Related papers: An Energetic Variational Approach for ion transpor…
The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for…
We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation…
In this work, we study the implementation of electrically-driven flow (EDF) models in the finite-volume framework of $\text{OpenFOAM}^\circledR$. The Poisson-Nernst-Planck model is used for the transport of charged species and it is coupled…
We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an…
We present a sampling method for the transition from relativistic hydrodynamics to particle transport, commonly referred to as particlization, which preserves the local event-by-event conservation of energy, momentum, baryon number,…
We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post Navier-Stokes equation, we find a…
We report on a new methodological approach to electrodynamics based on a fluidic viewpoint. We develop a systematic approach establishing analogies between physical magnitudes and isomorphism (structure-preserving mappings) between systems…
We study the role of electron-electron interactions for spin polarized transport using the Boltzmann equation and derive a set of coupled transport equations. For spin polarized transport the electron-electron interactions are important,…
We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent…
We consider different measure-valued solvability concepts from the literature and show that they could be simplified by using the energy-variational structure of the underlying system of partial differential equations. In the considered…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. The uniqueness of solutions of these problems is proved for piecewise constant electric charge and internal stress distributions having…
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
Particle transport through an open, discrete 1-D channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time dependent site energies, allows multiple occupation due to…
In this paper the response of ionic systems subjected to a spatially varying electric field is studied. Following the Nernst-Planck equation, two forces driving the mass flux are present, namely, the concentration gradient and the electric…
Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…