Related papers: Periodic Poisson Solver for Particle Tracking
The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation, for molecules represented as non-overlapping spherical cavities.…
The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
In this work, a method is described to extend the iterative Hirshfeld-I method, generally used for molecules, to periodic systems. The implementation makes use of precalculated pseudo-potential based charge density distributions, and it is…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
Imposing defined spinning to a particle beam increases its stability against perturbations from space charge~[Y.-L.~Cheon et al., Effects of beam spinning on the fourth-order particle resonance of 3D bunched beams in high-intensity linear…
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
Recently, a nonlinear Poisson equation has been introduced to model nonlinear and nonlocal hyperpolarization effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated…
This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over general two-dimensional (2D) domains, including domains with…
In this paper, we study well-posedness of random periodic solutions of stochastic differential equations (SDEs) of McKean-Vlasov type driven by a two-sided Brownian motion, where the random periodic behaviour is characterised by the…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
A common approach is present concerning the problem of Dirichlet, both for bounded 3D domains and their (unbounded) complements, regarding the fractional (3D) Poisson equation.
For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The…