98-467 Paolo Butta', Joel L. Lebowitz

Hydrodynamic Limit of Brownian Particles Interacting with Short and Long Range Forces (380K, PostScript) Jun 23, 98

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Abstract. We investigate the time evolution of a model system of interacting particles, moving in a $d$-dimensional torus. The microscopic dynamics are first order in time with velocities set equal to the negative gradient of a potential energy term $\Psi$ plus independent Brownian motions: $\Psi$ is the sum of pair potentials, $V(r)+\g^{d}J(\g r)$, the second term has the form of a Kac potential with inverse range $\g$. Using diffusive hydrodynamical scaling (spatial scale $\g^{-1}$, temporal scale $\g^{-2}$) we obtain, in the limit $\g\downarrow 0$, a diffusive type integro-differential equation describing the time evolution of the macroscopic density profile.

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