Statistical Physics of Complex and Disordered Systems

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9311580 Machta This proposal concerns the statistical physics of complex and disordered systems. In particular it concentrates on three areas. 1) A theory of phase transitions in porous media with wide distributions of pore sizes is being developed using Migdal- Kadanoff approximations. The PI is particularly interested in studying the 4helium superfluid transition in porous aerogel glasses. 2) The PI proposes to study a clean example of self- organized criticality - that of the lambda transition in 4helium in the presence of heat flow. 3) The PI plans to study the application of computational complexity theory (something which arose out of theoretical computer science) to problems in statistical physics by determining the time requirements (and therefore the algorithmic choice) to solve various models on parallel machines. %%% The proposed work involves theoretical and computational approaches to the understanding of phase transitions in disordered systems. Of particular interest is the understanding of how helium undergoes its superfuid transition in a porous medium - the long wavelength fluctuations which are usually present in such transitions are truncated by the presence of the pore cages. Another aspect of this work concerns the study of a metastable system; that of the so- called lambda-transition in helium in the presence of heat flow. This produces a clean example for the study of self-organized criticality - a concept which has been applied to phenomena as varied as stock-market pricing and earth-quake prediction. Lastly, the proposal attempts to classify various models for phase transitions according ideas that came out of theoretical computer science - ideas that concern how difficult, computationally, it is to solve these models. ***