Related papers: Unconditionally stable, second-order accurate sche…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order…
This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…
In this paper we propose and analyze a (temporally) third order accurate backward differentiation formula (BDF) numerical scheme for the no-slope-selection (NSS) equation of the epitaxial thin film growth model, with Fourier pseudo-spectral…
Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and…
In our previous work [J. Chem. Phys. \textbf{136}, 024502 (2012)], we reported a demixing phase transition of a two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we…
In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of…
The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
We study in this paper the accuracy and stability of partially and fully implicit schemes for phase field modeling. Through theoretical and numerical analysis of Allen-Cahn and Cahn-Hillard models, we investigate the potential problems of…
The stability of nonlinear explicit difference schemes with not, in general, open domains of the scheme operators are studied. For the case of path-connected, bounded, and Lipschitz domains, we establish the notion that a multi-level…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…
These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
When driven by nonequilibrium fluctuations, particle systems may display phase transitions and physical behaviour with no equilibrium counterpart. We study a two-dimensional particle model initially proposed to describe driven non-Brownian…