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-rw-r--r--new_schofield.nb15637
-rw-r--r--schofield.wl64
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
@@ -10,10 +10,10 @@
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}
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
]