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Re: To Wolfram Mathgroup. Help me..

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121033] Re: To Wolfram Mathgroup. Help me..
  • From: Peter Pein <petsie at dordos.net>
  • Date: Wed, 24 Aug 2011 03:14:33 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j2vt7c$2m0$1@smc.vnet.net>

Hi,

with a few minor changes,
Integrate[..] evaluates in ~3 minutes on my box.

please see the notebook at
http://dl.dropbox.com/u/3030567/Mathematica/ReflNorm.nb

(ca. 50 kB)

Peter

Am 23.08.2011 11:51, schrieb Jiwan Kim:
> Hello, mathgroup.
> 
> I send you this mail to ask your help in fixing the error.
> I have a minor error message in the following code.
> I have got a error message "No more memory available.Mathematica kernel has
> shut down." whenever I wanted to get ReflNorm[t] by integrating
> f[z]*Eta[z,t].
> This is not a complex code. This is strange.
> If I use 'NIntegrate' instead of 'Integrate', it seems working well.
> But, there appears another error message like following.
> 
> "NIntegrate::inumr: "The integrand 0.0247936\ \[ExponentialE]^<<1>>\ \
> Sign[<<1>>]\ (6.5\ Cos[1.08875-0.0389557\ z]-1.3\ Sin[1.08875-<<21>>\ \
> z]) has evaluated to non-numerical values for all sampling points in \
> the region with boundaries {{0,200}}.""
> 
> Could you help me to fix these errors ?
> Thank you in advance.
> 
> Best regards,
> Jiwan.
> 
> Remove["Global`*"];
> \[Rho] := 8910;(* mass density : kg/m^3 *)
> v := 4080;(* sound velocity : nm/ns *)
> \[Beta] := 1.3 10^-5;(* linear expansion : /K *)
> B := 1.8 10^11; (* bulk modulus : Pa *)
> c := 3 10^8; (* light speed : nm/ns *)
> \[Lambda] := 800; \[Omega] :=
>  2 \[Pi] c/\[Lambda]; (* light wavelength : nm *)
> Cl := 3.96 10^6; (* lattice heat cap. : J/m^3K = 26.1 J/mol.K *)
> g := 4.4 10^17; (* coupling constant : W/m^3.K *)
> K := 91; (* thermal conductivity : W/m.K *)
> Q1 := 0.2199; (* (g/K)^(1/2) : /nm *)
> \[Xi]1 := 13.5; (* pump absorption depth: nm *)
> \[Xi]2 := 14.5; (* probe absorption depth: nm *)
> Dl := 2.3 10^-5; (* diffusivity : m^2/s *)
> n := 2.48; k := 4.38 ;(* reflectivity index at 800 nm *)
> A1 := 1.3; A2 := 6.5; (* dn/d\[Eta], dk/d\[Eta] *)
> R := 0.3; (* reflection at interface *)
> \[Eta]0 := 1;
> 
> f0 = 8 (2 \[Pi])/\[Lambda] (n^2 (n^2 + k^2 - 1)^2 +
>      k^2 (n^2 + k^2 + 1)^2)^(1/2)/((n + 1)^2 + k^2)^2;
> \[Phi] = ArcTan[(k (n^2 + k^2 + 1))/(n (n^2 + k^2 - 1))];
> f[z_] := f0 (A1 Sin[(4 \[Pi] n z)/\[Lambda] - \[Phi]] +
>      A2 Cos[(4 \[Pi] n z)/\[Lambda] - \[Phi]]) Exp[-z/\[Xi]2];
> \[Eta][z_,
>    t_] := \[Eta]0 \[Xi]1 Q1 Sign[v t - z] Exp[-Q1 Abs[z - v t]];
> ReflNorm[t_] = Integrate[f[z]*\[Eta][z, t], {z, 0, Infinity}]
> Plot[ReflNorm[t], {t, -0.02, 0.05}, PlotRange -> All]
> 





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