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 ...

A bounded aspect-ratio coarsening sequence of an unstructured mesh M 0 is a sequence of meshes M 1 ; : : : ; M k such that: M i is a bounded aspect-ratio mesh, and M i is an approximation of M i?1 that has fewer elements, where a mesh is called a bounded aspect-ratio mesh if all its elements are of bounded aspect-ratio. The sequence is node-nested if the set of the nodes of M i is a subset of t...

Several approaches to reverse and re-engineering are based upon program slicing. Unfortunately, for large systems, such as those which typically form the subject of reverse engineering activities, the space and time requirements of slicing can be a barrier to successful application. Faced with this problem, several authors have found it helpful to merge Control Flow Graph (CFG) nodes, thereby i...

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio d of the attachment rate to the terrace diffusion coefficient. For generic parameters (d>0) the model exhibits a very slow crossover to a nontri...

Two-dimensional simulations of the coarsening process of the isotropic/smectic-A phase transition are presented using a high-order Landau-de Gennes type free energy model. Defect annihilation laws for smectic disclinations, elementary dislocations, and total dislocation content are determined. The computed evolution of the orientational correlation length and disclination density is found to be...

We study electric field driven deracemization in an achiral liquid crystal through the formation and coarsening of chiral domains. It is proposed that deracemization in this system is a curvature-driven process. We test this prediction using the recently obtained exact result for the distribution of hull-enclosed areas in two-dimensional coarsening with nonconserved scalar order parameter dynam...

In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of the dispersed phase species from one emulsion droplet (or foam bubble) to another. Previous studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can overcome the Laplace pressure differences that drive coarsening, and " osmotically stabilise ...