Related papers: A Stochastic Calculus Approach to Boltzmann Transp…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…
Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport…
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC…
This paper presents multilevel hybrid transport (MLHT) methods for solving the neutral-particle Boltzmann transport equation. The proposed MLHT methods are formulated on a sequence of spatial grids using a multilevel Monte Carlo (MLMC)…
Astrophysical observations originate from matter that interacts with radiation or transported particles. We develop a pragmatic approximation in order to enable multi-dimensional simulations with basic spectral radiative transfer when the…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
Recent advances have allowed to tackle path-space probabilistic representations of mesoscopic Boltzmann transport nonlinearly coupled to a sub-model of the force-field by step forward approaches in terms of continuous branching stochastic…
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the…
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on the Boltzmann-Fokker-Planck equation, formulated as an…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
For a class of piecewise deterministic Markov processes we introduce a stochastic calculus which is a certain non-Gaussian counterpart to the classical Malliavin calculus. As an application we investigate the regularity of densities of…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
In this review, we detail the commonality of mathematical intuitions that underlie three numerical methods used for the quantitative description of electron swarms propagating in a gas under the effect of externally applied electric and/or…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions. We consider the limit of…
Sequential Monte Carlo (SMC) methods are widely used to draw samples from intractable target distributions. Particle degeneracy can hinder the use of SMC when the target distribution is highly constrained or multimodal. As a motivating…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…