Related papers: An efficient method for computing stationary state…
In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths,…
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is…
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 relaxation of elastic excitations. This model…
We investigate stochastic Bregman proximal gradient (SBPG) methods for minimizing a finite-sum nonconvex function $\Psi(x):=\frac{1}{n}\sum_{i=1}^nf_i(x)+\phi(x)$, where $\phi$ is convex and nonsmooth, while $f_i$, instead of gradient…
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…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
Obtaining a thermodynamically accurate phase diagram through numerical calculations is a computationally expensive problem that is crucially important to understanding the complex phenomena of solid state physics, such as superconductivity.…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for…
Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
Phase field simulations play a key role in the understanding of microstructure evolution in additive manufacturing. However, they have been found extremely computationally expensive. One of the reasons is the small time step requirement to…
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
The well-known backward difference formulas (BDF) of the third, the fourth and the fifth orders are investigated for time integration of the phase field crystal model. By building up novel discrete gradient structures of the BDF-$\rmk$…
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…
The paper discusses a simple method of using the parametric continuation method to designate complex diagrams of steady states. The main advantage of the discussed approach is the fact that it does not require the installation of huge…
Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…