Re: How to plot field lines of conformal mapping
- To: mathgroup at smc.vnet.net
- Subject: [mg26204] Re: [mg26083] How to plot field lines of conformal mapping
- From: Christopher Lee French <clfrench at bellatlantic.net>
- Date: Sat, 2 Dec 2000 02:10:34 -0500 (EST)
- References: <200011280655.BAA02200@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jos,
ParametricPlot[
Evaluate[
{Re[f], Im[f]} /. List /@ Thread[z -> u + Range[-Pi/2, Pi/2, Pi/15] I],
{u, -3, 3},
PlotPoints -> 700]
This should work for you, right away!
Sorry, I did not provide any explanation or exactly reproduce your
original
lines.
Christopher French
Jos R Bergervoet wrote:
> I would like to plot a family of field lines obtained from a conformal
> mapping, as in the following code snippet. Is there a shorter way?
>
> f = z + I Sinh[z]
>
> ParametricPlot[{
> {Re[f], Im[f]} /. z->u-Pi/2I,
> {Re[f], Im[f]} /. z->u-1.5I,
> {Re[f], Im[f]} /. z->u-1.25I,
> {Re[f], Im[f]} /. z->u-1.0I,
> {Re[f], Im[f]} /. z->u-0.75I,
> {Re[f], Im[f]} /. z->u-0.5I,
> {Re[f], Im[f]} /. z->u-0.25I,
> {Re[f], Im[f]} /. z->u+0I,
> {Re[f], Im[f]} /. z->u+0.25I,
> {Re[f], Im[f]} /. z->u+0.5I,
> {Re[f], Im[f]} /. z->u+0.75I,
> {Re[f], Im[f]} /. z->u+1.0I,
> {Re[f], Im[f]} /. z->u+1.25I,
> {Re[f], Im[f]} /. z->u+1.5I,
> {Re[f], Im[f]} /. z->u+Pi/2I
> },
> {u,-3,3}, PlotPoints->700]
>
> I tried (without success) to do it after creating a table in advance:
>
> n = 1
> t = Table[{Re[f], Im[f]} /. z->u+i/n Pi/2I , {i, -n,n}]
> ParametricPlot[t, {u,-3,3}, PlotPoints->700]
>
> This does not work. Does anyone know an elegant solution?
>
> NB: I do not want the full CartesianMap[F , {-3,3}, {-Pi/2,Pi/2}]
> but only one of the two families of lines.
>
> Thanks in advance,
> Jos
>
> --
> Dr. Jozef R. Bergervoet Electromagnetism and EMC
> Philips Research Laboratories, Eindhoven, The Netherlands
> Building WS01 FAX: +31-40-2742224
> E-mail: Jos.Bergervoet at philips.com Phone: +31-40-2742403