Hydrodynamic Limits of the Kinetic Self-Organized Models

Hydrodynamic models of self-organized dynamics: derivation and existence theory

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 is the kinetic model considered in [10] with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in [10], the non-local effects of the alignment and attr...

Kinetic models for chemotaxis: Hydrodynamic limits and the back-of-the-wave problem

Particle, Kinetic, and Hydrodynamic Models of Swarming

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individual-based models based on “particle”-like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the mod...

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean field Fokker-Planck equation governing the evolution of the distribution...

A hybrid method for hydrodynamic-kinetic flow - Part II - Coupling of hydrodynamic and kinetic models

In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used ...