Interplay between an absorbing phase transition and synchronization in a driven granular system

Abstract

Absorbing phase transitions (APTs) are widespread in non-equilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in non-equilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2d vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

Figures (3)

• Figure 1: Numerical quasi-2d geometry used in realistic simulations. A vertical displacement $z_p(t)$ is imposed on the box in order to provide external energy to the system. Because of tangential frictional forces, the grains lose horizontal energy during collisions with the top and bottom walls. During non-planar collisions between grains, the vertical energy gained from the vibration of the plate is transferred to the $xy$ components of the velocities of the particles.
• Figure 2: Horizontal kinetic energy in the steady state as a function of $\phi$ for $h=1.88\sigma$ (a), $h=1.63\sigma$ (b) and different vibration amplitudes. c) Synchronization map in the $\{A,h\}$ parameter space. We note that the degree of synchronization $s$ exhibits a non-monotonous behaviour as a function of both $A$ and $h$. Simulations are performed with $N=10^{3}$ grains.
• Figure 3: Comparison between the theory and simulations. Effect of synchronization over the nature of transition and the critical packing fraction: $N = 20000$, $\hat{\tau}\Delta/\sigma = 0.025$, $\alpha = 0.95$ and $\hat{\tau}\gamma = 0.01$. The inset is a semi-log window of the small density behavior of the theory and simulation for the case without synchronization. The dashed vertical line represents the critical packing fraction predicted from the mean free path argument.