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Propagative Mode in a Lattice-Grain CA: Time Evolution and Timestep Synchronization

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7495)

Abstract

The void propagation defines a long-range interaction in granular matter. We detail a logic scheme simulating the propagation and implemented in a 2d cellular automata applied to granular flow. The CA belongs to the family of “lattice-grain” automata (LGrA) with one particle per cell. We focus first on the influence of inertia, or “memory effect”, on the flow patterns. The propagative mode is presented afterwards: it implies that transition and timestep must be considered at two different time scales. Although a CA is usually driven by local, nearest-neighbor communications, it follows here that the timestep termination must be detected at each transition, that involves a perpetual and global communication within the network to synchronize the timestep. An all-to-all “systolic gossiping” underlies the framework of this void propagation model.

Keywords

  • lattice-grain (cellular) automata (LGrA)
  • void propagation
  • memory effect
  • time evolution
  • timestep synchronization
  • systolic gossiping

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Désérable, D. (2012). Propagative Mode in a Lattice-Grain CA: Time Evolution and Timestep Synchronization. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-33350-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33349-1

  • Online ISBN: 978-3-642-33350-7

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