Mathematical Sciences: Dynamics of Detonations and Shock Induced Phase Changes

本研究涉及反应激波的动力学和相变的连续动力学。在第一个领域，首席研究员将研究多维爆轰低频不稳定性的非线性发展。对于一维几何结构，将对过渡到爆轰的细节进行数值研究。同时，对一维脉动爆轰进行了严格的分析。在激波诱发相变领域，将发展液化激波的数学理论。这一理论有望与ZND爆炸理论相类似。首席研究员将研究实验观察到的波分裂现象和液化激波锋的低频不稳定性。结合渐近方法，数值计算，和严格的分析将被用来实现这个项目的目标。

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.