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Re: Manipulate a complex expression
*To*: mathgroup at smc.vnet.net
*Subject*: [mg77807] Re: Manipulate a complex expression
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Sun, 17 Jun 2007 06:06:25 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <f505ip$qug$1@smc.vnet.net>
Daniele 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
Hi Daniele,
Your function definitions are missing the name of one or more variables.
I have made some modification in your code and and now it should work as
expected.
MeasuredCMF[vfrac_][f_] :=
vfrac*((EpsilonCell[f] - EpsilonMedium[f])/
(EpsilonCell[f] + 2*EpsilonMedium[f]))
omega[f_] := 2*Pi*f
EpsilonCyt[f_] := PermittivityCyt - (ConductivityCyt/omega[f])*I
EpsilonMembrane[f_] := PermittivityMembrane -
(ConductivityMembrane/omega[f])*I
EpsilonMedium[f_] :=
PermittivityMedium - (ConductivityMedium/omega[f])*I
CMFCell[f_] := (EpsilonCyt[f] - EpsilonMembrane[f])/
(EpsilonCyt[f] + 2*EpsilonMembrane[f])
v := CellRadius/(CellRadius - MembraneThickness)
EpsilonCell[f_] := EpsilonMembrane[f]*((v^3 + 2*CMFCell[f])/
(v^3 - CMFCell[f]))
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;
LogLinearPlot[Evaluate[Re[MeasuredCMF[0.1][f]]], {f, 1*10^5, 1*10^9}]
Manipulate[
LogLinearPlot[Evaluate[Re[MeasuredCMF[VolumeFraction][f]]],
{f, 1*10^5, 1*10^9}], {{VolumeFraction, 0.2}, 0.1, 0.5}]
Regards,
Jean-Marc
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