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Re: manipulate, NDSolve, Evaluate

  • To: mathgroup at
  • Subject: [mg98134] Re: manipulate, NDSolve, Evaluate
  • From: pajake <jtrexel at>
  • Date: Tue, 31 Mar 2009 04:17:32 -0500 (EST)
  • References: <gqkuu9$4ad$> <gqn8q9$t6g$>

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, 
(* 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> 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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