  We consider the minimisation of power-law repulsive-attractive interaction
energies which occur in many biological and physical situations. We show
existence of global minimizers in the discrete setting and get bounds for their
supports independently of the number of Dirac Deltas in certain range of
exponents. These global discrete minimizers correspond to the stable spatial
profiles of flock patterns in swarming models. Global minimizers of the
continuum problem are obtained by compactness. We also illustrate our results
through numerical simulations.

Classical Analysis and ODEs;Analysis of PDEs