Mathematical and Physical Paradigms for Periodic Pattern Formation

Abstract: Energy-driven pattern formation induced by competing short and long-range interactions is ubiquitous in science. Often patterns of different phases display a periodic structure. This talk will address mathematical and physical paradigms for periodic pattern formation. The mathematical paradigm consists of nonlocal perturbations to the well-studied Cahn-Hilliard and isoperimetric variational problems. The physical paradigm is microphase separation of diblock copolymers.

Mathematical issues associated with these functionals and their connection with diblock copolymers will be discussed. One particular focus of the talk will be the phase diagram from the perspective of the modern calculus of variations. Numerical simulations of appropriate gradient flows also play an important role, and simulations will be presented.

Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).