Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations

A. De Masi; P. A. Ferrari; J. L. Lebowitz

doi:10.1103/PhysRevLett.55.1947

Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations

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

Research output: Contribution to journal › Article › peer-review

97 Scopus citations

Abstract

We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) 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.

Original language	English (US)
Pages (from-to)	1947-1949
Number of pages	3
Journal	Physical review letters
Volume	55
Issue number	19
DOIs	https://doi.org/10.1103/PhysRevLett.55.1947
State	Published - 1985

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

Access to Document

10.1103/PhysRevLett.55.1947

Cite this

@article{8bbf3b96809046fe8c5f7099024a1ae4,

title = "Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations",

abstract = "We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) 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.",

author = "{De Masi}, A. and Ferrari, {P. A.} and Lebowitz, {J. L.}",

year = "1985",

doi = "10.1103/PhysRevLett.55.1947",

language = "English (US)",

volume = "55",

pages = "1947--1949",

journal = "Physical review letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "19",

}

TY - JOUR

T1 - Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations

AU - De Masi, A.

AU - Ferrari, P. A.

AU - Lebowitz, J. L.

PY - 1985

Y1 - 1985

N2 - We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) 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.

AB - We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) 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.

UR - http://www.scopus.com/inward/record.url?scp=4243825047&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243825047&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.55.1947

DO - 10.1103/PhysRevLett.55.1947

M3 - Article

AN - SCOPUS:4243825047

SN - 0031-9007

VL - 55

SP - 1947

EP - 1949

JO - Physical review letters

JF - Physical review letters

IS - 19

ER -

Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this