Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern
statistical mechanics. It is an extension of the highly successful method of classical density …

This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

Phase separation is a ubiquitous and emerging mechanism underlying intracellular
organization. Yet how distinct molecular compositions in phase-separated condensates are …

The nonlocal Allen--Cahn equation, a generalization of the classic Allen--Cahn equation by
replacing the Laplacian with a parameterized nonlocal diffusion operator, satisfies the …

Stability analyses and error estimates are carried out for a number of commonly used
numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the …

We construct unconditionally stable, unconditionally uniquely solvable, and second-order
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …

Here, we review the basic concepts and applications of the phase-field-crystal (PFC)
method, which is one of the latest simulation methodologies in materials science for …

In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to
obtain energy stable schemes for a class of phase field models. This novel auxiliary variable …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …