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.
|Number of pages||9|
|Journal||Physical review E: Statistical, nonlinear, and soft matter physics|
|Publication status||Published - 2001|
van der Meer, D., van der Weele, K., & Lohse, D. (2001). Bifurcation diagram for compartmentalized granular gases. Physical review E: Statistical, nonlinear, and soft matter physics, 63(6), . https://doi.org/10.1103/PhysRevE.63.061304