Begin forwarded message:
I am currently working on a problem of "Diffusion under thermal
gradient" in a two phase material.
I used fipy to solve the PDEs for a single phase alloy in 1D. Now I
am trying to extend it to two-phase alloy and 2D. I want to
introduce random circular nuclei of the second phase with a
Gaussian radius distribution. My system is a square domain in 2D
and I need to account for the volume/ area fraction of the nuclei
introduced. I would appreciate if you could suggest a way to do
this in fipy.
The NumPy library provides a bunch of random number generators. With
FiPy, we recommend that you get at it with
>>> from fipy.tools.numerix import random
(in sufficiently recent versions of FiPy, you can just do 'from fipy
import *' if you prefer).
You can then do
>>> help(random)
to get documentation on the different distributions available. I
would use 'normal' for your Gaussian radius distribution and
'uniform' to pick the positions.
Just set the seeds the way we do for the initial conditions, e.g.
>>> phase.setValue(1, where=(x-x0)**2 + (y-y0)**2 < r**2)
To get the volume (or area) fraction, you can then just say
>>> phase.getCellVolumeAverage()
If you want to prohibit overlapping nuclei, then that's just a
question of bookkeeping. Store your particle centers and radii and
check each new set to be sure that it's not too close to the previous
ones. There's nothing unique to FiPy or Python in that, though.
