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 …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

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 …

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 …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP)
in the sense that the time-dependent solution preserves for any time a uniform pointwise …

In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time
step** schemes, which are based on the newly developed invariant energy quadratization …

In this study, we present a robust and efficient fingerprint image restoration algorithm using
the nonlocal Cahn–Hilliard (CH) equation, which was proposed for modeling the …