Re: manipulate, NDSolve, Evaluate

• To: mathgroup at smc.vnet.net
• Subject: [mg98134] Re: manipulate, NDSolve, Evaluate
• From: pajake <jtrexel at ix.netcom.com>
• Date: Tue, 31 Mar 2009 04:17:32 -0500 (EST)

```Here is what I have done so far.

(* First is an injected current that is applied to the cell*)
i[t_] := If[t < 10 || t > 60, 0, 1]
(* now to plot the above equation *)
Plot[i[t], {t, 0, 100}, PlotStyle -> {Red, Thick}]
(* The equation for an RC circuit.  Note the IC, and that c = 1. *)
RCSoln1[R_, c_: 1, v0_: 0] :=  NDSolve[{v'[t] == 1/c (i[t] - v[t]/R),
v[0] == v0}, v, {t, 0, 100}]
(* Now plotting the above equation, and assigning R = 1 *)
Plot[Evaluate[v[t] /. {RCSoln1[1]}], {t, 0, 100},  PlotStyle -> {Red,
Thick}]
(* Now let R = 1, and change the value of the capacitance in the plot to
see what differences this makes *)
RCSoln1a[R_: 1, c_, v0_: 0] :=  NDSolve[{v'[t] == 1/c (i[t] - v[t]/R),
v[0] == v0}, v, {t, 0, 100}]
p1 = Plot[Evaluate[v[t] /. {RCSoln1a[1]}], {t, 0, 100},   PlotStyle ->
{Blue, Thick}]
p2 = Plot[Evaluate[v[t] /. {RCSoln1a[5]}], {t, 0, 100},   PlotStyle ->
{Red, Thick}]
Show[p1, p2]
Now compare the difference in the way the plots look when you change the
R (resistance) vs the c (capacitance).  In order for the capacitance to
change like shown.  What could cause the changes in the resistance and
the capacitance?

? What I would like is: to use Manipulate with a slider to vary "c" and
"R".  I tried to use this equation. NDSolve[{v'[t] == 1/(a*c) (i[t] -
v[t]/(b*R), v[0] == v0}, v, {t, 0, 100}].  I changed the equation by
putting (a*c) and (b*R).   Then with the plot I thought I could add:
Manipulate[Plot[Evaluate[v[t] /. {RCSoln1a[1]}], {t, 0, 100}, ,{a, 0,
5}, (b, 0, 5)
PlotStyle -> {Blue, Thick}]]

It did not work.

This is just the beginning of the text book that I am writing.  Thus I
did not go into the finer details of the soma's wall thickness and how
it changes capacitance.  I just wanted to show in a graphic manner what
could happen and illustrate a basic equivalent circuit for a cell
membrane. Later on in the book, I go into more details.

Can you help me now?
Thanks once again
Prof Jake

Sjoerd C. de Vries wrote:
> If you've already done it for a specific wall thickness it should be
> very easy to do the same in a Manipulate for variable thickness
> values.
>
> Please post more details if you want more specific assistence.
>
> Cheers -- Sjoerd
>
> On Mar 28, 12:42 pm, pajake <jtre... at ix.netcom.com> wrote:
>
>> I am trying to combine, NDSolve with a ODE then using Plot[evaluate] to
>> show the results, and then I would like to take it to the next step and
>> use Manipulate.
>>
>> I am working a cell membranes capacitance based on the wall thickness. =
>>
>
>
>> I would like the plot to show the the membrane voltage vs time,(I have
>> done this with NDSolve and Plot), but I would like to use a slider that
>> reflects the difference in the cell membranes thickness which affects
>> the capacitance.
>> Is this possible?
>> thanks
>> Prof. Jake
>>
>
>
>

```

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