This article provides an overview of recent advances, challenges, and opportunities in
multiscale computational modeling techniques for study and design of two-dimensional (2D) …

The phase-field crystal (PFC) method is known as a relatively new continuum approach for
describing the microstructural dynamics of materials during structural and phase transitions …

Topological defects and smooth excitations determine the properties of systems showing
collective order. We introduce a generic non-singular field theory that comprehensively …

In this paper, we derive a new Allen–Cahn type two-model phase-field crystal model based
on the conserved L 2-gradient flow approach to describe the face-centered-cubic (fcc) …

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 …

Using the phase field crystal model (PFC model), an analysis of slow and fast dynamics of
solid-liquid interfaces in solidification and melting processes is presented. Dynamical …

In this paper, we propose four time marching schemes for the two-mode phase field crystal
equation with the periodic boundary condition. The first-and second-order schemes are …

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in
colloidal and metallic systems. In the present work, the modified hyperbolic phase-field …

We present a theoretical method for deriving the stress tensor and elastic response of
ordered systems within a Ginzburg-Landau-type density field theory in the linear regime …

Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the
crystalline lattice. To investigate the kinetic anisotropy and velocity of different …