DynSyst_Special_Topics: Correlations and Stochastic Dynamics in Suspensions of Swimming Microorganisms

支持的工作将开发新的理论和计算方法来描述噪声的有效粗粒度随机动力学，非线性相互作用的代理在一个物理良好的接地模型系统：悬浮液的游泳微生物（微泳）。动力学表现出高度无序的行为，与直接数值模拟中观察到的长程统计相关性。然而，大多数的理论工作一直是基于确定性的方法，如平均场理论的有效行为。支持的工作的主要目标是将噪声的作用，在动态到一个系统的统计理论的相互作用microswimmer的有效动态。需要解决的两个核心问题是：（1）在自洽统计场论中参数化样本游泳者噪声的合理框架，以及（2）在有效统计场论中纳入微游泳者之间的相关性。许多复杂系统使用交互或通信来产生群体的涌现行为。一个关键的目标是更好地理解这些互动如何改变个体的有效动态，从而改变群体。例子包括各种各样的昆虫群，细菌群，鸟群，动物群，以及工程系统，如自主机器人设备，它们在追求目标或目标的过程中相互传递信息和状态。这些应用不仅涉及大量代理的交互，而且通常还涉及环境中的噪声、运动和/或通信。 这项赠款支持对游泳微生物（微泳者）悬浮液模型系统的研究，该模型系统具有将这些中心问题纳入系统的优点，其中管理动态具有明确的物理基础。这有利于发展的数学技术的有效行为的一组非线性相互作用的代理商与噪声功能。这项研究还与教育和外联工作相结合。支持的研究生将由PI的跨学科团队共同指导，使他或她接触到先进的数学方法，高质量的计算模拟和实际的工程应用。该项目正在通过伦斯勒的PREFACE方案，努力鼓励代表性不足的群体。

The supported work will develop new theoretical and computational approaches to describing the effective coarse-grained stochastic dynamics of noisy, nonlinearly interacting agents in a physically well-grounded model system: suspensions of swimming microorganisms (microswimmers). The dynamics exhibit highly disordered behavior, with long-ranged statistical correlations observed in direct numerical simulations. Yet most theoretical work has been based on deterministic methods such as mean field theories for the effective behavior. The primary goal of the supported work is to incorporate the role of noise in the dynamics into a systematic statistical theory for the effective dynamics of the interacting microswimmers. Two central issues to be addressed are: (1) a rational framework for parameterizing the noise of a sampled swimmer in a self-consistent statistical field theory, and (2) the incorporation of correlations between microswimmers in an effective statistical field theory.Many complex systems use interactions or communication to produce an emergent behavior of the group. A key goal is to better understand how those interactions can change the effective dynamics of the individuals, and thereby the group. Examples include wide varieties of swarms of insects, colonies of bacteria, flocks of birds, herds of animals, as well as engineered systems such as autonomous robotic devices which communicate information and status to each other in pursuit of a goal or target. These applications involve not only the interaction of a large number of agents, but also typically noise in the environment, motion, and/or communication. This grant supports research on a model system of suspensions of swimming microorganisms (microswimmers) which has the virtue of incorporating these central issues in a system where the governing dynamics have a clearly defined physical basis. This facilitates the development of the mathematical technology regarding the effective behavior of a group of nonlinearly interacting agents with noisy features. The research is also coupled with efforts on education and outreach. The supported graduate student will be co-mentored by the interdisciplinary team of PIs, exposing him or her to advanced mathematical methods, high quality computational simulations, and practical engineering applications. This project is being used in efforts to encourage under-represented groups through the PREFACE program at Rensselaer.