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Re: Help Plotting director fields

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120206] Re: Help Plotting director fields
  • From: Heike Gramberg <heike.gramberg at gmail.com>
  • Date: Wed, 13 Jul 2011 03:10:40 -0400 (EDT)
  • References: <201107121059.GAA22206@smc.vnet.net>

I think the problem is that ArcTan[y/x] in your definition of theta 
should actually be the
polar angle of the vector {x,y}. For x>0 this is indeed ArcTan[y/x], but 
for x<0 the polar
angle becomes ArcTan[y/x] + Pi for y>0 and ArcTan[y/x]-Pi for y<0.

One way around this is to define theta according to

theta = s Arg[x+I y] + theta0

so for example

AAA = {Cos[-1/2 Arg[x + I y] + 0], Sin[-1/2 Arg[x + I y] + 0]}

StreamPlot[AAA, {x, -1, 1}, {y, -1.5, 1.5}, StreamPoints -> 20, 
StreamScale -> None]

Heike.


On 12 Jul 2011, at 11:59, Liquid Crystal wrote:

> Hello,
>
> I am trying to plot a director field for nematic liquid crystals.
> The form of the director is, in pseudo-mathematica
>
> n = {Cos[theta],Sin[theta]}
>
> Where:
>
> theta = s ArcTan[y/x] + theta_0
>
> If you reference the following links, you will see the various
> disinclinations induced in the director field by choosing various s
> and theta_0
>
> http://learnliquid.blogspot.com/2011/07/test.html
>
> However, using the following code I am not able to produce these 
images.
> Any suggestions?
>
> AAA = {Cos[-1/2 ArcTan[y/x] + 0/2], Sin[-1/2 ArcTan[y/x] + 0/2]}
>
> StreamPlot[AAA, {x, -1, 1}, {y, -1, 1}, StreamPoints -> 12,
> AspectRatio -> 1, StreamScale -> None]
>
> Thank you,
>
> LL
>



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