Mathematical Sciences: Analysis of Transport Properties for Composites and Multi-Phase Flows with Application to Optimal Design

小行星9403866 我们解决了复合材料的设计及其应用结构的优化设计。在这里，我们研究了完全和不完全结合的复合材料的宏观性能，以及多相乳液和泡沫的最佳传输性能。在理论层面上，这项工作涉及均匀化理论，扰动理论和非线性泛函的伽玛收敛的基础研究。最终目标是创建有效的数值方法，用于复合材料结构的优化设计。 在这个建议中，我们处理几个主题涉及使用复合材料的最佳结构设计。复合材料及其输运特性是结构设计的核心，从飞机机翼的气动弹性到乳化液的优化设计。这里提出的设计方法的重点是找到最佳的结构性能所需的最佳复合材料性能。该计划已立即应用到不同的领域，从燃料效率的运输系统的设计到生物材料的运输特性的建模。

9403866 Lipton We address the design of composite materials and their application to optimal design of structures. Here we investigate the macroscopic properties for perfectly and imperfectly bonded composites as well as optimal transport properties for multi-phase emulsions and foams. On a theoretical level this work involves basic research in homogenization theory, perturbation theory, and gamma convergence of nonlinear functionals. The ultimate goal is the creation of efficient numerical methods for optimal design of structures built from composite materials. In this proposal we treat several topics involving the use of composites in optimal structural design. Composite materials and their transport properties are central to the design of structures ranging from the aeroelastic tayloring of airplane wings to optimal design of emulsions. The design approach put forth here focuses on finding the best composite material properties necessary for optimal structural performance. This program has immediate application to diverse areas ranging from design of fuel efficient transportation systems to the modeling of transport properties of biological materials.