We present efficient, second-order accurate and adaptive finite-difference methods to solve
the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface …

We characterize the coarsening dynamics associated with a convective Cahn-Hilliard
equation (cCH) in one space dimension. First, we derive a sharp-interface theory through a …

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an
infinite dimensional dynamical system and establish the existence of a compact attractor and …

We study anisotropic surface diffusion of curves with a small corner energy regularization.
The regularization allows the use of non-convex free energy densities and turns the …

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some
orientations the surface stiffness is negative. In the sharp-interface problem, the surface free …

Purpose–For a partial differential equation with a fourth-order derivative such as the Cahn-
Hilliard equation, it is always a challenge to design numerical schemes that can handle the …

Understanding the dynamics of crystalline surfaces on a nanometer scale is one of the key
issues for several semiconductor applications. We consider the thermal faceting of such …

Realistic interfacial energy densities are often non-convex, which results in backward
parabolic behavior of the corresponding anisotropic curve shortening flow, thereby inducing …

We consider a generalization of the Cahn–Hilliard equation that incorporates an elastic
energy density which, being quasi-convex, incorporates micro-structure formation on smaller …

We consider the directional solidification, in two dimensions, of a dilute binary alloy having a
large anisotropy of surface energy,(ie, orientations with negative surface stiffness), where …