First some background: I am an electrical engineering student working on the electromechanics of granular materials. I am *not* an expert in CA or any of the related areas---I just know enough to get by. The research atmosphere here is: "Huh, cellular automata? That sounds interesting." That is, almost everyone involved with my thesis is basically a beginner.

My experience has been an uphill battle all the way. At first, my advisor was somewhat hostile towards my intended research. He has been involved with particle electromechanics for many years, and my proposal to study the electromechanics of many (~ 10,000) particles using a CA-like method was too alien for him to accept. However, I, being a stubborn person, kept pushing him in that direction by various devious ploys. Finally, my persistence paid off, and he started to understand why I chose to employ ideas rooted in complex systems and CA. The bottom line is that I'm defending my proposal in two weeks, and the reaction of my committee has been surprisingly positive. The concepts and elegance of CA and related subjects appealed to them. My thesis advisor is even looking for students to continue my work after I graduate!

Just in case anyone is interested, I'll describe some of the more interesting aspect of my problem:

• I deal with chargeless, finite volume, mono-sized, polarizable,

  spherical particles driven by a time and spatially varying
  

  electromagnetic field on a square lattice.

• The particles are not treated as test particles so they affect the local field and thus have mutual influence upon each other (many-body problem.)

• I have free surfaces which separate the phases (coastline between "holes" and particles). I am interested in the formation of field induced microstructures with self-similar features at different scales.

• Because I work with finite volume spherical particles, collisions

  can almost instantaneous propagate momentum out of a local
  

  neighborhood if a path of connected particles exists. Consequently, during any time-step, a particle's state at a given site of the lattice can be affected by particles outside of a local region.

• I used a probabilistic approach to define "velocities" of particles on a lattice. For each time-step, the probability of a particle moving is proportional to its "velocity" vector. As a result, the system is reminiscent of the flow of probability densities in a limited form of phase space (a point in configuration space X a distribution in velocity space.) Also, I had to come up with some guidelines to interpret the occurance of physical events (something like making an observation in quantum mechanics.) This aspect of my thesis makes me very uneasy. My friends in the physics department didn't laugh at my ideas too much so I guess my guidelines are not too unreasonable. One of them even suggested that my probabilistic approach effectively increased the symmetry group of the underlying lattice space.

• From preliminary results, I came to the conclusion that a square lattice is not adequate. By the way, I know of the results from Lattice Gas Automata, although I don't understand the group theory behind it. My problem is the limited particle-to-particle orientation allowed in my current limitation. Therefore, a future version will have a higher resolution square lattice where the particles have a diameter of two lattice constants. A key consequence is the allowance of dislocations.

• I am in the process of incorporating my C code into _Python_, an object oriented, user extendable (at the interpreter level), dynamic language. The end product should be something like Basic with specialized data structures and methods for simulating the dynamics of granular materials using a CA-like approach.

Chak Tan