![]() ![]() There exists empirical evidence supporting both metric and topologic interactions 3, 4, 7, 24, 25, 26, and which kind is present strongly depends on the nature of the particles the system is made of 1. 1(a)), or topologically where particles interact with a fixed number α l of their first neighbors regardless of their relative distance (like in Ballerini et al., see Fig. ![]() These short-range interactions can be defined either metrically, where each particle interacts with all others within some distance r 0 (like in the standard Vicsek model, see Fig. Most of these models are based on local (or short-range) alignment interactions where individuals modify their direction of motion to match the average direction of their immediate neighbors, plus some noise 11, 22, 23. In these, the main problem has been to determine the nature of the interactions between particles and the mechanisms needed for the system to build up states of collective motion. In the last decades, various models of collective motion have been proposed and a number of studies have been carried out, both theoretical 10, 11, 12, 13, 14, 15, 16, 17 and empirical 4, 18, 19, 20, 21. To the best of our understanding, most of the flocking models that have been proposed describe the mechanisms that generate spontaneous coordinated motion during relatively short periods of time without considering the ultimate long-term goal of such collective motion. However, even in the clear cases in which the reason is migration, this activity can last days or weeks, and in the meantime the group has to remain together. As far as we know, there is no consensus among biologist about the evolutionary reasons for the collective motion of many species, although for some other species the reasons are as diverse as cannibalism for cannibal locust 7, foraging for monkeys 8, 9 or migration for ducks and monarch butterflies. Starling flocks and fish schools also display collective motion which is not necessarily consistent with migration, foraging or looking for a suitable habitat 4, 5, 6. For example, marching locusts, when placed within a 2D circular track start moving in a collective way at high enough density, without any apparent long-term goal such as migration or foraging 3. While the long-term goal of the collective motion of many species of animals is to forage or migrate, this is not always the case. The coordinated motion of the system as a whole, where all individuals form a localized group in space and move approximately in the same direction, is an emergent property resulting from the interactions between all the individuals (or “particles”) comprising the system. This finding was verified for other models in addition to the Vicsek one, suggesting its generality and revealing the importance that long-range interactions can have for the cohesion of the flock.Ĭollective motion is one of the most spectacular displays of coordinated behavior in nature, exhibited by systems of very different kinds, ranging from cell populations to various species of insects and vertebrates, such as flocks of starlings, sheep herds, fish shoals and human crowds 1, 2. We show that just a small number of these interactions is enough for the system to build up long lasting ordered states of collective motion in open space and in the presence of noise. Here we extend the Vicsek model of collective motion by introducing long-range alignment interactions between the particles. While the phase transition has been thoroughly studied, the conditions to keep the flock cohesive in open space are still poorly understood. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |