91福利

The Physics of Swarming

Swarming is a non-equilibrium phenomenon observed in several animal species, including insects, birds, fish and mammals. In spite of this our understanding of the process is actually remarkably undeveloped. To a physicist the ordering is reminiscent of that found elsewhere in nature, e.g. in liquid crystals. Most models involve members of a swarm aligning their velocities with those of their immediate neighbours’ (plus some noise). However, both metric-based and metric-free versions of these local models have fundamental pathologies that are frequently overlooked, e.g. the swarm evaporates in the absence of an ad hoc long-range attraction unless confined within an artificial box. We discuss how individuals might respond to a projection of the swarm and argue why this is biologically plausible. A simple class of candidate models then arises naturally in which there is a single additional scalar parameter controlling the tendency of all individuals to fly in a direction that is characteristic of the particular projection pattern that they see. This naturally leads to swarms that remain localized. We identify a surprisingly rich variety of phenotypical behaviour that is reminiscent of birds, fish and insects. An intriguing emergent property also appears - swarms self-select a particular density at which they are marginally opaque. We argue that this property is seen in bird flocks. It implies a non-trivial scaling relationship between the swarm density and the number of individuals: in 2D and in 3D. We argue that some evidence for such scaling already exists. This model therefore makes several experimentally testable predictions. It may even provide a mechanism for classifying the behaviour of different swarming animals according to the relative strength of their alignment and projection terms. Finally, it would also appear to provide emergent biological fitness, given that marginal opacity provides for rapid, long-range information transfer, another feature not present in local models with diffusive dynamics.