Modeling and Analysis of Multi-Constituent Systems with Long Range Interaction

Energy-driven pattern formation induced by competing short and long range interaction in multi-species systems is pervasive in the natural world. The phenomenon of self-organization during pattern formation is quite common, and encountered in a variety of fields, such as biological systems like animal coats and skin pigmentation, and physics. As an example, we cite the block copolymers, whose remarkable ability of self-assembling ordered structures at nanoscale can be exploited to create materials with desired mechanical, optical, electrical, ionic, and magnetic properties.This project investigates complex, and previously intractable, geometric structures in physical systems of three or more constituents, by computational and analytic approaches, in order to deepen and broaden research on inhibitory systems, which is currently limited to simpler structures and almost exclusively to binary systems. This project will solve important questions, such as navigating the energy landscape of ternary systems, predicting the phase diagram of quaternary systems and identifying parameters in multi-constituent systems. Geometric structures like Hopf links, double and triple bubbles, minimal surfaces, surfaces of constant mean curvature, and Willmore surfaces, have been studied by geometers and topologists for their intrinsic beauty, leading to the deep and diverse mathematical theories […]

Faculty Supervisor:

Stanley Alama;Lia Bronsard

Student:

Partner:

Columbia University

Discipline:

Mathematics

Sector:

Education

University:

McMaster University

Program: