Related papers: Hydrodynamic limit of the zero range process on a …
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
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…
We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally…
We rigorously prove that, in any relativistic kinetic theory whose non-hydrodynamic sector has a finite gap, the Taylor series of all hydrodynamic dispersion relations has a finite radius of convergence. Furthermore, we prove that, for…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
We consider the asymmetric zero range process in dimensions $d \geq 2$. Assume the initial density profile is a perturbation of the constant density, which has order $N^{-\alpha}$, $\alpha \in (0,1)$, and is constant along the drift…
We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the…
We consider the one-dimensional totally asymmetric zero-range process starting from a step decreasing profile leading in the hydrodynamic limit to the rarefaction fan of the associate hydrodynamic equation. Under that initial condition, we…
We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in…
In this paper, we introduce a random environment for the exclusion process in $\mathbb{Z}^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion…
We present a series of analytically solvable axisymmetric flows on the torus geometry. For the single-component flows, we describe the propagation of sound waves for perfect fluids, as well as the viscous damping of shear and longitudinal…
In this note, we study the hydrodynamic limit, in the hyperbolic space-time scaling, for a one-dimensional unpinned chain of quantum harmonic oscillators with random masses. To the best of our knowledge, this is among the first examples,…
The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero…
The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel…
We uncover a universal sector of relativistic fluid dynamics by taking a novel ultrarelativistic limit in which the temperature tends to zero while the flow simultaneously approaches the speed of light. In this regime, hydrodynamics becomes…
This paper summarizes results and some open problems about the large-scale and long-time behavior of asymmetric, disordered exclusion and zero-range processes. These processes have randomly chosen jump rates at the sites of the underlying…
We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
We consider two-dimensional hydroelastic waves, in which a free fluid surface separates two fluids of infinite vertical extent. Elastic effects are accounted for at the interface, with a parameter measuring the elastic bending force and…
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…