Spring 2016

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.

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Date: February 26, 2016

Speaker: David Shirokoff
Department of Mathematical Sciences,
NJIT

Title: "Approximate Global Minimizers for Pairwise Interaction Problems"

Abstract:

A wide range of material systems exhibit energy driven pattern formation governed by an underlying non-convex energy functional. Although numerically finding and verifying local minima to these functionals is relatively straight-forward, the computation and verification of global minimizers is much more difficult. Here the verification of global minimizers is often important in understanding the material phase diagram, especially at low temperatures. In this talk I will examine a general class of model functionals: those arising in non-local pairwise interaction problems. I will present a new approach for computing approximate global minimizers based on a convex relaxation of the underlying energy landscape, along with a recovery technique. The approach is sometimes exact, and also provides a numerical recovery guarantee for the approximate minimizer that is often within a few percent of the global minimum. The approach sometimes predicts exact lattice minimizers, and generates a dual decomposition for the energy landscape that leads to the emergence of new preferred low energy length scales.