Complex Systems and Boundary Interactions

Princeton University, Princeton NJ

Investigators

Abstract

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.