Related papers: Some random batch particle methods for the Poisson…
In the present work, we develop a novel particle method for a general class of mean field control problems, with source and terminal constraints. Specific examples of the problems we consider include the dynamic formulation of the…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
A proper treatment of electrostatic interactions is crucial for the accurate calculation of forces in computer simulations. Electrostatic interactions are typically modeled using Ewald based methods, which have become one of the…
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…
We discuss stochastic phase-space methods within the truncated Wigner approximation and show explicitly that they can be used to solve non-equilibrium dynamics of bosonic atoms in one-dimensional traps. We consider systems both with and…
While collisionless plasmas are ubiquitously present near astrophysical compact objects, the impact that their composition has on the high-energy emission is presently unknown. We present the first investigation of particle-acceleration…
We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks…
The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…
The main aim of this paper is to demonstrate the method called "the Bosonization of Nonlocal Currents" (BNC), used for calculations of bound states in a quark model, within the simplest relativistic quantum field model of two scalar fields…
We propose a parallel stochastic Newton method (PSN) for minimizing unconstrained smooth convex functions. We analyze the method in the strongly convex case, and give conditions under which acceleration can be expected when compared to its…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $\epsilon$ in general bounded smooth domains (including multiply connected domains) under the…
The Poisson-Boltzmann (PB) model is a widely used implicit solvent model in protein simulations. Although variants, such as the size modified PB and nonlocal modified PB models, have been developed to account for ionic size effects and…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly…