Dimensionality reduction of a multistable, stochastically forced coarse-grained active fluid: a weakly nonlinear approach.

An active matter system is a collection of discrete agents, each dissipating energy on its own ''microscopic'' scale in the bulk, thus having irreversible dynamics. This definition includes all systems whose constituents are motile (self-propelled), for instance, bird flocks, bacterial solutions, etc... It has become increasingly clear that interactions between the microscopic constituents, whether they are direct or indirect (through the medium), could translate into collective dynamics at the macroscopic level. 

Active matter systems can exhibit spontaneous reorganization from one state to another. These reorganizations can result from random fluctuations making the system transition from one stable state to another. Transitions are increasingly rare as the intensity of the fluctuations is weak. Such transition phenomena remain particularly complicated to study analytically, due to the generally large number of degrees of freedom and the out-of-equilibrium nature of the considered systems.

This talk will focus on the coarse-grained version of the Saintillan-Shelley model for dilute suspension of active particles. It was shown by Ohm and Shelley (2022) that multiple stable steady states, where the particles exhibit a coherent preferred orientation over some regions of space, can co-exist. This co-existence of stable solutions can lead to fluctuations-induced transitions in this active suspension system. We aim at computing these rare transition statistics and associated instanton trajectories.

For that purpose, we will generalize the mathematical technique used by Ohm and Shelley (2022) for the reduction of the original model to a minimal-order system, to a case where the former is subject to stochastic forcing. Crucially, the low dimensionality of the reduced system makes it possible to establish noise-induced transition statistics at an extremely low numerical cost. Then, the Adpative Multilevel Algorithm from Cérou and Guyader (2007), will be implemented directly on the coarse-grained version of the Saintillan-Shelley model (without prior dimensionality reducing, thus relaxing the hypothesis made in the first part), and the results from both approaches are compared.