Formation of multiple flocks in a simple nonlocal aggregation model

TL;DR

This paper investigates how specific nonlocal interaction kernels with a well-barrier shape lead to the formation of multiple flocks in a population, using advanced mathematical techniques to analyze energy minimizers.

Contribution

It introduces a novel analysis of flock formation driven by well-barrier shaped kernels using the concentration compactness principle.

Findings

Multiple flock formation driven by kernel shape.

Existence of energy minimizers despite flock separation.

Mathematical framework for flock dynamics.

Abstract

We consider a family of interaction energies given by kernels having a ''well-barrier'' shape, and investigate how these kernels drive the formation of multiple flocks within a larger population. We use the dichotomy case of the concentration compactness principle to obtain an energy minimizer, even though minimizing sequences are expected to break apart into flocks which may move far away from one another.