<計算0>  u[0,T]=f[T], u[1,T]=-d/dT u[1,T]

<計算1> 初期分布=0、表面濃度=(一定)の場合。 u[0,T]=0, u[1,T]=-d/dT u[1,T], u[X,0]=(const)

Clrea[X, a1, a2, a] ; 
(*** ** ** ** ** **     計算パラメ - タ         ************)

L = 1 * 10^-6 ;             &nbs ... p;              (* 拡散時間 *)

S2 = 10^6 ;                               

N0 = 1 ;                ...                 

F[X_] := 0 ;              & ... nbsp;カルシウムイオン濃度 NCa[X, T] の計算         ************)

NCa[X_, T_] = N0 * (1 - L * S2/(1 + L * S2) * X) + Sum[a[[n]] * Sin[ramda[[n]] * X] * Exp[-r ... p; 右端でのカルシウムイオンの流速          ************)

flux[X_, T_] = D[NCa[X, T], X] ;

fluxCa[T_] = flux[1, T] ; 

(*** ** ** ** ** **     計算結果の表示         ************)

Plot[{NCa[X, 0], NCa[X, 0.001], NCa[X, 0.01], NCa[X, 0.1], NCa[X, 1], NCa[X, 10], NCa[X, 100], NCa[X, 1000]}, {X, 0, 1}, PlotRange -> All] ;

Plot[-fluxCa[T], {T, 0, 10}, PlotRange -> All] ;

Null

[Graphics:HTMLFiles/index_28.gif]

[Graphics:HTMLFiles/index_29.gif]

tau

1/1000

Plot3D[NCa[X, T], {X, 0, 1}, {T, 0, 10}, PlotRange -> All] ;

[Graphics:HTMLFiles/index_33.gif]

<計算2> 初期分布=(直線)、表面濃度=0 の場合。 u[0,T]=1, u[1,T]=-d/dT u[1,T], u[X,0]=(const)

Clrea[X, a1, a2, a] ; 
(*** ** ** ** ** **     計算パラメ - タ         ************)

L = 1 * 10^-6 ;             &nbs ... p;              (* 拡散時間 *)

S2 = 1000 ;                               

N0 = 0 ;                ...                 

F[X_] := -0.5 * X + 1 ;            &n ... nbsp;カルシウムイオン濃度 NCa[X, T] の計算         ************)

NCa[X_, T_] = N0 * (1 - L * S2/(1 + L * S2) * X) + Sum[a[[n]] * Sin[ramda[[n]] * X] * Exp[-r ... p; 右端でのカルシウムイオンの流速          ************)

flux[X_, T_] = D[NCa[X, T], X] ;

fluxCa[T_] = flux[1, T] ; 

(*** ** ** ** ** **     計算結果の表示         ************)

Plot[{NCa[X, 0], NCa[X, 0.001], NCa[X, 0.01], NCa[X, 0.1], NCa[X, 1], NCa[X, 10], NCa[X, 100], NCa[X, 1000]}, {X, 0, 1}, PlotRange -> All] ;

Plot[-fluxCa[T], {T, 0, 10}, PlotRange -> All] ;

Null

[Graphics:HTMLFiles/index_45.gif]

[Graphics:HTMLFiles/index_46.gif]

Plot3D[NCa[X, T], {X, 0, 1}, {T, 0, 1}, PlotRange -> All] ;

[Graphics:HTMLFiles/index_48.gif]

Clear[x, t, f, D0] ;

D0 = 10^4 ;

x = 10^-2 ;

f[t_] = (4 * Pi * D0 * t)^(-0.5) * Exp[-x^2/(2 * D0 * t)]

Plot[f[t], {t, 0, 1.*10^-7}]

(0.00282095 E^(-1/(200000000 t)))/t^0.5

[Graphics:HTMLFiles/index_55.gif]

- Graphics -

g[t_] = D[f[t], t]

(1.41047*10^-11 E^(-1/(200000000 t)))/t^2.5 - (0.00141047 E^(-1/(200000000 t)))/t^1.5

g[t_] = g[t]// Simplify

(E^(-1/(200000000 t)) (1.41047*10^-11 t^1.5 - 0.00141047 t^2.5))/t^4.

h[t_] = g[t][[3]]

1.41047*10^-11 t^1.5 - 0.00141047 t^2.5

Solve[h[t] == 0, t][[2]]

{t -> 1.*10^-8}

Plot[f[t], {t, 0, 2.*10^-8}]

[Graphics:HTMLFiles/index_66.gif]

- Graphics -

Plot[Erfc[x], {x, 0, 1}]

[Graphics:HTMLFiles/index_69.gif]

- Graphics -


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