相关论文: Double Fourier Sphere Methods with Low Rank Approx…
We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the…
In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
The objective of this paper is twofold. First, we propose two composable block solver methodologies to solve the discrete systems that arise from finite element discretizations of the double porosity/permeability (DPP) model. The DPP model,…
We extend the two-particle self-consistent method proposed by Vilk and Tremblay (J. Phys. I France 7, 1309-1368 (1997)) to study superconductivity in multi-orbital systems. Starting with the sum rules for the spin and charge…
Block copolymers play an important role in materials sciences and have found widespread use in many applications. From a mathematical perspective, they are governed by a nonlinear fourth-order partial differential equation which is a…
We investigate the dynamics of the spin-boson model when the spectral density of the boson bath shows a resonance at a characteristic frequency $\Omega$ but behaves Ohmically at small frequencies. The time evolution of an initial state is…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the $k$-step BDF convolution quadrature to discretize the time-fractional derivative with order…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…
We provide {\it a priori} error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizs\"acker (TFW) model and of the Kohn-Sham model, within the local density…
In a superfluid system, Off-Diagonal Long-Range Order (ODLRO) is expected to be exhibited in the appropriate reduced density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently far…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
We investigate the long tim behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equation in a periodic box: $$ \frac{3\omega^{n+1}-4\omega^n+\omega^{n-1}}{2k} +…
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method.…
In this paper, we propose two efficient block preconditioners to solve the mass-conserved Ohta-Kawasaki equation with finite element discretization. We also study the spectral distribution of these two preconditioners, \textit{i.e.,} Schur…
Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy on the invariant degree of polymerization…