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 review how phase-field models contributed to the understanding of various aspects of
crystal nucleation, including homogeneous and heterogeneous processes, and their role in …

We introduce a dislocation density tensor and derive its kinematic evolution law from a
phase field description of crystal deformations in three dimensions. The phase field crystal …

We present a multiphase-field theory for describing pattern formation in multidomain and/or
multicomponent systems. The construction of the free energy functional and the dynamic …

We use the amplitude expansion in the phase field crystal framework to formulate an
approach where the fields describing the microscopic structure of the material are coupled to …

We present a mesoscale description of deformations and defects in thin, flexible sheets with
crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation …

Abstract The Swift–Hohenberg (SH) and phase-field crystal (PFC) models are minimal yet
powerful approaches for studying phenomena such as pattern formation, collective order …

We derive a phase field crystal model that couples the diffusive evolution of a microscopic
structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the …

We consider a microscopic modeling approach for active systems. The approach extends
the phase field crystal (PFC) model and allows us to describe generic properties of active …

Most field theories for active matter neglect effects of memory and inertia. However, recent
experiments have found inertial delay to be important for the motion of self-propelled …