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 …

Rapid solidification is a relevant physical phenomenon in material sciences, whose
theoretical analysis requires going beyond the limits of local equilibrium statistical physics …

This book surveys significant modern contributions to the mathematical theories of
generalized heat wave equations. The first three chapters form a comprehensive survey of …

Additive manufacturing (AM) of titanium alloys is a rapidly growing field due to an increase in
design flexibility of parts. However, AM parts are highly anisotropic in material microstructure …

Solute trap** is an important phenomenon in rapid solidification of alloys, for which the
continuous growth model (CGM) of Aziz et al.[1] is a popular sharp interface theory. By …

We present and discuss the development of an unconditionally stable algorithm used to
solve the evolution equations of the phase field crystal (PFC) model. This algorithm allows …

In this paper, we consider numerical approximations for the viscous Cahn–Hilliard equation
with hyperbolic relaxation. This type of equations processes energy-dissipative structure …

In recent years, a number of dynamical density functional theories (DDFTs) have been
developed for describing the dynamics of the one-body density of both colloidal and atomic …

A novel method based on molecular dynamics (MD) is developed to make the kinetic phase-
field (PF) model quantitative in predicting non-equilibrium crystal growth during rapid …

The phase-field model of Echebarria, Folch, Karma, and Plapp [Phys. Rev. E 70, 061604
(2004) PLEEE8 1539-3755 10.1103/PhysRevE. 70.061604] is extended to the case of rapid …