Collective dynamics and patterns of rapid granular fluid and amplitude equation


It is known that the spatial and temporal distortions of uniform flow can be described by the amplitude equation formalism which is based on the fact that near the onset the evolution of slowly varying distortions of periodic patterns can be described qualitatively by the amplitude equation. Using this amplitude approach, the collective dynamics of sheared and vibrated granular materials will be discussed in the first part of talk. In the second part, the effects of three-dimensional perturbation on the nonlinear states of five types of linear instability modes, the nature of their bifurcations and the resulting nonlinear patterns will be discussed for granular plane shear flow using a Landau type amplitude equation. For all instabilities, the vortical motion on the cross-stream plane will be presented in terms of the critical points (source, sink, spiral, saddle, etc.) of the underlying flow.

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