Related papers: An optimal-transport finite-particle method for dr…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates.…
The Maximum Entropy (MaxEnt) technique is applied to the derivation of the Gaussian Dispersion Plume Model as well as to more complex transport phenomena such as the one-dimensional advection equation, the one-dimensional diffusion…
We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
There are several approaches to describe flows with particles e.g. Lattice-Gas Automata (LGA), Lattice-Boltzmann method (LBM) or smoothed particle hydrodynamics (SPH). These approaches do not use fixed grids on which the Navier-Stokes…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the…
Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601 (2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and extensive Brownian dynamics simulations, we study particle transport through…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
The least gradient problem (minimizing the total variation with given boundary data) is equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain, which is in turn…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
We discuss analytical results for a run-and-tumble particle (RTP) in one dimension in presence of boundary reservoirs. It exhibits `kinetic boundary layers', nonmonotonous distribution, current without density gradient, diffusion…
The Exact Regularized Point Particle (ERPP) method is extended to treat the interphase momentum coupling between particles and fluid in the presence of walls by accounting for the vorticity generation due to the particles close to solid…
We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations…
In numerical studies of the dynamics of unbound quantum mechanical systems, absorbing boundary conditions are frequently applied. Although this certainly provides a useful tool in facilitating the description of the system, its applications…