Maria Giovanna Mora

Università di Pavia

Equilibrium measures for nonlocal interaction energies with anisotropy

Nonlocal interaction energies are continuum models for large systems of particles, where each particle interacts not only with its immediate neighbors, but also with particles far away. This kind of energies arises in many different applications, such as biology (population dynamics), physics (Ginzburg–Landau vortices), and material science (dislocation theory). The mathematical literature on nonlocal interactions is huge, but not much is known for interactions that are not radially symmetric. In this talk I will first discuss a model coming from dislocation theory, whose main feature is anisotropy. I will then build on this example to show how anisotropy may affect the optimal distribution of particles at equilibrium (the so-called equilibrium measure) and, in particular, its dimensionality.