Date/Time
Date(s) - 28/03/2025
1:30 pm - 2:30 pm

Speaker: Dr. Ihsan Topaloglu (Virginia Commonwealth University)
Research areas: calculus of variations, partial differential equations and geometric measure theory

Location: Hamilton Hall, Room 410

Title: Perimeter regularization of attractive-repulsive nonlocal energies

Abstract: We consider a nonlocal interaction model defined over sets of given volume where an attractive-repulsive interaction is perturbed by a surface energy controlled by a parameter. These energies are directly connected to some aggregation models, which has a wide range of applications from collective behaviour such as biological and robotic swarming to models of graular media and self-assembly of nanoparticles. We first show that while attractive-repulsive energies do not admit minimizers for small volumes, this regularization restores the existence of minimizers for all values. We furthermore investigate the stability thresholds of the ball, and obtain its loca minimality. Our results show that for small perimeter regularizations, the ball is a stable critical point of the energy for small and large volumes; however, it loses its stability for intermediate values of volume.

This is joint work with Marco Bonacini.