Phases and phase transitions in ocking systems (Yuhai Tu)

IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
Abstract:  In this paper, we briefly review some recent theoretical and numerical progress in understanding flocking dynamics. On the theoretical side, a continuum model has been successfully used in explaining the hydrodynamic properties of the flock dynamics. In particular, the long-range ordered state has been shown to be stable even in two dimensions. On the numerical side, study of a discrete model which includes both body force interaction and alignment force reveals a very rich phase diagram. The potential of such models in describing finite flocks is discussed. In the end, we list some unanswered questions and new directions for future studies.
(c) 2000 Published by Elsevier Science B.V. All rights reserved.

Collective motion of organisms in three dimensions (Andras Cziroka; Maria Vicsek, Tamas Vicsek)

Department of Biological Physics, Etvos University, Budapest; Department of Computer Science, Budapest University of Economics; Budapest,
Abstract: We study a model of flocking in order to describe the transitions during the collective motion of organisms (e.g., birds) in three dimensions. In this model the particles representing the organisms are self-propelled, i.e., they move with the same absolute velocity. In addition, the particles locally interact by choosing at each time step the average direction of motion of their neighbours and the eects of fluctuations are taken into account as well. We present the first results for large-scale flocking in the presence of noise in three dimensions. We show that depending on the control parameters both disordered and long-range ordered phases can be observed. The corresponding phase diagram has a number of features which are qualitatively dierent from those typical for the analogous equilibrium models.
(c) 1999 Elsevier Science B.V. All rights reserved.