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 …

We highlight some recent developments that widen the scope and reach of mesoscopic thin-
film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films …

Reaction–diffusion systems are an intensively studied form of partial differential equation,
frequently used to produce spatially heterogeneous patterned states from homogeneous …

In this book we consider solution branches and bifurcations in nonlinear partial differential
equations (PDEs) as models from science (and some economics). Given a nonlinear PDE …

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational
coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already …

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid
surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far …

We discuss an active phase field crystal (PFC) model that describes a mixture of active and
passive particles. First, a microscopic derivation from dynamical density functional theory is …

This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded
Euler–Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to …

The wetting of soft polymer substrates brings in multiple complexities when compared with
the wetting on rigid substrates. The contact angle of the liquid is no longer governed by …

Abstract The classical Cahn–Hilliard (CH) equation corresponds to a gradient dynamics
model that describes phase decomposition in a binary mixture. In the spinodal region, an …