Related papers: Trefftz Functions for Nonlocal Electrostatics
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
The local approach to computing electrostatic interactions proposed by Maggs and adapted by Pasichnyk for molecular dynamics simulations is extended to situations where the dielectric background medium is inhomogeneous. We furthermore…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…
In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
We use a holographic method to investigate thermalization of a boost-invariant strongly interacting non-Abelian plasma. Boundary sourcing, a distorsion of the boundary metric, is employed to drive the system far from equilibrium.…
We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and…
Delivering the full benefits of first principles calculations to battery materials demands the development of accurate and computationally-efficient electronic structure methods that incorporate the effects of the electrolyte environment…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
A different formulation of the effective interaction hyperspherical harmonics (EIHH) method, suitable for non-local potentials, is presented. The EIHH method for local interactions is first shortly reviewed to point out the problems of an…
The influence of a chemically or electrically heterogeneous distribution of interaction sites at a planar substrate on the number density of an adjacent fluid is studied by means of classical density functional theory (DFT). In the case of…
The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields vary appreciably across the molecular length scale. Rather than incrementally adding higher…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
So far no mechanism is known, which could connect the two measurements in an Aspect-type experiment. Here, we suggest such a mechanism, based on the phase of a photon's field during propagation. We show that two polarization measurements…
We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which…
Many important applications of electronic structure methods involve molecules or solid surfaces in a solvent medium. Since explicit treatment of the solvent in such methods is usually not practical, calculations often employ continuum…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…