Pinky, are you pondering what I'm pondering?

Whew! I'd say the odds of that are terribly slim.

---Pinky and the Brain

My current research involves the application of computational mechanics to physical systems, particularly polytypism. Polytypism is the phenomenon of a solid built up from identical layers, called modular layers, differing only in their orientation. Found in dozens materials, one of the best studied of the polytypes is zinc sulphide. There are approximately 185 identified crystalline structures and many samples are also disordered. Some crystalline structures of ZnS have unit cells extending over 100 modular layers. These different stacking sequences can occur under virtually identical thermodynamic growth conditions. My interest is how to discover and describe the stacking order in disordered single crystals from the diffraction pattern. It is known that without the assumption of strict crystallinity, it is not possible to invert the diffraction spectrum to find the structure that gave rise to it. Nonetheless, I have developed a technique to build a model that describes the stacking that invokes the least complexity. This model is known to be unique and minimal and from it I can calculate the average stacking fault energy as well as other physical quantities. I have demonstrated this procedure on ZnS diffraction spectra.

I am also interested in the general question of how one builds a model of a process from a power spectrum. Model building, or epsilon-machine reconstruction, is well understood for those cases where one has data in the form of a time or spacial series. Many physical measurements, however, yield power spectra, and the general question of epsilon-machine reconstruction in these cases remains an open question.

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