Related papers: Hydrodynamic limit of the directed exclusion proce…
In this paper, we consider the hydrodynamic limit for the fluid-particle flows governed by the Vlasov-Fokker-Planck equation coupled with the compressible Navier-Stokes equation as the Deborah number tends to zero. The limit is valid…
We study the hydrodynamic and the hydrostatic behavior of the Simple Symmetric Exclusion Process with \emph{slow boundary}. The term \emph{slow boundary} means that particles can be born or die at the boundary sites, at a rate proportional…
The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes…
Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated…
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by…
Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop is modelled by a cloud of many non-touching particles, initially randomly distributed inside a spherical volume…
Burdzy, Pal, and Swanson considered solid spheres of small radius moving in the unit interval, reflecting instantaneously from each other and at x=0, and killed at x=1, with mass being added to the system from the left at constant rate. By…
We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
We derive the hydrodynamic limit for two degenerate lattice gases, the \emph{facilitated exclusion process} (FEP) and the \emph{facilitated zero-range process} (FZRP), both in the symmetric and the asymmetric case. For both processes, the…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…
We consider a singular limit problem for the complete compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem - the anelastic Euler system - in the case of well prepared initial data. The…
We develop a hydrodynamic theory for a height-dependent version of the totally asymmetric simple exclusion process in which the jump rate at a growth site is sampled from a macroscopic two-dimensional speed function evaluated at the spatial…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
We review the theoretical development in the study of critical thresholds for hyperbolic balance laws. The emphasis is on two classes of systems: Euler-Poisson-alignment (EPA) systems and hyperbolic relaxation systems. We start with an…
We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is…
Hidden symmetry in dissipationless terms of arbitrary hydrodynamics equations is recognized. We demonstrate that all fluxes are generated by a single function and derive conventional Euler equations using proposed formalism.
In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with…
We revisit in this short article the hydrostatic limit for the exclusion process with slow boundary. The original proof of this result relies on estimates of the correlation functions. We achieve the same result based on analysis of two…
We develop a rigorous theory for a structure-preserving discretisation of the incompressible Euler and Navier--Stokes equations, based on discrete exterior calculus on prismatic Delaunay--Voronoi meshes over closed Riemannian manifolds. The…