Mathematical Sciences: Dynamics of Detonations and Combustion Fronts

9311659 roythburd PI将继续研究与非线性波传播相关的应用分析和科学计算。工作内容包括：1)爆震波低频不稳定性的非线性演化和爆震波沿圆柱管传播现象的渐近理论；ii)研究一类自由边界（自由界面）问题，这些问题自然地作为无气燃烧和快速凝固的简化概念模型出现。这些自由边界问题展示了各种本质上是低维的动力模式。这些模型问题的定性行为及其与锋面运动描述的联系将进行分析和数值研究。提出的理论研究将有助于更好地理解一些工程问题，包括：高能推进剂的设计和安全使用；安全处理爆炸物；通过固体燃烧合成某些陶瓷和金属合金的过程；爆炸固化薄膜等。另一方面，PI建议研究的数学模型似乎是通用的，并且在其他上下文中也会遇到简单的构建块。他们的研究将导致动力系统理论的进步。＊＊＊

9311659 Roytburd The PI will continue research in applied analysis and scientific computing related to nonlinear wave propagation. The work will include: i) The nonlinear evolution of low-frequency instabilities of detonation waves and an asymptotic theory for the phenomenon of detonation waves propagating along a cylindrical tube; ii) The study of a class of free boundary (free interface) problems which arise naturally as simplified conceptual models of gasless combustion and fast solidification. These free boundary problems demonstrate a variety of dynamical patterns that are essentially low-dimensional. The qualitative behavior of these model problems and their connections with the front motion description will be investigated both analytically and numerically. %%% The proposed theoretical investigation will contribute to a better understanding of a number of engineering problems that include: the design and safe use of highly energetic propellants; safe handling of explosives; the process of synthesizing of certain ceramic and metallic alloys via solid combustion; explosive solidification of thin films and others. On the other hand, the mathematical models that the PI proposes to investigate appear to be generic and are encountered as simple building blocks also in other contexts. Their investigation will lead to progress in dynamical systems theory. ***