diff options
author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-05-07 17:11:59 +0200 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-05-07 17:11:59 +0200 |
commit | b59fef3c0518a9c1b20801116b7c7c9fb4167569 (patch) | |
tree | fbb4bf381d5238182f228ac2550ac07c8d8c2b59 | |
parent | a0a4103c46857e1785cfa5de613980a88b864453 (diff) | |
download | mma-b59fef3c0518a9c1b20801116b7c7c9fb4167569.tar.gz mma-b59fef3c0518a9c1b20801116b7c7c9fb4167569.tar.bz2 mma-b59fef3c0518a9c1b20801116b7c7c9fb4167569.zip |
Much work.
-rw-r--r-- | new_schofield.nb | 6868 | ||||
-rw-r--r-- | schofield.wl | 29 |
2 files changed, 6411 insertions, 486 deletions
diff --git a/new_schofield.nb b/new_schofield.nb index 343497b..fa371a4 100644 --- a/new_schofield.nb +++ b/new_schofield.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 3329224, 64012] -NotebookOptionsPosition[ 3303946, 63607] -NotebookOutlinePosition[ 3304343, 63623] -CellTagsIndexPosition[ 3304300, 63620] +NotebookDataLength[ 3683055, 69934] +NotebookOptionsPosition[ 3650784, 69417] +NotebookOutlinePosition[ 3651182, 69433] +CellTagsIndexPosition[ 3651139, 69430] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -29,7 +29,23 @@ Cell[BoxData[ 3.8278488730224733`*^9, 3.827848876357965*^9}, {3.827916449928692*^9, 3.827916450999913*^9}}, CellLabel-> - "In[360]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], + "In[684]:=",ExpressionUUID->"e595a667-7f25-4f98-9f12-a321a236d113"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"SetAttributes", "[", + RowBox[{"untilSuccess", ",", "HoldAll"}], "]"}], 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"Output",ExpressionUUID->"b7f39439-0c1d-40f8-af40-5fed6fd931de"], +Cell[3650581, 69410, 175, 3, 25, "Output",ExpressionUUID->"2b7f8ec2-0126-4787-92e3-a6d9dd600de2"] }, Open ]] }, Open ]] } diff --git a/schofield.wl b/schofield.wl index 7f6bed8..c4ebc32 100644 --- a/schofield.wl +++ b/schofield.wl @@ -30,18 +30,12 @@ $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}]]] +OverBar[s] := 1.357838341706595496 -h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] hBasis[[2 * i + 2]], {i, 0, n}] /. x -> θ / θc +t[θ_] := ((θ)^2 - 1) h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i]LegendreP[(2 * i + 1), θ/θc], {i, 0, n}] -*) -h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i]θ^(2 * i + 1), {i, 0, n}] RFLow[B_, θc_][θ_] := (1/\[Pi])(2 E^(1/( B \[Theta]c)) \[Theta]c ExpIntegralEi[-(1/(B \[Theta]c))] + @@ -52,19 +46,24 @@ ExpIntegralEi[1/(B \[Theta] - B \[Theta]c)] - B \[Theta] + B \[Theta]c))]) 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), {i, 0, n}] +RF[n_][θ_] := AL RFLow[B, θc][θ] + AH RFHigh[θ0][θ] + Sum[A[i] LegendreP[(2 i), θ/θc] , {i, 0, n}] RFReg[n_][θ_] := AL (1/\[Pi])(2 E^(1/( B \[Theta]c)) \[Theta]c ExpIntegralEi[-(1/(B \[Theta]c))] - E^(1/(B \[Theta] + B \[Theta]c)) (\[Theta] + \[Theta]c) ExpIntegralEi[-(1/( - B \[Theta] + B \[Theta]c))]) + AH RFHigh[θ0][θ] + Sum[A[i] LegendreP[2i, θ], {i, 0, n}] + B \[Theta] + B \[Theta]c))]) + AH RFHigh[θ0][θ] + Sum[A[i] LegendreP[(2 i), θ/θc], {i, 0, n}] dRFc[n_][m_] := Piecewise[{{AL m! Gamma[m - 1] B^(m - 1) / π, m>1}, {0, True}}] + D[RFReg[n][θ], {θ, m}] /. θ -> θc 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))]) ddξ[h_][f_] := D[f, θ] / D[h[θ] / RealAbs[t[θ]]^Δ[2], θ] +ddη[h_][f_] := D[f, θ] / D[t[θ] / h[θ]^(1 / Δ[2]), θ] dFdξLow[n_, h_][m_] := Module[{ff, hh}, Nest[ddξ[hh], ff[θ] / t[θ]^2 - Log[t[θ]^2] / (8 π), m] /. θ -> θc /. Map[Derivative[#][ff][θc] -> dRFc[n][#] &, Range[0, m]] /. hh -> h] dFdξHigh[n_, h_][m_] := Module[{ff, hh}, Nest[ddξ[hh], ff[θ] / t[θ]^2 - Log[t[θ]^2] / (8 π), m] /. θ -> 0 /. Map[Derivative[#][ff][0] -> eqHighRHS[RF[n]][#] &, Range[0, m]] /. hh -> h] +dFdη[n_, h_][m_][tt_] := Module[{ff, hh}, Nest[ddη[hh], h[θ]^(-2 / Δ[]) (ff[θ] - t[θ]^2 Log[hh[θ]^2] / (8 π Δ[])), m] /. θ -> tt /. Map[Derivative[#][ff][tt] -> Derivative[#][RF[n]][tt] &, Range[0, m]] /. hh -> h] +dFdξLowList[n_, h_][m_] := Module[{ff, hh}, NestList[ddξ[hh], ff[θ] / t[θ]^2 - Log[t[θ]^2] / (8 π), m] /. θ -> θc /. Map[Derivative[#][ff][θc] -> dRFc[n][#] &, Range[0, m]] /. Map[Derivative[#][hh][θc] -> Derivative[#][h][θc] &, Range[0, m]]] +dFdξHighList[n_, h_][m_] := Module[{ff, hh}, NestList[ddξ[hh], ff[θ] / t[θ]^2 - Log[t[θ]^2] / (8 π), m] /. θ -> 0 /. Map[Derivative[#][ff][0] -> eqHighRHS[RF[n]][#] &, Range[0, m]] /. hh -> h] +dFdηList[n_, h_][m_][tt_] := Module[{ff, hh}, NestList[ddη[hh], h[θ]^(-2 / Δ[2]) (ff[θ] - t[θ]^2 Log[hh[θ]^2] / (8 π Δ[2])), m] /. θ -> tt /. Map[Derivative[#][ff][tt] -> Derivative[#][RF[n]][tt] &, Range[0, m]] /. hh -> h] 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 @@ -99,7 +98,10 @@ eqMid[F_, h_][m_] := D[ -2.639978 10^-4, -5.140526 10^-4, 2.08856 10^-4, - -4.4819 10^-5 + -4.4819 10^-5, + 3.16 10^-7, + 4.31 10^-6, + -1.99 10^-6 } Gls = { @@ -139,13 +141,14 @@ dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)! GlRules = MapIndexed[dRule[Gl], Gls]; GhRules = MapIndexed[dRule[Gh], Ghs]; +ClearAll[gC] rules := Join[ΦRules, GlRules, GhRules] (*ξ0 := 0.18930*) (*gC[0] := 1*) tC[0] := 1 -gC[0] := 1 +(*gC[0] := 1*) -eq[n_, g_][m_] := Flatten[Join[{ruleB[g], ruleθ0[g]},{eqLow[n, g][#](*, eqMid[F, g][#]*)} & /@ Range[0, m], eqHigh[n, g] /@ Range[0, m, 2]]] //. rules /. Around[x_, _] :> x +eq[n_, g_][m_, p_, q_] := Flatten[Join[{ruleB[g], ruleθ0[g], g'[0] - 1}, eqLow[n, g][#] & /@ Range[0, m],eqMid[RF[n], g][#] & /@ Range[0, p], eqHigh[n, g] /@ Range[0, q, 2]]] //. rules /. Around[x_, _] :> x (* *) chiSquaredLow[n_, g_][m_] := Total[(((#[[1]] /. rules)["Value"] - #[[2]])^2 / (#[[1]] /. rules)["Uncertainty"]^2)& /@ ({Gls[[#+1]], dFdξLow[n, g][#] / #!} & /@ Range[0, m])] |