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Bifurcation Diagram for Compartmentalized Granular Gases

Devaraj van der Meer·Ko van der Weele·Detlef Lohse
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Abstract

The bifurcation diagram for a vibro-fluidized 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, N=2, 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 multi-peaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.

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Devaraj van der Meer, Ko van der Weele, Detlef Lohse. 2001-03-15. Bifurcation Diagram for Compartmentalized Granular Gases. https://doi.org/10.1103/physreve.63.061304

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