Equilibrium measures for nonlocal interaction energies: The role of anisotropy

Speaker: Maria Giovanna Mora (Università di Pavia)
Occasion: Mathematical and Computational Materials Science
Date: February 17, 2021

Abstract: Particle systems subject to long-range interactions can be described, for large numbers of particles, in terms of continuum models involving nonlocal energies. For radially symmetric interaction kernels, several authors have established qualitative properties of minimizers for this kind of energies. But what can be said for anisotropic kernels? Starting from an example describing dislocation interactions in metals, I will discuss how the anisotropy may affect the equilibrium measure and, in particular, its dimensionality.