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MathGroup Archive 2008

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Re: The show command freezes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90291] Re: The show command freezes
  • From: Aaron Fude <aaronfude at gmail.com>
  • Date: Fri, 4 Jul 2008 04:00:50 -0400 (EDT)
  • References: <g4d2sh$ep1$1@smc.vnet.net>

Fair enough. Here's the code!

F = 1000;
K1 = 2;  K2 = 1; g = 0.01; H1 = 14*F; H2 = 6*F; H = H1 + H2;
\[CapitalDelta]1[c_, k_] := c^2/K1^2 - 1;
\[CapitalGamma]1[c_, k_] := g/(k*K1^2);
U1[c_, k_] :=
  Power[\[CapitalGamma]1[c, k], 2] - 4*\[CapitalDelta]1[c, k];
Q1[c_, k_] := Sqrt[U1[c, k]];
A1[c_, k_] := 1/2 k*Q1[c, k]*H1;
\[CapitalPhi]1[c_, k_] := E^(-(1/2) k \[CapitalGamma]1[c, k] H1)/(
  2 I c Cosh[A1[c, k]]);
\[CapitalDelta]2[c_, k_] := c^2/K2^2 - 1;
\[CapitalGamma]2[c_, k_] := g/(k*K2^2);
U2[c_, k_] :=
  Power[\[CapitalGamma]2[c, k], 2] - 4*\[CapitalDelta]2[c, k];
Q2[c_, k_] := Sqrt[U2[c, k]];
A2[c_, k_] := 1/2 k*Q2[c, k]*H2;
\[CapitalPhi]2[c_, k_] := E^(1/2 k \[CapitalGamma]2[c, k] H2)/(
  2 I c Cosh[A2[c, k]]);
M[c_, k_] := (\[NoBreak]{
    {0, -2 \[CapitalDelta]1[c, k] Tanh[
       A1[c, k]], -2  \[CapitalDelta]2[c, k] Tanh[A2[c, k]]},
    {g, 0,  c k (Q2[c, k] + \[CapitalGamma]2[c, k] Tanh[A2[c, k]])},
    {g,  c k (Q1[c, k] - \[CapitalGamma]1[c, k] Tanh[A1[c, k]]), 0}
   }\[NoBreak]);
\[NoBreak]ns[c_, k_, tol_] := NullSpace[M[c, k], Tolerance -> tol]
(*fh[c_,k_]:=Det[M[c, k]]*)
fh[c_, k_] := \[CapitalDelta]1[c, k]*
    Tanh[A1[c,
      k]]*(Q2[c, k] + \[CapitalGamma]2[c, k]*
       Tanh[A2[c, k]]) + \[CapitalDelta]2[c, k]*
    Tanh[A2[c,
      k]]*(Q1[c, k] - \[CapitalGamma]1[c, k]*Tanh[A1[c, k]]);
ff[c_, k_] :=
  Piecewise[{{fh[c, k], ( U1[c, k] >= 0) && (U2[c, k] >= 0)}}, None];


FirstRoot[k_, p_] :=
  c /. FindRoot[(ff[c, m] /. m -> k) == 0, {c, 1.2},
    WorkingPrecision -> p + 5, PrecisionGoal -> p];

Needs["VectorFieldPlots`"]
k = 0.001;
c = FirstRoot[k, 40];

NS = ns[c, k, 10^-12];

ZRange = {0, H};

TicksYes = True;
L = 2*H;

vf1[x_, z_] := {\[CapitalGamma]1[c, k] + Q1[c, k], -2
      I \[CapitalDelta]1[c, k]}*E^(
    1/2 k (\[CapitalGamma]1[c, k] - Q1[c, k])
     z) - {\[CapitalGamma]1[c, k] - Q1[c, k], -2
      I \[CapitalDelta]1[c, k]}*E^(
    1/2 k (\[CapitalGamma]1[c, k] + Q1[c, k]) z);
vf2[x_, z_] := {\[CapitalGamma]2[c, k] + Q2[c, k], -2
      I \[CapitalDelta]2[c, k]}*E^(
    1/2 k (\[CapitalGamma]2[c, k] - Q2[c, k]) (z -
       H)) - {\[CapitalGamma]2[c, k] - Q2[c, k], -2
      I \[CapitalDelta]2[c, k]}*E^(
    1/2 k (\[CapitalGamma]2[c, k] + Q2[c, k]) (z - H));
vf[x_, z_] := Re[Piecewise[{
      {\[CapitalPhi]1[c, k] NS[[1]][[2]]*vf1[x, z], z < H1},
      {\[CapitalPhi]2[c, k] NS[[1]][[3]]*vf2[x, z], z > H1}}]*E^(
    I k (x - 2*c) )];
profile =
  ParametricPlot[{Abs[Norm[vf[0, z]]], z}, {z, 0, H},
   AxesOrigin -> {0, 0}, AspectRatio -> 1/1.5,
   Ticks -> {TicksYes, Automatic}, PlotStyle -> {Thick, Black},
   PlotRange -> {Full, ZRange},
   AxesLabel -> {"|v|", "z"}, PlotPoints -> 1000];

S0 = Graphics[{Dashed, Line[{{0, H1}, {1, H1}}]}];

Show[profile]
(*Show[profile, S0]*)   (* This line makes it freeze *)


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