Re: To Wolfram Mathgroup. Help me..

• To: mathgroup at smc.vnet.net
• Subject: [mg121030] Re: To Wolfram Mathgroup. Help me..
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Wed, 24 Aug 2011 03:14:00 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108230948.FAA02706@smc.vnet.net>

```Hello Jiwan,
Before showing you how to get the plot, I would like to recommend using
SetDelayed (:=) and Set(=) differently from what you are using. It
may be useful for you to do a bit of background reading on the
differences. I like to use this example to instruct my students:

wasDate = DateString[]'
isDate := DateString[]
Table[Pause[1]; {i, wasDate, isDate}, {i, 1, 5}]

OK, for your plot, I was able to create it from your code by using the

integrand[t_] :=  f[z]*=CE=B7[z, t]
refNormF[t_] := NIntegrate[integrand[t], {z, 0, Infinity}]
Plot[refNormF[t], {t, -.02, .05}]

If you don't like plotting  that singularity at t  approx .002, you
could eliminate it with the Exclusions option in Plot.  You can also
find good advice in this group about defining integrand with a NumericQ
restricted pattern, but it is not necessary in this particular case.

Kind Regards, Craig

On 23 Aug,   2011, at 5:48 AM, Jiwan Kim wrote:

> 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 ?
>
> 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]
>
> --
> =
--------------------------------------------------------------------------=
-----------------------
> Institute of Physics and Chemistry of Materials Strasbourg (IPCMS)
> Department of Ultrafast Optics and Nanophotonics (DON)
> 23 rue du Loess, B.P. 43,
> 67034 STRASBOURG Cedex 2, France

```

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