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一个物理基础良好的模型系统中有噪声的、非线性相互作用的有效粗粒度随机动力学：游泳微生物（微游泳者）的悬浮液。动力学表现出高度无序的行为，在直接数值模拟中观察到长期的统计相关性。然而，大多数理论工作都是基于确定性方法，如有效行为的平均场理论。支持工作的主要目标是将噪声在动力学中的作用纳入一个系统的统计理论，用于相互作用的微游泳者的有效动力学。需要解决的两个核心问题是：(1)在自洽统计场理论中参数化采样游泳者噪声的合理框架；(2)在有效的统计场理论中纳入微游泳者之间的相关性。许多复杂的系统使用交互或通信来产生群体的紧急行为。一个关键的目标是更好地理解这些相互作用如何改变个人的有效动态，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，它们在追求一个目标或目标时相互传递信息和状态。这些应用程序不仅涉及大量代理的交互，而且还涉及环境、运动和/或通信中的典型噪声。该基金支持对游动微生物（微游泳者）悬浮液模型系统的研究，该模型系统的优点是将这些核心问题纳入一个控制动力学具有明确定义的物理基础的系统中。这促进了关于一组具有噪声特征的非线性相互作用主体的有效行为的数学技术的发展。这项研究还与教育和推广工作相结合。支持的研究生将由跨学科的pi团队共同指导，让他或她接触先进的数学方法，高质量的计算模拟和实际的工程应用。这个项目正在通过伦斯勒大学的前言项目来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.