Related papers: Convergence to equilibrium for cross diffusion sys…
Usually, in a non-equilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems,…
A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…
Consider a diffusion process X, solution of a time-homogeneous stochastic differential equation. We assume that the diffusion process X is observed at discrete times, at high frequency, which means that the time step tends toward zero. In…
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…
In this paper we study the asymptotic behavior of a very fast diffusion PDE in 1D with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in…
We study a nonlocal aggregation equation with degenerate diffusion, set in a periodic domain. This equation represents the generalization to $m > 1$ of the McKean-Vlasov equation where here the "diffusive" portion of the dynamics are…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by supporting discontinuous approximating functions on general…
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…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
We consider a finite region of a $d$-dimensional lattice, $d\in\mathbb{N}$, of weakly coupled harmonic oscillators. The coupling is provided by a nearest-neighbour potential (harmonic or not) of size $\varepsilon$. Each oscillator weakly…