Related papers: An optimal-transport finite-particle method for dr…
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…
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
The effects of the propagation of particles which have a finite life time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source…
The transport and deposition of heavy particles over complex surface topography by turbulent fluid flow is an important problem in a number of disciplines, including sediment and snow transport, ecology and plant pathology, aeolian…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…
We have established previously, in a lead-in study, that the spreading of liquids in particulate porous media at low saturation levels, characteristically less than 10% of the void space, has very distinctive features in comparison to that…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
Using the analytical Fick-Jacobs approximation formalism and extensive Brownian dynamics simulations we study particle transport through two-dimensional periodic channels with triangularly shaped walls. Directed motion is caused by the…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In [Bailo, Carrillo, Hu. SIAM J. Appl. Math. 2023] the authors introduce a finite-volume method for aggregation-diffusion equations with non-linear mobility. In this paper we prove convergence of this method using an Aubin--Simons…
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories.…