Particle, kinetic, and hydrodynamic models of swarming

  • José A. Carrillo
  • Massimo Fornasier
  • Giuseppe Toscani
  • Francesco Vecil
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individual-based models based on “particle”-like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the modelling, in the derivation of continuum models and in the understanding of the complex behavior of the system.


Kinetic Model Boltzmann Equation Kinetic Theory Hydrodynamic Model Particle Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • José A. Carrillo
    • 1
  • Massimo Fornasier
    • 2
  • Giuseppe Toscani
    • 3
  • Francesco Vecil
    • 2
  1. 1.ICREA - Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)LinzAustria
  3. 3.Department of MathematicsUniversity of PaviaPaviaItaly

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