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Reaction-diffusion equations for interacting particle systems

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Abstract

We study interacting spin (particle) systems on a lattice under the combined influence of spin flip (Glauber) and simple exchange (Kawasaki) dynamics. We prove that when the particle-conserving exchanges (stirrings) occur on a fast time scale of order ɛ−2 the macroscopic density, defined on spatial scale ɛ−1, evolves according to an autonomous nonlinear diffusion-reaction equation. Microscopic fluctuations about the deterministic macroscopic evolution are found explicitly. They grow, with time, to become infinite when the deterministic solution is unstable.

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Author notes

  1. A. De Masi

    Present address: Dipartimento di Matematica Pura e Applicata, Università dell'Aquila, 67100, L'Aquila, Italy

  2. P. A. Ferrari

    Present address: Instituto de Matematica e Estatistica, Universidade de São Paulo, São Paulo, Brasil

Authors and Affiliations

  1. Department of Mathematics and Physics, Rutgers University, 08903, New Brunswick, New Jersey

    A. De Masi, P. A. Ferrari & J. L. Lebowitz

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  1. A. De Masi
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  2. P. A. Ferrari
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  3. J. L. Lebowitz
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Additional information

This work was supported by NSF Grant DMR81-14726-02.

Partially supported by CNR.

Partially supported by CNPq Grant No. 201682-83.

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De Masi, A., Ferrari, P.A. & Lebowitz, J.L. Reaction-diffusion equations for interacting particle systems. J Stat Phys 44, 589–644 (1986). https://doi.org/10.1007/BF01011311

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