{
  "id": "cond-mat/9809331",
  "version": "v1",
  "published": "1998-09-24T13:51:17.000Z",
  "updated": "1998-09-24T13:51:17.000Z",
  "title": "Hydrodynamic Limit of Brownian Particles Interacting with Short and Long Range Forces",
  "authors": [
    "Paolo Butta`",
    "Joel L. Lebowitz"
  ],
  "comment": "37 pages, in TeX (compile twice), to appear on J. Stat. Phys., e-mail addresses: pbutta@math.rutgers.edu, lebowitz@math.rutgers.edu",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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, $V(r)+\\gamma^d J(\\gamma r)$, the second term has the form of a Kac potential with inverse range $\\gamma$. Using diffusive hydrodynamical scaling (spatial scale $\\gamma^{-1}$, temporal scale $\\gamma^{-2}$) we obtain, in the limit $\\gamma\\downarrow 0$, a diffusive type integro-differential equation describing the time evolution of the macroscopic density profile.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-24T13:51:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long range forces",
      "brownian particles interacting",
      "hydrodynamic limit",
      "type integro-differential equation describing",
      "time evolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}