标题： 关于格点上活性物质模型的流体力学 显示英文标题

标题： On the hydrodynamics of active matter models on a lattice

摘要： 活性物质近年来被广泛研究，因为它具有丰富的现象学，而其数学理解仍然是不完全的。 我们提出了一些基于[8, 17]的结果，这些结果将微观晶格气体与其宏观极限联系起来，并探讨了当前数学状态如何从各种类型的微观动力学推导出它们的流体动力学极限。 我们将讨论当应用于弱不对称活性模型时，这一理论的一些关键方面。 我们评论了在设计活性晶格气体时应考虑的具体挑战，并特别强调梯度模型和非梯度模型之间的数学和现象学差异。 我们的目的是为物理界以及不专门从事晶格气体尺度极限数学推导的数学界成员提供一些定义微观模型和推导其流体动力学极限的关键要素。 显示英文摘要

摘要： 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 underline mathematical and phenomenological differences between gradient and non-gradient models. Our purpose is to provide the physics community, as well as member of the mathematical community not specialized in the mathematical derivation of scaling limits of lattice gases, some key elements in defining microscopic models and deriving their hydrodynamic limit.