Related papers: Trefftz Functions for Nonlocal Electrostatics
The convergence of iterative schemes to achieve self-consistency in mean field problems such as the Schr\"odinger-Poisson equation is notoriously capricious. It is particularly difficult in regimes where the non-linearities are strong such…
Numerous evolution equations with nonlocal convolution-type interactions have been proposed. In some cases, a convolution was imposed as the velocity in the advection term. Motivated by analyzing these equations, we approximate advective…
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties…
We present a nonlocal formulation of contact mechanics that accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The analytical formulation considers the effects of nonlocal mesoscopic…
Different schemes for the treatment of long-ranged electrostatic interactions will be examined for water simulations using the polarizable fluctuating charge potential. Several different methods are compared, including Ewald sums, potential…
We investigate electric polarizations emergent perpendicular to an applied thermal gradient in insulating systems. The thermally-induced electric polarization, known as thermopolarization, has been studied conventionally in the case that an…
We develop an efficient Ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates, where we may apply an electric field with an arbitrary…
Ionic crystals play a central role in functional applications. Mesoscale descriptions of these crystals are based on the continuum polarization density field to represent the effective physics of charge distribution at the scale of the…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on…
The electrostatic interaction between two non-identical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically…
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of…
The paper presents an automatic generator of approximate nonreflecting boundary conditions, analytical and numerical, for scalar wave equations. This generator has two main ingredients. The first one is a set of local Trefftz functions --…
The paper examines local approximation errors of finite difference schemes in electromagnetic analysis. Despite a long history of the subject, several accuracy-related issues have been overlooked and/or remain controversial. For example,…
Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
In electromagnetics and photonics, "nonlocality" refers to the phenomenon by which the response/output of a material or system at a certain point in space depends on the input field across an extended region of space. While nonlocal effects…
The inclusion of electronic polarization is of crucial importance in molecular simulations of systems containing charged moieties. When neglected, as often done in force field simulations, charge-charge interactions in solution may become…