格点上活性物质模型的流体力学
On the hydrodynamics of active matter models on a lattice
摘要：
活性物质因其丰富的唯象学内容，近年来得到了广泛的研究，但对其数学理解仍然是片面的。我们提出了一些结果，基于[8，17]将微观晶格气体与其宏观极限联系起来，并探索了数学最新技术如何允许从各种类型的微观动力学导出其流体动力学极限。我们提出了这个理论的一些关键方面时，适用于弱不对称的主动模型。我们评论的具体挑战时，应该考虑设计一个积极的格子气，并特别强调梯度和非梯度模型之间的数学和现象学的差异。我们的目的是提供物理界，以及数学界的成员不专门在晶格气体的标度极限的数学推导，在定义微观模型和推导其流体动力学极限的一些关键要素。
英文摘要：
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.
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