Equilibrium measures for nonlocal energies: The effect of anisotropy
Analysis and Geometry Seminar
1st May 2018, 3:00 pm – 4:00 pm
Howard House, 2nd Floor Seminar Room
Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels? Motivated by the example of dislocation interactions in materials science, we pushed the methods developed for nonlocal energies beyond the case of radially symmetric potentials, and discovered surprising connections with random matrices and fluid dynamics.