Stochastic Active Flows

Abstract

This thesis contains novel results on stochastic interacting particle systems pertaining to mesoscopic fluctuations as well as noise-induced synchronisation at the macro scale.

At the macro scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite, simulations of corresponding microscopic dynamics exhibit stochastic effects which can induce a variety of interesting behaviours not present in the large system limit. This thesis contains a systematic examination of finite-size fluctuations in a general class of particle models whose statistics correspond to those of stochastic kinematic flows. Doing so, we are able to characterise phenomena including: anomalous bulk sub-diffusion in porous media; and travelling wave fluctuations in a model of bacterial swarming.

Another application of stochastic kinematic flows is in modelling vehicle traffic. When a new vehicle joins a lane, those behind may have to temporarily slow to accommodate them. Changing lane can be forced due to lane drops or junctions, but may also take place spontaneously at discretion of drivers, and recent studies have found that traffic jams and traffic oscillations can form even without such bottlenecks. We extend the model of interacting particles to allow stochastic lane changes. In this instance we find a consistent bias towards lower velocities than a system without lane changes. By extending the model to three lane traffic we find a larger impact on the flow of the middle lane compared to the side lanes.

A common application of stochastic interacting particle systems is in the study of synchronisation phenomena. Typically, these systems rely on deterministic coupling or common forcing to induce global synchronisation. The addition of intrinsic noise to such models typically serves to drive disorder, increasing the stability of the incoherent state. Through our general model of interacting particles we show that the reverse is also possible. We propose and analyse a simple model of purely noise coupled oscillators whose linear response around incoherence is identical to that of the paradigmatic Kuramoto model, but which exhibits binary phase locking instead of full coherence.

Date of Award	27 Mar 2024
Original language	English
Awarding Institution	University of Bath
Supervisor	Tim Rogers (Supervisor) & Paul Milewski (Supervisor)