Related papers: Poisson solvers for self-consistent multi-particle…
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Boson sampling can simulate physical problems for which classical simulations are inefficient. However, not all problems simulated by boson sampling are classically intractable. We consider a situation in which it is known that the outcome…
We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson--Nernst--Planck (PNP) equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically…
We describe a new hybrid N-body/hydrodynamical code based on the particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in solving problems related to the evolution of large-scale structure, galaxy clusters, and…
This paper addresses a detection problem where several spatially distributed sensors independently observe a time-inhomogeneous stochastic process. The task is to decide between two hypotheses regarding the statistics of the observed…
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…
We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR)…
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poisson system can be written as the composition of (1) a…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
Many problems in beam physics and plasma physics require the solution of Poisson's equation with free-space boundary conditions. The algorithm proposed by Hockney and Eastwood is a popular scheme to solve this problem numerically, used by…
We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…
Multigrid solvers are among the most efficient methods for solving the Poisson equation, which is ubiquitous in computational physics. For example, in the context of incompressible flows, it is typically the costliest operation. The present…
In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a…