Slow time scales in a dense vibrofluidized granular material

Abstract

Modeling collective motion in non-conservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed the evidence of many time scales: fast ballistic, intermediate caged, slow superdiffusive, very slow diffusive. A numerical investigation has demonstrated that tracer's superdiffusion is related to slow rotating drifts of the granular medium. Here we offer a deeper insight into the slow scales of the granular medium, and propose a new phenomenological model for such a "secular" dynamics. Based upon the model for the granular medium, we also introduce a model for the tracer (fast and slow) dynamics, which consists in a stochastic system of equations for three coupled variables, and is therefore more refined and successful than previous models.

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• Collective drifts in vibrated granular packings: the interplay of friction and structure
• Reducing segregation in vibrated binary-sized granular mixtures by excessive small particle introduction
• Statistical features of systems driven by non-Gaussian processes: theory & practice
• Self-assembly and non-equilibrium phase coexistence in a binary granular mixture
• Enhancing the accuracy of a data-driven reconstruction of bivariate jump-diffusion models with corrections for higher orders of the sampling interval
• Hydrodynamics of simple active liquids: the emergence of velocity correlations