Transitions and optimal self-organization in the collective motion in driven systems

Vicsek, Tama´s; Helbing, Dirk; Cziro´k, Andra´s
February 2000
AIP Conference Proceedings;2000, Vol. 501 Issue 1, p273
Academic Journal
Organisms moving in the same environment typically self-organize into coherently moving groups. This grouping can be successfully described using simple models of driven particles for collective motion. Here we discuss simulations of flocking and a principle related to driven motion in general for which, as an example, the motion of humans in a corridor is used. We treat the collective motion of organisms in the presence of fluctuations. In our models the particles corresponding to organisms locally interact with their neighbors by choosing at each time step a velocity depending on their positions. i) Numerical studies of our models of flocking indicate the existence of new types of transitions. Depending on the control parameters both disordered and long-range ordered phases can be observed, and the corresponding phase space domains are separated by singular “critical lines.” In particular, we demonstrate both numerically and analytically that there is a disordered to ordered motion transition at a finite noise level even in one dimension. ii) We present computational and analytical results indicating that driven systems with repulsive interactions tend to reach an optimal state corresponding to minimal interaction and minimal dissipation. The associated extremal principle is expected to be relevant for biological or social systems involving entities interacting due to their driven motion. © 2000 American Institute of Physics.


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