One motivation of the study of active matter by physicists is the rich phenomenology associated to this field.
[1] Physicists have a great interest in this model as it is minimal and describes a kind of universality.
It consists in point-like self-propelled particles that evolve at constant speed and align their velocity with their neighbours' one in presence of noise.
Such a model shows collective motion at high density of particles or low noise on the alignment.
As this model aims at being minimal, it assumes that flocking is due to the combination of any kind of self propulsion and of effective alignment.Since velocities of each particle is a constant, the net momentum of the system is not conserved during collisions.
The average normalized velocity acts as the order parameter for this system, and is given by
The whole model is controlled by three parameters: the density of particles, the amplitude of the noise on the alignment and the ratio of the travel distance
An Enskog-like kinetic theory, which is valid at arbitrary particle density, has been developed.
At large noise or low density, particles are on average not aligned, and they can be described as a disordered gas.
At low noise and large density, particles are globally aligned and move in the same direction (collective motion).
In the co-existence region, finite-size liquid bands[7] emerge in a gas environment and move along their transverse direction.
Recently, a new phase has been discovered: a polar ordered Cross sea phase of density waves with inherently selected crossing angle.
[8] This spontaneous organization of particles epitomizes collective motion.
Since its appearance in 1995 this model has been very popular within the physics community; many scientists have worked on and extended it.
For example, one can extract several universality classes from simple symmetry arguments concerning the motion of the particles and their alignment.
[9] Moreover, in real systems, many parameters can be included in order to give a more realistic description, for example attraction and repulsion between agents (finite-size particles), chemotaxis (biological systems), memory, non-identical particles, the surrounding liquid.