Related papers: Unconditionally stable, second-order accurate sche…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly…
In this paper, we present and analyze a linear fully discrete second order scheme with variable time steps for the phase field crystal equation. More precisely, we construct a linear adaptive time stepping scheme based on the second order…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…
Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for…
The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
In this work a state transformation is presented that transforms a given state-space system to a normal form related to mechanical systems. The underlying state-space system must meet certain requirements such that a transformation exist.…
In the setting of continuum elasticity, phase transformations involving martensitic variants are modeled by a free energy density function that is non-convex in strain space. Here, we adopt an existing mathematical model in which we…
We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…
Starting from an ideal crystalline state, we numerically study a nonequilibrium dynamical order- disorder transition promoted by the application of a periodic shearing protocol at low temperatures in model systems in two and three…
We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary…
The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of central heavy ion reactions are parameterized in terms of time dependent thermodynamical variables in the Fermi liquid sense. This allows one to…
In this paper, we construct efficient schemes based on the scalar auxiliary variable (SAV) block-centered finite difference method for the modified phase field crystal (MPFC) equation, which is a sixth-order nonlinear damped wave equation.…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
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…
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
We use holography to develop a physical picture of the real-time evolution of the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order, thermal phase transition. We numerically solve Einstein's…
Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…