diff options
Diffstat (limited to 'schofield.wl')
| -rw-r--r-- | schofield.wl | 30 |
1 files changed, 14 insertions, 16 deletions
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[] |