Mathematical Sciences: "Studies in Applied Mathematics"

DMS-9504122 Avellaneda这个项目涵盖了目前对应用数学感兴趣的两个领域。第一部分是关于具有随机初始数据的双曲型守恒律的模式形成问题。将从数学的角度分析解的统计性质、其概率分布函数和复杂模式。这些问题出现在统计物理、湍流建模和宇宙学的各种环境中。该项目的第二部分涉及含压电元件的先进复合材料的数学建模。解决这些问题的数学方法包括偏微分方程解的渐近性，包括齐次化理论、概率和数值模型。聚合物/压电陶瓷复合材料是构建高性能传感器和执行器的理想材料，可用于各种工业和医疗应用。

DMS-9504122 Avellaneda This project covers two areas of current interest in Applied Mathematics. The first part concerns problems in pattern formation arising from hyperbolic conservation laws with random initial data. The statistical properties of solutions, their probability distribution functions and the complex patterns will be analyzed from a mathematical standpoint. These problems arise in various settings in Statistical Physics, in turbulence modeling and in Cosmology. The second part of this project is concerned with the mathematical modeling of advanced composite materials with piezoelectric constituents. The mathematical methods that will be brought to bear on these problems include asymptotics for partial differential equations, including homogenization theory, probability and numerical modeling.Polymer/piezoceramic composites are ideal materials to construct high-performance sensors and actuators that can be used in a variety of industrial and medical applications.