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Department of Mathematics pres.

Applied Interdisciplinary Mathematics (AIM) Seminar

Levitating granular cluster: typical behavior and noise-induced rare events

Granular matter is ubiquitous in nature and exhibits a variety of nontrivial phenomena. In addition, granular medium is intrinsically far from equilibrium, as particles collide inelastically, and a continuous energy input is required to ensure a steady state. Within the same system, different regions of granular media can be at a solid or a gas phase. Here we focus on a granular Leidenfrost effect: a solid-like cluster is levitating above the "hot" granular gas [1]. This state was observed experimentally, when granular matter was vertically vibrated in a two-dimensional container [2]. The solid-gas coexistence can be described by using granular hydrodynamics with the properly measured transport coefficients [3]. We performed extensive molecular dynamics simulations of a simple model of inelastic hard spheres driven by a "thermal" bottom wall. Simulations showed that for low wall temperatures, the levitating cluster is stable, while for high wall temperatures, it breaks down, and the hot gas bursts out resembling a volcanic explosion [4]. We found a hysteresis: for a wide range of bottom wall temperatures, both the clustering state and the broken state are stable. However, even if the system is at the (stable) clustering state, a "volcanic explosion" is possible: it is a rare event driven by large fluctuations. We used techniques from the theory of rare events to compute the mean time for cluster breaking to occur; this required the introduction of a two-component reaction coordinate [4].

[1] B. Meerson, T. Pöschel, and Y. Bromberg, Phys. Rev. Lett. 91, 024301 (2003).
[2] P. Eshuis, K. van der Weele, D. van der Meer, and D. Lohse, Phys. Rev. Lett. 95, 258001 (2005); N. Rivas, A.R. Thornton, S. Luding, and D. van der Meer, Phys. Rev. E 91, 042202 (2015).
[3] E. Khain, Phys. Rev. E 98, 012903 (2018).
[4] E. Khain and L. M. Sander, Phys. Rev. E 94, 032905 (2016).
Speaker(s): Evgeniy Khain (Oakland University)

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