Since we are talking about CA-related PhD thesis topics, I thought I'd chime in because I am living the experience at the moment.
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:
spherical particles driven by a time and spatially varyingelectromagnetic field on a square lattice.
can almost instantaneous propagate momentum out of a localneighborhood 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.