Coarsening in Nonlocal Interfacial Systems

Coarsening in Nonlocal Interfacial Systems

We consider coarsening in interfacial systems driven by nonlocal energies. Of particular interest are the nonlocal Cahn–Hilliard equation and models of biological aggregation. The energies considered cause the system to separate into phases. The pattern of interfaces evolves under nonlocal surfacetension-type effects. The typical length scales grow and the pattern coarsens. We prove a rigorous ...

Surface morphology coarsening in a nonlocal system

Direct comparison is made of the steady-sates and coarsening dynamics in a local system and its nonlocal generalization. The example system is the surface of a solid film in a strong electric field; the morphological evolution of the surface is described, in the long-wavelength approximation, by the amplitude PDE for the film height function. It is shown that the amplitude of the steady-state a...

Coarsening in Multicomponent Multiphase Systems

Domain statistics in coarsening systems

We study the domain number and size distributions in the one-dimensional Ising and q-state Potts models subject to zero-temperature Glauber dynamics. The survival probability of a domain S(t);t and an unreacted domain Q1(t);t 2d are characterized by two independent nontrivial exponents. For the Ising case, we find c50.126 and d51.27 using numerical simulations. We develop an independent interva...

Precipitate coarsening in multicomponent systems

Expressions to obtain composition shifts due to capillarity are presented when the chemical potential shifts of the precipitate phase are taken into account. These are applied to calculate the precipitate coarsening kinetics in multicomponent systems, showing dependence on the solution thermodynamics followed by the continuous phase. 2002 Published by Elsevier Science Ltd. on behalf of Acta Mat...