Mathematical Sciences: Dynamics of Detonations and Shock Induced Phase Changes

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This research is concerned with the dynamics of reacting shock waves and continuum dynamics of phase transitions. In the first area, the principal investigator will study the nonlinear development of low frequency instabilities of multidimensional detonations. For one-dimensional geometry, the details of transition to detonation will be studied numerically. Simultaneously, the rigorous analysis of one-dimensional pulsating detonations will be performed. In the area of shock induced phase transitions, a mathematical theory for liquefaction shocks will be developed. This theory is expected to be analogous to the ZND theory of detonations. The principal investigator will study the experimentally observed phenomena of wave splitting and the low frequency instabilities of liquefaction shock fronts. A combination of asymptotic methods, numerical computations, and rigorous analysis will be used to achieve the goals of this project.