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介质动力学。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，将用数值方法研究过渡到爆轰的细节。同时，将对一维脉动爆轰进行严格的分析。在冲击诱导相变领域，将发展液化冲击的数学理论。这一理论预计将类似于爆轰的ZND理论。主要研究人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。将结合渐近方法、数值计算和严格的分析来实现该项目的目标。

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.