Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics

Frank Schweitzer, Werner Ebeling, and Benno Tilch
Phys. Rev. E 64, 021110 – Published 27 July 2001
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Abstract

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the takeup/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of nonequilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e., for active motion, and (b) interactions between the particles based on global couplings. We derive analytical expressions for the nonequilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.

  • Received 16 March 2001

DOI:https://doi.org/10.1103/PhysRevE.64.021110

©2001 American Physical Society

Authors & Affiliations

Frank Schweitzer*

  • Real World Computing Partnership—Theoretical Foundation, GMD Laboratory, Schloss Birlinghoven, 53754 Sankt Augustin, Germany

Werner Ebeling

  • Institute of Physics, Humboldt University, Invalidenstraße 110, 10115 Berlin, Germany

Benno Tilch

  • II. Institute of Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57/III, D-70550 Stuttgart, Germany

  • *Electronic address: schweitzer@gmd.de http://ais.gmd.de/∼frank/
  • Electronic address: ebeling@physik.hu-berlin.de http://summa.physik.hu-berlin.de/tsd/
  • Electronic address: benno@theo2.physik.uni-stuttgart.de http://www.theo2.physik.uni-stuttgart.de/

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Issue

Vol. 64, Iss. 2 — August 2001

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