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Re: manipulate, NDSolve, Evaluate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98183] Re: manipulate, NDSolve, Evaluate
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Wed, 1 Apr 2009 05:59:03 -0500 (EST)
  • References: <gqkuu9$4ad$1@smc.vnet.net> <gqn8q9$t6g$1@smc.vnet.net>

Hi,

Here is my reworked version of your code. I removed your comments and
inserted mine indicating the changes.


i[t_] := If[t < 10 || t > 60, 0, 1]
Plot[i[t], {t, 0, 100}, PlotStyle -> {Red, Thick}]
RCSoln1[R_, c_: 1, v0_: 0] =
  DSolve[{v'[t] == 1/c (i[t] - v[t]/R), v[0] == v0}, v[t], t][[1, 1=
,
    2]];
(*Removed N, DSolve can do it fine. Picked the v[t] out of the \
solution using Part. Using Set (=) instead of SetDelayed (:=) means \
we don't have to use Evaluate in the Plot command. It's often quicker
\
too. *)
Plot[RCSoln1[1], {t, 0, 100}, PlotStyle -> {Red, Thick},
 MaxRecursion -> 9]
(* Now the solution can be used directly. Increased MaxRecursion to \
improve the plotting of the discontinuity *)
RCSoln1a[R_, c_, v0_] =
  DSolve[{v'[t] == 1/c (i[t] - v[t]/R), v[0] == v0}, v[t], t][[1, 1=
,
    2]];
(* Same as above. Also removed use of default values here. It would \
result in ambiguous calling possibilities: in your definition with \
RCSoln1a[R_: 1,c_,v0_: 0] RCSoln1a[2,3] would have worked, but which \
variable now gets its default value? Is it RCSoln1a[2,3,0] or \
RCSoln1a[1,2,3]?  The only unambiguous use of default values would be
\
to use them at the end*)
Show[
 Plot[RCSoln1a[1, 1, 0], {t, 0, 100}, PlotStyle -> {Blue, Thick},
  MaxRecursion -> 9],
 Plot[RCSoln1a[1, 5, 0], {t, 0, 100}, PlotStyle -> {Red, Thick},
  MaxRecursion -> 9]
 ]

Manipulate[
 Plot[RCSoln1a[R, c, 0], {t, 0, 100}, PlotStyle -> {Blue, Thick},
  MaxRecursion -> 9]
 , {R, 1, 5}, {c, 1, 5}]
(* There were so many syntax errors in your version of this line of
code that I feel that either you don't have Mathematica 6 or 7, which
is required for Manipulate or you have syntax coloring switched off,
which you shouldn't do. *)

Cheers -- Sjoerd

On Mar 31, 11:17 am, pajake <jtre... at ix.netcom.com> wrote:
> 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 t=
o
> 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 b=
y
> 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] t=
o
> >> show the results, and then I would like to take it to the next step an=
d
> >> 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 tha=
t
> >> reflects the difference in the cell membranes thickness which affects
> >> the capacitance.
> >> Is this possible?
> >> thanks
> >> Prof. Jake



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