Mathematical Sciences: "Studies in Applied Mathematics"

DMS-9504122 Avellaneda这个项目涵盖了应用数学中当前感兴趣的两个领域。第一部分是关于随机初值下双曲型守恒律的斑图形成问题。从数学的角度分析解决方案的统计特性，它们的概率分布函数和复杂的模式。 这些问题出现在统计物理学、湍流建模和宇宙学的各种环境中。该项目的第二部分是关于先进的复合材料与压电成分的数学建模。 数学方法，将带来承担这些问题，包括渐近偏微分方程，包括均匀化理论，概率和数值modeling.Polymer/piezoceramic复合材料是理想的材料，以构建高性能的传感器和执行器，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.