Dynamics of a first order transition to an absorbing state

Abstract

A granular system confined in a quasi two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can be reached for any density lower than the one corresponding to one complete monolayer, which is then the critical density. Below this critical value, the transition to the absorbing state is of first order, with long metastable periods, followed by rapid transitions driven by homogeneous nucleation. Molecular dynamics simulations and experiments show that there is a dramatic increase on the metastable times far below the critical density; in practice, it is impossible to observe spontaneous transitions close to the critical density. This peculiar feature is a consequence of the non-equilibrium nature of this first order transition to the absorbing state. A Ginzburg-Landau model, with multiplicative noise, describes qualitatively the observed phenomena and explains the macroscopic size of the critical nuclei. The nuclei become of small size only close to a second critical point where the active phase becomes unstable via a saddle node bifurcation. It is only close to this second critical point that experiments and simulations can evidence spontaneous transitions to the absorbing state while the metastable times grow dramatically moving away from it.

14 pages, 18 figures. Accepted in Phys. Rev. E

References in corpus (1)

• Directed percolation criticality in turbulent liquid crystals

Cited by in corpus (16)

• Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states
• (Ir)reversibility in dense granular systems driven by oscillating forces
• Enhancing (quasi-)long-range order in a two-dimensional driven crystal
• Critical Phenomena in Quasi-Two-Dimensional Vibrated Granular Systems
• Interplay between an absorbing phase transition and synchronization in a driven granular system
• Finite-size scaling for discontinuous nonequilibrium phase transitions
• The pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres
• Homogeneous dynamics in a vibrated granular monolayer
• Reducing segregation in vibrated binary-sized granular mixtures by excessive small particle introduction
• Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks
• Attractor non-equilibrium stationary states in perturbed long-range interacting systems
• A simple mechanism leading to first-order phase transitions in a model of tax evasion
• Confined granular gases under the influence of vibrating walls
• Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
• Noise induces rare events in granular media
• Diffusion and velocity correlations of the phase transitions in a system of macroscopic rolling spheres