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

9403866 Lipton 我们致力于复合材料的设计及其在结构优化设计中的应用。在这里，我们研究完美和不完美粘合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，这项工作涉及均质化理论、微扰理论和非线性泛函伽玛收敛性的基础研究。最终目标是创建有效的数值方法来优化复合材料结构的设计。 在本提案中，我们讨论了涉及在优化结构设计中使用复合材料的几个主题。复合材料及其传输特性对于结构设计至关重要，从飞机机翼的气动弹性泰勒到乳液的优化设计。这里提出的设计方法侧重于寻找最佳结构性能所需的最佳复合材料特性。该程序可立即应用于各个领域，从节能运输系统的设计到生物材料运输特性的建模。

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.