Hydrodynamic limit for interacting Ornstein–Uhlenbeck particles

Mean field limit for interacting particles

Zero Temperature Limit for Interacting Brownian Particles

We consider a system of interacting Brownian particles in R with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the part...

Interacting particle systems: hydrodynamic limit versus high density limit

In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach for different scenarios: the law of large numbers, the central limit theorem, and the large deviations principle. It is given a special attention to a recen...

Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces

We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term 9 plus independent Brownian motions: 9 is the sum of pair potentials, V(r)+#J(#r); the second term has the form of a Kac potential with inverse range #. Using di...

Hydrodynamic Limit for the Vlasov - Navier - Stokes Equations . Part II : Fine Particles Regime coro

The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes equations.This system is intended to model the evolution of particles interacting with a fluid. The coupling arises from the force terms. The limit problem is the Navier-Stokes system with non constant density. The density which is involved in this system is the sum of the (constant) density of the fluid a...