Material Mixing in Space-Time and Dynamic Control in the Coefficients of Linear Hyperbolic Equations

这项工作将集中于动力学中物质混合的概念。这一概念引入了时空复合材料，即在时空中组装和维持的材料微观结构。这种复合材料将在运动介质的麦克斯韦系统以及弹性动力学和声学的相对论方程的框架内进行研究。对于一些实际示例，将明确指定相关的有效参数集（g闭包）。g闭包的知识对于分析运动介质动力学中出现的材料优化问题至关重要，特别是在声学和水声以及高频电子工程中。当以材料系数作为控制因素时，这样的认识使许多这样的问题得到很好的解决。从物理上讲，这是因为时空中的最佳材料布局通常会将自己塑造成微观结构。这项工作的目的是准备一个概念基础，为后续的研究材料优化动力学。

This work will be focused on the concept of material mixing in dynamics.This concept introduces spatio-temporal composites, i.e. material microstructuresassembled and maintained in space-time. Such composites will be investigated in the framework of a Maxwell system for moving dielectrics as well as for the relativistic equations of elastodynamics and acoustics. The relevant set of effective parameters (G-closures) will be explicitly specified for a number of practical examples.The knowledge of G-closures is crucial for the analysis of material optimizationproblems that arise in dynamics of moving media, particularly in acoustics and hydroacoustics, as well as in high frequency electronic engineering. Such a knowledge makes many of these problems well-posed when the material coefficientsact as the control factors. Physically, this is because the optimal material layouts in space-time generally shape themselves as microstructures.This work is aimed to prepare a conceptual basis for a subsequent investigation of material optimization in dynamics.