Related papers: On Power Law Scaling Dynamics for Time-fractional …
For the time-fractional phase field models, the corresponding energy dissipation law has not been settled on both the continuous level and the discrete level. In this work, we shall address this open issue. More precisely, we prove for the…
Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
Phase field crystals (PFC) are a tool for simulating materials at the atomic level. They combine the small length-scale resolution of molecular dynamics (MD) with the ability to simulate dynamics on mesoscopic time scales. We show how PFC…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
Globally conserved phase ordering dynamics is investigated in systems with short range correlations in the initial condition. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are…
In this work, we apply phase field simulations to examine the coarsening behavior of morphologically complex two-phase microstructures in which the phases have highly dissimilar mobilities, a condition approaching that found in experimental…
We construct explicit examples of microscopic models that stabilize a variety of fractionalized phases of strongly correlated systems in spatial dimension bigger than one, and in zero external magnetic field. These include models of charge…
When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling…
Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…
The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…
We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on…
In order to understand the nature of friction in closely-packed granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the…
We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse…
Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…