Complex Systems and Boundary Interactions

带电粒子与复杂流体相互作用的系统在科学中非常重要，并且出现在从等离子体物理到生物学和医学的各种背景中。这个项目的重点是边界和界面的相互作用。本研究的统一理论方法的两个不同的应用突出了在该项目中：一个是工程和生物学兴趣的流体中带电粒子的边界相互作用，另一个是由于热带风暴（风暴潮）的极端沿海事件的模型。在该项目中开发的方法是广泛适用的，从小尺度粒子相互作用的领域和溶剂，大尺度的地球物理现象。该项目与邻近科学和工程学科的研究直接相关。近年来，扩展系统中非局部相互作用的研究取得了重大进展，并将其应用于自由边界演化和复杂流体。该项目考虑电磁场，带电粒子和复杂的流体通过非线性和非局部方程耦合。该项目的目的是介绍，发展和扩展耦合系统的处理方法，其中有尺寸对比，特别是活动界面和边界。提出了多尺度和非局部分析的新发展，以解决具有活动界面和边界的非线性系统所带来的挑战。基于自然路径空间的拉格朗日-欧拉方法将结合随机描述来开发，随机描述适用于随机力影响大尺度行为的系统。

Systems in which charged particles interact with complex fluids are of great importance in science and arise in a great variety of contexts, from plasma physics to biology and medicine. The emphasis of this project is on boundary and interface interactions. Two different applications of the unified theoretical approach of this research are highlighted in the project: one to boundary interaction of charged particles in fluids of engineering and biological interest, and the other, to models of extreme coastal events due to tropical storms (storm surge). The methodology developed in the project is widely applicable, from small scale particles interacting with fields and solvents, to large scale geophysical phenomena. The project is directly relevant to studies in neighboring scientific and engineering disciplines. In recent years, there has been significant progress in the study of nonlocal interaction in extended systems, with application to free boundary evolution and complex fluids. The project considers electromagnetic fields, charged particles, and complex flu ids coupled through nonlinear and nonlocal equations. This project is aimed at introducing, developing and extending methods of treatment of coupled systems in which there are dimensional contrasts, in particular, active interfaces and boundaries. New developments in multi-scale and nonlocal analysis are proposed to address the challenges presented by the nonlinear systems with active interfaces and boundaries. Lagrangian-Eulerian methods based on natural path spaces will be developed in conjunction with stochastic descriptions which are appropriate for systems in which random forces influence large scale behavior.