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Authors: Timo Hanke, Christoph A. Weber, Erwin Frey
Dynamic, biologically inspired models for driven colloidal particles display a wide variety of collective patterns such as swarming clusters and vortex formation. In these models, particles interact via strong attracting and repulsive forces giving rise to velocity alignment [1-3]. However, similar collective behavior can also emerge in a minimal model of isotropic agents solely due to inelastic collisions [4]. Here we present a detailed study and comparison of various dynamic swarming models [1-4], and restrict to the case of weak repulsive interactions between the soft colloidal particles. By means of a binary scattering study we show that the basic alignment mechanisms are identical for a range of dynamic swarming models [1-3]. We investigate the ensuing collective phenomena and present a detailed phase diagram that depends on density and noise amplitude. In addition to the well-known transition to collective motion - the existence of clusters and bands - we find a second transition to a jammed state. Below the jamming threshold we discover a strong increase of the time required to develop a bulk polar state. Moreover, we analyze the polar patterning process in detail: We report the existence of force chains reminiscent of similar observations in passive systems as foams and glasses. To characterize the dynamics of these force chains we determine their velocity distribution and characteristic damping time scale. [1] H. Levine, W.-J. Rappel and I. Cohen. Self-organization in systems of self-propelled particles. Physical Review E, 63:017101, 2000. [2] Alexander S. Mikhailov, Damian H. Zanette. Noise-induced breakdown of coherent collective motion in swarms. Physical Review E, 60, 1999. Udo Erdmann, Werner Ebeling, and Alexander S. Mikhailov. Noise-induced transition from translational to rotational motion of swarms. Physical Review E, 71:051904, 2005. Yao-li Chuang, Maria R. D'Orsogna, Daniel Marthaler, Andrea L. Bertozzi, and Lincoln S. Chayes. State transitions and the continuum limit for a 2d interacting, self- propelled particle system, Physica D 232, 2007. [3] Benno Tilch, Frank Schweitzer, Werner Ebeling: Directed motion of Brownian particles with internal energy depot, Physica A 273, 1999. Robert Mach and Frank Schweitzer. Modeling vortex swarming in Daphnia, Bulletin of Mathematical Biology, 69:539-562, 2007. [4] D. Grossman, I. S. Aranson, and E. Ben Jacob. Emergence of agent swarm migration and vortex formation through inelastic collisions. New Journal of Physics, 10, 2008. |
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