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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-23 11:24:29 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-23 11:24:29 +0100
commit36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118 (patch)
tree1fd387c455109664a5279965d09d0d98499a92ea
parent63aba3f33f80b56e82c7f8c29cd49fac0002c2f5 (diff)
downloadmma-36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118.tar.gz
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Got the basic matching working!
-rw-r--r--new_schofield.nb7584
-rw-r--r--schofield.wl30
2 files changed, 6995 insertions, 619 deletions
diff --git a/new_schofield.nb b/new_schofield.nb
index 7aafe40..b73ca0d 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
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WindowFrame->Normal*)
(* Beginning of Notebook Content *)
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+ Annotation[#, "Charting`Private`Tag$13125#5"]& ]}, {}},
+ Axes->{True, True},
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}, Open ]],
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Cell[CellGroupData[{
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Cell[CellGroupData[{
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}, Open ]],
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}, Open ]],
Cell[CellGroupData[{
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+Cell[741882, 14363, 804, 22, 53, "Input",ExpressionUUID->"13e1541b-4ad9-4a40-89f2-be40a0e4d6fd"],
+Cell[742689, 14387, 479, 13, 50, "Output",ExpressionUUID->"dff49a57-ddf5-4e9d-aa0a-55006221f3c2"]
}, Open ]],
Cell[CellGroupData[{
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Cell[CellGroupData[{
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+Cell[751655, 14615, 1059, 26, 47, "Input",ExpressionUUID->"3bd71288-3233-4171-a393-57251fb3dc52"],
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}, Open ]],
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}
diff --git a/schofield.wl b/schofield.wl
index 7597891..0d18848 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -31,31 +31,29 @@ $Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0, γ > 0}
]
Δ[D_:2] := β[D] δ[D]
+t[θ_] := (θ)^2 - 1
+h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
-f[θ_] := θ^2 - 1
-g[gC_:gC, θc_:θc][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}]
-I\[ScriptCapitalM]f[y_] := (1 + 1 / x) Exp[-1/x]
-R\[ScriptCapitalM]f[y_] := (1 - y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)
+ruleB[g_] := π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
-R\[ScriptCapitalM][2][B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[B(θc - θ)] - R\[ScriptCapitalM]f[B(θc + θ)])
-
-ruleB[2][f_, g_] := π / (2 1.3578383417066) (Δ g[θc] f[θc]^(-Δ[2]-1) f'[θc] - g'[θc] / f[θc]^Δ[2])
-
-eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] / f[θ]^Δ[D]],
+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}]
]
-eqHigh[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + (-f[θ])^β[D] Gh'[g[θ] / (-f[θ])^Δ[D]],
+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}]
]
-eqMid[D_:2][f_, g_][m_] := SeriesCoefficient[
- R\[ScriptCapitalM][D][B, θc, M0][θ] + g[θ]^(1/δ[D]) ((2 - α[D]) Φ'[η] - η Φ'[η]) / Δ[D] /. η -> f[θ] / g[θ]^(1 / Δ[D]),
+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]
+ /. η -> t[θ] / h[θ]^(1 / Δ[2]),
{θ, 1, m},
Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
]
@@ -103,9 +101,9 @@ dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)!
GlRules = MapIndexed[dRule[Gl], Gls];
GhRules = MapIndexed[dRule[Gh], Ghs];
-rules[f_, g_] := Join[{B -> ruleB[2][f, g]}, ΦRules, GlRules, GhRules]
+rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
-eq[D_:2][f_, g_][m_] := Select[Flatten[{eqLow[D][f, g][#], eqMid[D][f, g][#], eqHigh[D][f, g][#]} & /@ Range[0, m]] /. rules[f, g], # != 0 &]
+eq[F_, g_][m_] := Select[Flatten[{eqLow[F, g][#], eqMid[F, g][#], eqHigh[F, g][#]} & /@ Range[0, m]] /. rules[g], !(# === 0) &]
EndPackage[]