Diffusion Processes in Composite Media and Related Problems

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9625642 Zheng ABSTRACT The investigator will continue the study of diffusion process related to heat propagation in a composite medium. The proposed research is related to several areas of probability theory: the theory of Dirichlet forms and Markov processes, weak convergence theory, stochastic calculus and martingale theory. The investigator is mainly interested in the following problems: 1) Time-dependent Dirichlet form and moving boundary problems; 2) The analysis of the Markov chain models which give approximating solutions for the above problems; 3) The estimate of the rate of weak convergence when a sequence of Markov chains approach a diffusion process. The investigator expects that this proposed study will introduce more applications of the existing results of diffusion process theory thereby enriching the whole theory. The main purpose of this investigation is to study problems related to the temperature evolution of an object composed of several different materials. Two examples are the melting-freezing process of ice hills on the oceans and temperature control inside a nuclear reactor. For those problems, the real computations are very complicated and sometimes applied scientists do not even know if their computational result is precise enough to the applicable to the real world. The investigator will use a special mathematical model known as "diffusion processes" to simulate the real temperature evolution on those objects. Moreover, the investigator will study how to realize this process on a computer and how accurate the computer simulation result will be.