Collaborative Research: Hierarchical kinetic models for chemically and hydrodynamically coupled organisms

这个项目发展了自推进粒子动力学理论的数学基础。 一个动力学理论的方法是用来描述的概率密度的位置和速度的所有粒子。数学分析改编自用于描述分子集合的理论，包括自推进。 由此产生的方程提供了一种方法，通过它的统计特性的流体动力学相互作用，自推进粒子的集合可以计算。 使用这些方法，自推进粒子的动力学的三个属性进行了探索-他们的流体动力学耦合，他们的出生和死亡，他们与boundarys.The自推进粒子的动力学是一个物理模型相关的范围广泛的现实世界的系统，包括动物群集，细菌游泳，和多机器人合奏。 需要新的、更有效的数学工具来有效地计算粒子群的主要性质。该项目使用动力学理论开发此类工具，其中函数描述每个粒子具有特定位置和速度的概率。 这些功能服从的方程推导和他们的解决方案进行了探索和分析。 使用适当的方程，研究人员研究粒子如何通过共同的流体环境相互耦合，粒子如何湮灭和复制，以及粒子在固体边界附近的行为。 在这个项目中获得的洞察力的应用包括潜在的机械理解细菌生物膜如何形成，水生生物如何优化它们的游泳，以及如何更好地控制一系列通信的人造机器人，如自主海洋车辆。

This project develops the mathematical foundations underlying the kinetic theory of self-propelled particles. A kinetic theory approach is used to describe the probability densities of the positions and velocities of all the particles. The mathematical analysis is adapted from theories used to describe ensembles of molecules, to include self-propulsion. The resulting equations provide a means by which statistical properties of a collection of hydrodynamically interacting, self-propelled particles can be computed. Using these methods, three properties of the dynamics of self-propelled particles are explored--their hydrodynamic coupling, their birth and death, and their interactions with boundaries.The dynamics of self-propelled particles is a physical model relevant to a wide range of real-world systems including animal swarming, bacterial swimming, and multi-robot ensembles. New, more efficient mathematical tools are needed to efficiently compute the main properties of swarms of particles. This project develops such tools using kinetic theory, in which functions describing the probabilities of each particle having a certain position and velocity. Equations that these functions obey are derived and their solutions explored and analyzed. Using the appropriate equations, the investigators study how particles couple to each other through their common fluid environment, how particles annihilate and reproduce, and how particles behave near solid boundaries. Applications of the insight gained during this project include potentially a mechanistic understanding of how bacterial biofilms form, how aquatic organisms optimize their swimming, and how a collection of communicating man-made robots, such as autonomous marine vehicles, can be better controlled.