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标题: 数值积分问题，函数求极小值问题求助各位大佬。 [打印本页]

作者: bartked 时间: 6 天前
标题: 数值积分问题，函数求极小值问题求助各位大佬。
Clear["Global`*"]
mu = SetPrecision[5/1000, 20];
\[CapitalLambda] = SetPrecision[65/100, 20];
Gs = SetPrecision[493/100, 20];
r = SetPrecision[1/10, 20];
a0 = SetPrecision[675/100, 20];
a1 = SetPrecision[-195/100, 20];
a2 = SetPrecision[2625/1000, 20];
a3 = SetPrecision[-744/100, 20];
b3 = SetPrecision[75/100, 20];
b4 = SetPrecision[75/10, 20];
T0 = SetPrecision[27/100, 20];
b2[T_] := a0 + a1*(T0/T) + a2*(T0/T)^2 + a3*(T0/T)^3;
U[\[CapitalPhi]_, \[CapitalPhi]\[CapitalPhi]_,
T_] := (-(1/2)*
b2[T]*\[CapitalPhi]*\[CapitalPhi]\[CapitalPhi] - (b3/
6)*(\[CapitalPhi]^3 + \[CapitalPhi]\[CapitalPhi]^3) + (b4/
4)*(\[CapitalPhi]*\[CapitalPhi]\[CapitalPhi])^2)*T^4;
f1[w_?NumberQ,
M_?NumberQ, \[CapitalPhi]_?NumberQ, \[CapitalPhi]\[CapitalPhi]_?
NumberQ, uu_?NumberQ, T_?NumberQ] :=
Re[NIntegrate[
Sum[(Pt)*((BesselJ[n + 1, Pt*r])^2 + (BesselJ[n,
Pt*r])^2)*(3*(Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*
w) +
T*(Log[1 +
3*\[CapitalPhi]*
Exp[-(-uu +
Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w)/T] +
3*\[CapitalPhi]\[CapitalPhi]*
Exp[(-2*(-uu +
Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w))/T] +
Exp[(-3*(-uu +
Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w))/T]] +
Log[1 +
3*\[CapitalPhi]\[CapitalPhi]*
Exp[-(uu + Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w)/
T] + 3*\[CapitalPhi]*
Exp[(-2*(uu +
Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w))/T] +
Exp[(-3*(uu +
Sqrt[(Pt)^2 + (Pz)^2 + (M)^2] - (n + 1/2)*w))/
T]])), {n, -5, 5, 1}], {Pt, 0, \[CapitalLambda]}, {Pz,
0, Sqrt[\[CapitalLambda]^2 - Pt^2]}, AccuracyGoal -> 10]];
\[CapitalOmega][w_, M_, \[CapitalPhi]_, \[CapitalPhi]\[CapitalPhi]_,
uu_, T_] := (M - mu)^2/(4*Gs) -
1/(Pi^2)*
f1[w, M, \[CapitalPhi], \[CapitalPhi]\[CapitalPhi], uu, T] +
U[\[CapitalPhi], \[CapitalPhi]\[CapitalPhi], T];
h2[w_, uu_, T_] :=
FindMinimum[\[CapitalOmega][w,
M, \[CapitalPhi], \[CapitalPhi]\[CapitalPhi], uu,
T], {{M, 2/10}, {\[CapitalPhi], 3/
100}, {\[CapitalPhi]\[CapitalPhi], 5/100}}] // AbsoluteTiming;
h2[5/10, 1/10, 1/10]

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