I believe that free software is a must for open science. I maintain a git repository with my codes so hopefully we can collaborate while tackling these problems (or so at least you don't need to reinvent the wheel).
My thesis advisors were Alejandro Kolton and José Luis Iguain. We studied domain walls as driven elastic interfaces in disordered media by developing theories and numerical simulations.
Magnetic domain as seen using Magneto-Optic Microscopy by paredom.