拡散  (ガウス分布: 総量一定)

2007/07/18  aito

Clear[f, g, x, t, N0, D0] ;

f[x_, t_] = N0 * (4 * Pi * D0 * t)^-0.5 * Exp[-x^2/(4 * D0 * t)] ;     & ... , t], t]//Simplify ;      (* 拡散 : ガウス分布 *)
h[x_, t_] = g[x, t][[5]] ;

N0 = 1 ; D0 = 1 ;       (*  パラメ - タ設定*)
Print["N0 = ", N0, "   D0 = ", D0] ;

grph1 = Plot3D[f[x, t], {x, 0, 1}, {t, 0.0001, 1}, AxesLabel -> {"x", "t", "n"}, PlotRange -> {0, 1}, DisplayFunction -> Identity] ;

grph2 = Plot3D[f[x, t], {t, 0.0001, 1}, {x, 0, 1}, AxesLabel -> {"t", "x", "n"}, PlotRange -> {0, 1}, DisplayFunction -> Identity] ;

grph3 = Plot[{f[x, 0.1], f[x, 0.5], f[x, 1], f[x, 1.5]}, {x, 0, 1}, PlotLabel -> "t=0.1, ... ;, AxesLabel -> {"x", "n"}, PlotRange -> {0, 1}, DisplayFunction -> Identity] ;

grph4 = Plot[{f[0.1, t], f[0.5, t], f[1, t], f[1.5, t]}, {t, 0.0001, 1}, PlotLabel -> "x ...  AxesLabel -> {"t", "n"}, PlotRange -> {0, 1}, DisplayFunction -> Identity] ;

eq = h[x, t] == 0        (*  最大値をとる時間の計算 *)

s[t_] = Solve[eq, t][[2, 1, 2]]//Simplify

grph5 = Plot[s[t], {x, 0, 1}, AxesLabel -> {"x", "t_Max"}, DisplayFunction -> Identity] ;

grphA = Plot[{f[x, 0.01], f[x, 0.02], f[x, 0.03], f[x, 0.04], f[x, 0.05], f[x, 0.06], f[x, 0 ... uot;, AxesLabel -> {"x", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

grphB = Plot[{f[x, 0.1], f[x, 0.2], f[x, 0.3], f[x, 0.4], f[x, 0.5], f[x, 0.6], f[x, 0.7], f ... uot;, AxesLabel -> {"x", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

grphC = Plot[{f[x, 1], f[x, 2], f[x, 3], f[x, 4], f[x, 5], f[x, 6], f[x, 7], f[x, 8], f[x, 9 ... t;, AxesLabel -> {"x", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

grpha = Plot[{f[0.01, t], f[0.02, t], f[0.03, t], f[0.04, t], f[0.05, t], f[0.06, t], f[0.07 ... uot;, AxesLabel -> {"t", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

grphb = Plot[{f[0.1, t], f[0.2, t], f[0.3, t], f[0.4, t], f[0.5, t], f[0.6, t], f[0.7, t], f ... uot;, AxesLabel -> {"t", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

grphc = Plot[{f[1, t], f[2, t], f[3, t], f[4, t], f[5, t], f[6, t], f[7, t], f[8, t], f[9, t ... t;, AxesLabel -> {"t", "n"}, PlotRange -> All, DisplayFunction -> Identity] ;

Show[GraphicsArray[{{grph1, grph2}, {grph3, grph4}, {grph5}}]] ;

Show[GraphicsArray[{{grphA, grphB, grphC}, {grpha, grphb, grphc}}]] ;

N0 = 1   D0 = 1

-0.141047 t^2.5 + 0.0705237 t^1.5 x^2 == 0

0.5 x^2

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