0, m, 2]]] /. rules[g]
EndPackage[]