We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of theâ€¦ (More)

We present a kinetic theory for swarming systems of interacting, self-propelled discrete particles. Starting from the Liouville equation for the many-body problem we derive a kinetic equation for theâ€¦ (More)

This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attractionrepulsion. The starting point isâ€¦ (More)

We study the McKeanâ€“Vlasov equation on the finite tori of length scale L in dâ€“dimensions. We (re)derive the necessary and sufficient conditions for the existence of a phase transition â€“ firstâ€¦ (More)

The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernelsâ€¦ (More)

The authors offer new laboratory methods for comprehensive assessment of the health status of the newborns. Introduction of these methods in practical activity of clinical diagnostic laboratories ofâ€¦ (More)

We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles areâ€¦ (More)