Related papers: Solution of Poisson's equation for finite systems …
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable…
We introduce a model of Poisson random waves in $\mathbb{S}^{2}$ and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity.…
We apply the Poisson sum rule to obtain formal expressions for the Fourier coefficients of the potential of a lattice of generalized charge. Each generalized charge is assumed to contribute to the potential a term which depends only on the…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system,…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems.…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
In this letter we present a procedure for the calculation of the Casimir functions of finite-dimensional Poisson systems which avoids the burden of solving a set of partial differential equations, as it is usually suggested in the…
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
This article describes Monte-Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and…
We propose a new finite-size correction scheme for the formation energy of charged defects and impurities in one-dimensional systems within density functional theory. The energy correction in a supercell geometry is obtained by solving the…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…