Related papers: Poisson solvers for self-consistent multi-particle…
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the…
Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that…
In many natural and industrial applications, turbulent flows encompass some form of dispersed particles. Although this type of multiphase turbulent flow is omnipresent, its numerical modeling has proven to be a remarkably challenging…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Optimal exploitation of supercomputing resources for the evaluation of electrostatic forces remains a challenge in molecular dynamics simulations of very large systems. The most efficient methods are currently based on particle-mesh Ewald…
An efficient numerical algorithm for the laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the…
Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a Fast Fourier method, we obtain highly accurate electrostatic potentials for…
Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well…
With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…
We introduce a new type of recurrence in the space of continuous and bounded functions. The property is easily verifiable, and can be considered for differential equations. This time, the existence and asymptotic stability of modulo…
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…
Boson sampling has been theoretically proposed and experimentally demonstrated to show quantum computational advantages. However, it still lacks the deep understanding of the practical applications of boson sampling. Here we propose that…
The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are…
Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…
A solver for the Poisson equation for 1D, 2D and 3D regular grids is presented. The solver applies the convolution theorem in order to efficiently solve the Poisson equation in spectral space over a rectangular computational domain.…
Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into…