Bifurcation diagram for compartmentalized granular gases

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The bifurcation diagram for a vibrofluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution ~in which the gas is equi-partitioned over the compartments! is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N52, this transition takes place via a pitchfork bifurcation but for all N.2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multipeaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.
Original languageEnglish
Article number061304
Number of pages9
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Issue number6
Publication statusPublished - 2001


  • IR-36522
  • METIS-202180


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