van der Meer D, van der Weele K, Lohse D
Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Jun;63(6 Pt 1):061304. doi: 10.1103/PhysRevE.63.061304. Epub 2001 May 18.
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, 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 multipeaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.
构建并讨论了处于 N 个相连隔室中的振动流化颗粒气体的分岔图。在剧烈驱动下，均匀分布（气体在各隔室中均匀分配）是稳定的。但当驱动强度降低时，这种均匀分布变得不稳定，并让位于聚集状态。对于最简单的情况，N = 2，这种转变通过叉形分岔发生，但对于所有 N>2 的情况，转变涉及鞍结分岔。随着 N 的增加，相关的滞后现象变得越来越明显。在分岔图中，除了均匀分布和单峰分布外，还出现了许多多峰解。这些是瞬态。在稳定性分析的背景下讨论了它们的物理相关性。
