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.
