New Stochastic Field Theory for Understanding Active Matter

The out-of-equilibrium nature of active matter can give rise to interesting properties in both small and large concentrations of the active objects. This includes local and global correlations between active particles and enhanced fluctuations and mixing. It is important to understand how hydrodynamic interactions between active agents cause and/or alter the suspension properties. Agent based models can incorporate fluctuations and interactions, but are limited to smaller systems. It can also more difficult to extract physical insight from the results. One of the most successful alternative approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing even in conditions where there is no large-scale group behavior.