Lots of work.

author: Jaron Kent-Dobias <jaron@kent-dobias.com> 2021-04-19 21:01:26 +0200
committer: Jaron Kent-Dobias <jaron@kent-dobias.com> 2021-04-19 21:01:26 +0200
commit: 613e0265bd0ac2229e0640e4f78fe13e535e6a04 (patch)
tree: 201ab14ccbdb57895d95ff33f7d428f75a7959d5
parent: 86302ed839cc3e783e68fe5177ac41496e5db145 (diff)
download: mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.tar.gz
mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.tar.bz2
mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.zip
2 files changed, 11992 insertions, 3709 deletions
diff --git a/new_schofield.nb b/new_schofield.nb
index 620abc1..578be9d 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
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+   3.827833641521347*^9},
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 Cell[CellGroupData[{
-Cell[2778384, 53965, 1853, 38, 71, "Input",ExpressionUUID->"6f764f4a-8e60-4ade-81f6-342ce8502e9b"],
-Cell[2780240, 54005, 17826, 324, 138, "Output",ExpressionUUID->"073b197f-bc4b-40a2-a232-0cc8f06d961e"]
+Cell[3231173, 62157, 1853, 38, 71, "Input",ExpressionUUID->"6f764f4a-8e60-4ade-81f6-342ce8502e9b"],
+Cell[3233029, 62197, 17826, 324, 138, "Output",ExpressionUUID->"073b197f-bc4b-40a2-a232-0cc8f06d961e"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[2798103, 54334, 480, 11, 22, "Input",ExpressionUUID->"afe99e33-748e-47f2-ba2a-c0c57008e3ff"],
-Cell[2798586, 54347, 7596, 187, 177, "Output",ExpressionUUID->"76d79e7a-9d2d-45b3-bb8a-8f918994420a"]
+Cell[3250892, 62526, 480, 11, 22, "Input",ExpressionUUID->"afe99e33-748e-47f2-ba2a-c0c57008e3ff"],
+Cell[3251375, 62539, 7596, 187, 177, "Output",ExpressionUUID->"76d79e7a-9d2d-45b3-bb8a-8f918994420a"]
 }, Open  ]]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[2806231, 54540, 165, 3, 50, "Section",ExpressionUUID->"747c9bc3-63ef-45c3-af83-bc456177b1c8"],
-Cell[2806399, 54545, 800, 21, 40, "Input",ExpressionUUID->"ebc19a92-5a4d-4254-8fad-8cadbfa1bd32"],
+Cell[3259020, 62732, 165, 3, 50, "Section",ExpressionUUID->"747c9bc3-63ef-45c3-af83-bc456177b1c8"],
+Cell[3259188, 62737, 800, 21, 40, "Input",ExpressionUUID->"ebc19a92-5a4d-4254-8fad-8cadbfa1bd32"],
 Cell[CellGroupData[{
-Cell[2807224, 54570, 886, 24, 24, "Input",ExpressionUUID->"f224ec13-7431-41d4-919e-0ad10e8ff5b2"],
-Cell[2808113, 54596, 299, 6, 25, "Output",ExpressionUUID->"5043975f-bf54-4984-bf97-09e0c59f4acf"]
+Cell[3260013, 62762, 886, 24, 24, "Input",ExpressionUUID->"f224ec13-7431-41d4-919e-0ad10e8ff5b2"],
+Cell[3260902, 62788, 299, 6, 25, "Output",ExpressionUUID->"5043975f-bf54-4984-bf97-09e0c59f4acf"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[2808449, 54607, 1529, 43, 24, "Input",ExpressionUUID->"bdb2aaf8-6c60-4fd6-b0aa-d74503ebfe5d"],
-Cell[2809981, 54652, 216, 4, 39, "Output",ExpressionUUID->"672f3cb6-b559-424b-b6e9-dff18bdab931"]
+Cell[3261238, 62799, 1529, 43, 24, "Input",ExpressionUUID->"bdb2aaf8-6c60-4fd6-b0aa-d74503ebfe5d"],
+Cell[3262770, 62844, 216, 4, 39, "Output",ExpressionUUID->"672f3cb6-b559-424b-b6e9-dff18bdab931"]
 }, Open  ]],
 Cell[CellGroupData[{
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-Cell[2812565, 54725, 584, 12, 18, "Message",ExpressionUUID->"926f5636-f494-4b80-9e0f-998a05d07881"],
-Cell[2813152, 54739, 420, 8, 25, "Output",ExpressionUUID->"3c60fc73-ad7e-4b33-a3eb-fdc35776a150"]
+Cell[3263023, 62853, 2328, 62, 24, "Input",ExpressionUUID->"9581e610-c27e-4ccd-9de0-7344556f685a"],
+Cell[3265354, 62917, 584, 12, 18, "Message",ExpressionUUID->"926f5636-f494-4b80-9e0f-998a05d07881"],
+Cell[3265941, 62931, 420, 8, 25, "Output",ExpressionUUID->"3c60fc73-ad7e-4b33-a3eb-fdc35776a150"]
 }, Open  ]],
-Cell[2813587, 54750, 1234, 32, 24, "Input",ExpressionUUID->"3a793a2c-1a2c-433a-873f-55e7861acacf"],
+Cell[3266376, 62942, 1234, 32, 24, "Input",ExpressionUUID->"3a793a2c-1a2c-433a-873f-55e7861acacf"],
 Cell[CellGroupData[{
-Cell[2814846, 54786, 379, 9, 24, "Input",ExpressionUUID->"6a4616ab-41e4-44cc-8806-ee9851e65934"],
-Cell[2815228, 54797, 21750, 374, 177, "Output",ExpressionUUID->"7ae541cc-49f0-4346-9e8f-3995505a8e9f"]
+Cell[3267635, 62978, 379, 9, 24, "Input",ExpressionUUID->"6a4616ab-41e4-44cc-8806-ee9851e65934"],
+Cell[3268017, 62989, 21750, 374, 177, "Output",ExpressionUUID->"7ae541cc-49f0-4346-9e8f-3995505a8e9f"]
 }, Open  ]],
-Cell[2836993, 55174, 2535, 66, 24, "Input",ExpressionUUID->"02eee1a8-8fdf-4ef6-8fa3-737b3067106e"],
+Cell[3289782, 63366, 2535, 66, 24, "Input",ExpressionUUID->"02eee1a8-8fdf-4ef6-8fa3-737b3067106e"],
 Cell[CellGroupData[{
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-Cell[2840047, 55256, 22737, 390, 179, "Output",ExpressionUUID->"3a7e88f8-603a-4c66-8a1b-065c43aff3cd"]
+Cell[3292342, 63436, 491, 10, 24, "Input",ExpressionUUID->"8858ddfc-1e71-4778-a0b8-512abba3d901"],
+Cell[3292836, 63448, 22737, 390, 179, "Output",ExpressionUUID->"3a7e88f8-603a-4c66-8a1b-065c43aff3cd"]
 }, Open  ]],
-Cell[2862799, 55649, 3849, 95, 75, "Input",ExpressionUUID->"954f68de-17bb-4b28-b089-18f4c1840d53"],
+Cell[3315588, 63841, 3849, 95, 75, "Input",ExpressionUUID->"954f68de-17bb-4b28-b089-18f4c1840d53"],
 Cell[CellGroupData[{
-Cell[2866673, 55748, 448, 10, 24, "Input",ExpressionUUID->"fd8d9fbd-6567-43cc-a4dc-4c986b02e466"],
-Cell[2867124, 55760, 26854, 485, 178, "Output",ExpressionUUID->"b7f39439-0c1d-40f8-af40-5fed6fd931de"]
+Cell[3319462, 63940, 448, 10, 24, "Input",ExpressionUUID->"fd8d9fbd-6567-43cc-a4dc-4c986b02e466"],
+Cell[3319913, 63952, 26854, 485, 178, "Output",ExpressionUUID->"b7f39439-0c1d-40f8-af40-5fed6fd931de"]
 }, Open  ]]
 }, Open  ]]
 }
diff --git a/schofield.wl b/schofield.wl
index 1c9482c..b26b662 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -30,27 +30,36 @@ $Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0, γ > 0, ξ0 > 0}
   }
 ]
 
+OverBar[s] := 1.357838341706595496
+
 Δ[D_:2] := β[D] δ[D]
 t[θ_] := ((θ)^2 - 1)
+
 (*
 hBasis = Orthogonalize[x^# & /@ Range[0, 20], Function[{f, g}, Integrate[f g (1 - x^2)^2, {x, -1, 1}]]]
+
 h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] hBasis[[2 * i + 2]], {i, 0, n}] /. x -> θ / θc
-*)
 h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i]θ^(2 * i + 1), {i, 0, n}]
+*)
+h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i]LegendreP[(2 * i + 1), θ/θc], {i, 0, n}]
 
-RFLow[B_, θc_][θ_] := (2 E^(1/(
+RFLow[B_, θc_][θ_] := (1/\[Pi])(2 E^(1/(
    B \[Theta]c)) \[Theta]c ExpIntegralEi[-(1/(B \[Theta]c))] + 
   E^(1/(B (-\[Theta] + \[Theta]c))) (\[Theta] - \[Theta]c) \
 ExpIntegralEi[1/(B \[Theta] - B \[Theta]c)] - 
   E^(1/(B \[Theta] + 
     B \[Theta]c)) (\[Theta] + \[Theta]c) ExpIntegralEi[-(1/(
      B \[Theta] + B \[Theta]c))])
-RFHigh[ξ0_][ξ_] := (1+(ξ/ξ0)^2)^(5/6) - 1
+RFHigh[ξ0_][ξ_] := (ξ^2+ξ0^2)^(5/6)
 
-RF[n_][θ_] := AL RFLow[B, θc][θ] + AH RFHigh[θ0][θ] + Sum[A[i] θ^(2(i+1)), {i, 0, n}]
+RF[n_][θ_] := AL RFLow[B, θc][θ] + AH RFHigh[θ0][θ] + Sum[A[i] LegendreP[2i, θ], {i, 0, n}]
 
-ruleB[g_] := B - π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
+RFC[n_][θ_] := RF[n][θ] + AL I Sign[Im[θ]] ((θ-θc)Exp[-1/(B(θ-θc))]-(-θ-θc)Exp[-1/(B(-θ-θc))])
+
+ruleB[g_] := B - (2 * OverBar[s] / π) * (- g'[θc] / t[θc]^Δ[2])
 ruleθ0[g_] := Simplify[g[I θ0]/(-t[I θ0])^Δ[2]/I] - 0.18930
+ruleAL[g_] := AL + t[θc]^2 OverBar[s] / (2 π) * (- g'[θc] / t[θc]^Δ[2])
+ruleg0[g_] := 1 - g'[0]
 
 eqLowRHS[F_][m_] := SeriesCoefficient[F[θ], {θ, θc, m}, Assumptions -> Join[{θ < θc, θ > 1}, $Assumptions]]
 
@@ -71,6 +80,8 @@ eqMid[F_, h_][m_] := D[
     /. η -> t[θ] / h[θ]^(1 / Δ[2]),
   {θ, m} ] /. θ -> 1
 
+δ0 = 10^-16;
+
 Φs = {
   -1.197733383797993,
   -0.318810124891,
@@ -83,15 +94,15 @@ eqMid[F_, h_][m_] := D[
 }
 
 Gls = {
-  0,
-  -1.3578383417066,
-  -0.048953289720,
-  0.038863932,
-  -0.068362119,
-  0.18388370,
-  -0.6591714,
-  2.937665,
-  -15.61,
+  Around[0, δ0],
+  Around[-OverBar[s], δ0],
+  Around[−0.048953289720, 2 10^(-12)],
+  Around[ 0.0388639290, 1 10^(-10)],
+  Around[-0.068362121, 1 10^(-9)],
+  Around[ 0.18388371, 1 10^(-8)],
+  Around[-0.659170, 1 10^(-6)],
+  Around[ 2.937665, 3 10^(-6)],
+  Around[-15.61, 10^(-2)],
   96.76,
   -679,
   5340
@@ -100,15 +111,15 @@ Gls = {
 Ghs = {
   0,
   0,
-  -1.8452280782328,
+  Around[ -1.84522807823, 10^(-11)],
   0,
-  8.333711750,
+  Around[  8.3337117508, 10^(-10)],
   0,
-  -95.16896,
+  Around[-95.16897, 10^(-5)],
   0,
-  1457.62,
+  Around[1457.62, 3 10^(-2)],
   0,
-  -25891,
+  Around[-25891, 2],
   0,
   502000
 }
@@ -119,20 +130,23 @@ 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[g_] := Join[ΦRules, GlRules, GhRules]
+rules := Join[ΦRules, GlRules, GhRules]
 (*ξ0 := 0.18930*)
-gC[0] := 1
+(*gC[0] := 1*)
 tC[0] := 1
 
-eq[F_, g_][m_] := Flatten[Join[{ruleB[g], ruleθ0[g]},{eqLow[F, g][#](*, eqMid[F, g][#]*)} & /@ Range[0, m], eqHigh[F, g] /@ Range[2, m, 2]]] //. rules[g]
+eq[F_, g_][m_] := Flatten[Join[{ruleg0[g], ruleB[g], ruleθ0[g]},{eqLow[F, g][#](*, eqMid[F, g][#]*)} & /@ Range[0, m], eqHigh[F, g] /@ Range[0, m, 2]]] //. rules /. Around[x_, _] :> x
+
+chiSquaredLow[F_, g_][m_] := Total[(((#[[1]] /. rules)["Value"] - #[[2]])^2 / (#[[1]] /. rules)["Uncertainty"]^2)& /@ Solve[0 == (eqLow[ff, g] /@ Range[0, m]), Derivative[#][Gl][0]& /@ Range[0, m]][[1]]] /. ff -> F
+chiSquaredHigh[F_, g_][m_] := Total[(((#[[1]] /. rules)["Value"] - #[[2]])^2 / (#[[1]] /. rules)["Uncertainty"]^2)& /@ Solve[0 == (eqHigh[ff, g] /@ Range[2, m, 2]) /. ff'[0] -> 0, Derivative[#][Gh][0]& /@ Range[2, m, 2]][[1]]] /. ff -> F
 
-newSol[eqs_, oldSol_, newVars_, δ_:0, opts___] := FindRoot[
+newSol[eqs_, oldSol_, newVars_, δ_:0, γ_:0, opts___] := FindRoot[
   eqs,
   Join[
-    oldSol /. Rule -> List,
+    {#1, #2 + γ * RandomVariate[NormalDistribution[]]} & @@@ (oldSol /. Rule -> List),
     Thread[{newVars, δ * RandomVariate[NormalDistribution[], Length[newVars]]}]
   ],
-  MaxIterations -> 500,
+  MaxIterations -> 1000,
   opts
 ]
author	Jaron Kent-Dobias <jaron@kent-dobias.com>	2021-04-19 21:01:26 +0200
committer	Jaron Kent-Dobias <jaron@kent-dobias.com>	2021-04-19 21:01:26 +0200
commit	613e0265bd0ac2229e0640e4f78fe13e535e6a04 (patch)
tree	201ab14ccbdb57895d95ff33f7d428f75a7959d5
parent	86302ed839cc3e783e68fe5177ac41496e5db145 (diff)
download	mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.tar.gz mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.tar.bz2 mma-613e0265bd0ac2229e0640e4f78fe13e535e6a04.zip