Related papers: A Particle method for stationary transport equatio…
We propose and study a method called FLOT that estimates scene flow on point clouds. We start the design of FLOT by noticing that scene flow estimation on point clouds reduces to estimating a permutation matrix in a perfect world. Inspired…
Motion planning is a key element of robotics since it empowers a robot to navigate autonomously. Particle Swarm Optimization is a simple, yet a very powerful optimization technique which has been effectively used in many complex…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct…
We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled…
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…
Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
This paper is devoted to studying the stationary solutions of a general constrained optimization problem through its associated unconstrained penalized problems. We aim to answer the question, "what do the stationary solutions of a…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…