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MathGroup Archive 2007

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Re: Manipulate a complex expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77824] Re: Manipulate a complex expression
  • From: Daniele <d.malleo at gmail.com>
  • Date: Sun, 17 Jun 2007 06:19:46 -0400 (EDT)
  • References: <f505ip$qug$1@smc.vnet.net>

Hello,
as a follow up to my previous post, I think I can clarify my question
with a simpler example.

Once I define the following:

complexEps[permittivity_, conductivity_, omega_] := permittivity - (I
conductivity/omega);
epsilonCyt := complexEps[permittivityCyt, conductivityCyt, omega];
omega := 2 Pi f
permittivityCyt := 50;

Why does this work:

Manipulate[Plot[Im[Evaluate[complexEps[permittivityCyt,
conductivityCyt, omega]]], {f, 1 10^5,1 10^10}], {conductivityCyt,
0.1, 0.5}]

While this doesn't:

Manipulate[Plot[Im[Evaluate[epsilonCyt]], {f, 1 10^5, 1 10^10}],
{conductivityCyt, 0.1, 0.5}]

I would think that the two 'Manipulate' expressions would be
equivalent, but obviously I'd be wrong....

thanks.

On 16 Jun, 09:04, Daniele <d.mal... at gmail.com> wrote:
> Hello,
> I'm trying to use the new Manipulate function to evaluate a complex
> expression. I'm getting a headache, as I'm not familiar with the
> Mathematica notation (I do most of my work, numerically, with another system).
> Maybe somebody here can help debug these few lines?
>
> The expression I want to 'manipulate' is the following:
>
> MeasuredCMF := VolumeFraction ( EpsilonCell - EpsilonMedium)/
> ( EpsilonCell + 2 EpsilonMedium)
>
> Where VolumeFraction is a parameter, and the other variables are
> complex and a function of 'f'.
> They are defined below.
>
> omega := 2 Pi f
> EpsilonCyt := PermittivityCyt - ( ConductivityCyt/omega) I
> EpsilonMembrane := PermittivityMembrane - (ConductivityMembrane/omega)
> I
> EpsilonMedium := PermittivityMedium - (ConductivityMedium/omega) I
>
> CMFCell := ( EpsilonCyt - EpsilonMembrane)/( EpsilonCyt + 2
> EpsilonMembrane)
> v := CellRadius/(CellRadius - MembraneThickness)
> EpsilonCell := EpsilonMembrane *(v^3 + 2 CMFCell)/(v^3 - CMFCell)
>
> Epsilon0 = 8.85 10^-12;
> PermittivityCyt = 120 Epsilon0;
> PermittivityMembrane = 6 Epsilon0;
> PermittivityMedium = 80 Epsilon0;
> ConductivityCyt = 0.15;
> ConductivityMedium = 0.15;
> ConductivityMembrane = 1 10^-9;
> CellRadius = 10 10^-6;
> MembraneThickness = 9 10^-9;
>
>  if I define VolumeFraction (eg. VolumeFraction=0.1) and plot
> Re[MeasuredCMF] vs. f, I have no problem.
> But I am unable to successfully do the following (I get a blank plot)
>
> Manipulate[
>  LogLinearPlot[
>   Evaluate[Re[MeasuredCMF]], {f, 1 10^5, 1 10^9}], {{VolumeFraction,
>    0.2}, 0.1, 0.5}]
>
> Can somebody help? I suspect I'm not using the assignment syntax
> correctly.
> Thanks
>
> Daniele Malleo




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