Derivation of the Leroux system as the hydrodynamic limit of a two-component lattice gas

Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries

We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation law, with boundary conditions in the sense of Bardos, Leroux and Nédélec. For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured in \cite{ps}, and show that it is robust with respect to perturbations of the boundaries.

Onsager relations and Eulerian hydrodynamics for systems with several conservation laws

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities for a wide class of models. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of…

非多项式分数阶扩散的推导：来自带慢势垒的广义排斥过程

Derivation of non-polynomial fractional diffusions from the generalized exclusion with a slow barrier

本文在流体动力学极限下，从长程相互作用且跳跃率依赖局部占据的随机粒子系统推导出广义分数阶多孔介质方程，并研究了慢势垒对质量流动的阻碍效应。

On the hydrodynamics of active matter models on a lattice

Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic limit, and explore how the mathematical state of the art allows to derive from various types of microscopic dynamics their hydrodynamic limit. We present some of the crucial aspects of this theory when applied to weakly asymmetric active models. We comment on the specific challenges one should consider when designing an active lattice gas, and in particular und…

Hydrodynamic limit for a disordered harmonic chain

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity. Furthermore, it follows from our proof that the temperature pro…

带碰撞的多组分慢边界WASEP的流体动力学极限

Hydrodynamic limit of the multi-component slow boundary WASEP with collisions

本文研究带碰撞的多组分慢边界WASEP的流体动力学极限，分析排他、碰撞和边界注入移除三种动力学叠加下的宏观行为，并揭示边界条件随参数θ取值而发生剧烈变化。