Nonlinear Sciences – Cellular Automata and Lattice Gases
Scientific paper
1997-04-29
J. Stat. Phys. 87(1/2), 37--61, 1997
Nonlinear Sciences
Cellular Automata and Lattice Gases
amstex with macros (included in the file), tex twice, 20 pages
Scientific paper
10.1007/BF02181479
We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.
Giacomin Giambattista
Lebowitz Joel. L.
No associations
LandOfFree
Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171374