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Flocking, the collective motion of systems consisting of many agents, is a ubiquitous phenomenon in nature, observed both in biological and artificial systems. The understanding of such systems is important from both a theoretical point of view, as it extends the field of statistical physics to non-equilibrium systems, and from a practical point of view, due to the emergence of applications that are based on the modelling. In the present thesis I numerically investigated several aspects of flocking dynamics, simulating systems consisting of up to millions of particles. One first problem I worked on regarded the flocks response to external perturbations, something that had received little attention so far. The result was a scaling relation, connecting the asymptotic response of a flock to the strength of the external fleld affecting it. Additionally, my preliminary results point towards a generalised fluctuation-dissipation relation for the short-time response, with two different effective temperatures depending on the direction at which the perturbing field is applied. Another aspect I studied was the stability and dynamical properties of non-confined active systems (finite flocks in open space). The results showed that these flocks are stable only when an attracting 'social force' keeps the agents from drifting away from each other. The velocity fluctuations correlations were found to be different than the asymptotic limit predictions of hydrodynamic theories for infinite flocks. Finally, I studied the clustering dynamics of flocking systems. The conclusion was that the non-equilibrium clustering in the ordered phase is regulated by an anisotropic percolation transition, while it does not drive the order-disorder transition, contrary to earlier conjectures. I believe the results of this work answer some important questions in the field of ordered active matter, while at the same time opening new and intriguing ones, that will hopefully be tackled in the near future. |
