The Beker-Döring System and Its Lifshitz-Slyozov Limit

The role of discrete-particle noise in the Ostwald ripening

– We investigate the role of discrete-particle noise in interface-controlled Ostwald ripening. We introduce the noise within the framework of the Becker-Döring equations, and employ both Monte Carlo simulations and direct numerical solution of these equations. We find that the noise drives the system towards a unique scaling regime describable by a limiting solution of a classical continuum the...

On a Diffusive Version of the Lifschitz-Slyozov-Wagner Equation

This paper is concerned with the Becker-Döring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW equations is derived from the BD equations. Existence and uniqueness theorems for this diffusive LSW system are proved. The major part of the paper is taken up with proving that solutions of the diffusive LSW system conver...

Some Remarks on Large-Time Asymptotic of the Lifshitz–Slyozov Equations

as time becomes large. This equation has been introduced by Lifshitz and Slyozov (1) as a model for phase transition phenomena. Details on (1) can also be found in the more recent paper of Sagalovich and Slyozov (2) and in the classical book of Lifshitz and Pitaevski. (3) It is intended to model the evolution of aggregates interacting in a solution with free particles or monomers. The aggregate...

A Numerical Study on Large-Time Asymptotics of the Lifshitz-Slyozov System

We numerically investigate the long time behavior of solutions of the Lifshitz– Slyozov system. We propose a numerical scheme in which the numerical dissipation is controlled in such a way that the results for large time are meaningful. In this respect, we find the long time behavior to crucially depend on the distribution of largest aggregates present in the solution. This fact proved, in some...

Lifshitz-Slyozov kinetics of a nonconserved system that separates into phases of different density.