Absorbing-State Transitions in Granular Materials Close to Jamming

Abstract

We consider a model for driven particulate matter in which absorbing states can be reached both by particle isolation and by particle caging. The model predicts a non-equilibrium phase diagram in which analogues of hydrodynamic and elastic reversibility emerge at low and high volume fractions respectively, partially separated by a diffusive, non-absorbing region. We thus find a single phase boundary that spans the onset of chaos in sheared suspensions to the onset of yielding in jammed packings. This boundary has the properties of a non-equilibrium second order phase transition, leading us to write a Manna-like mean-field description that captures the model predictions. Dependent on contact details, jamming marks either a direct transition between the two absorbing states, or occurs within the diffusive region.Non-equilibrium phase transitions into absorbing states are of fundamental interest and relevant to applications such as spreading of infectious disease and reaction-diffusion problems [1,2]. Driven granular materials, both semi-dilute (volume fraction φ ≈ 0.1) and jammed (φ > φ J ≈ 0.64 (in 3D)), have proven to be useful experimental systems in which to study such transitions [3,4], but the behaviour close to φ J itself is unclear.In non-Brownian suspensions under oscillatory shear, non-hydrodynamic particle contacts arise above a φdependent critical strain amplitude γ c , moving the system from a Stokesian-reversible state to a chaotic, fluctuating one [3,[5][6][7][8][9]. Meanwhile, jammed packings exhibit a transition from elastic reversibility to plastic cage deformation at a γ c associated with yielding [4, 10-15]. The order parameter for both transitions may be chosen as the fraction A of particles that are 'alive', that is, those whose position changes after successive shear cycles at steady state. For γ > γ c , time-irreversible particle contacts (φ < φ J ) and plastic rearrangements (φ > φ J ) render the systems active: they have diffusion coefficient D > 0, with A > 0 and all particles spending part of the time alive. Below γ c the systems reach absorbing states with A 0 and D = 0 due to hydrodynamic (elastic) reversibility when φ < φ J (φ > φ J ). In absorbing states most particles are never alive, but A need not strictly vanish: isolated per-cycle displacements are permitted provided the system is trapped in a finite basin of the phase space [16].The nonconserved order parameter A carried by a conserved total number of particles, and the existence of multiple symmetry-unrelated absorbing states, should place these systems in the Manna class of non-equilibrium second order phase transitions [17][18][19]. This is borne out below φ J in experiments [6], molecular dynamics simulations [20] and in simplified models in which shear is mimicked by displacing overlapping particles [6,8,21]. Above φ J , however, experimentalists have reported both second [4] and first [22] order behaviour, with simulations [20, 22, 23] consistently predicting the latter. First order behaviour could be due to long-range e...

Mean field theory of yielding under oscillatory shear

“…From the fluid side, our theory predicts that Y vanishes continuously, reminiscent of e.g. the second order transition scenario of [40]. Closer inspection reveals that samples initialized above the threshold energy display critical behaviour at γ * 0 , where the yield rate decays as Y (t) ∼ t −b , with an α-dependent exponent b ≤ 1.…”

Dynamical arrest of topological defects in 2D hyperuniform disk packings

“…Disordered hyperuniformity describes an amorphous state of matter that suppresses variations in the density of particles on large length scales. Hyperuniform patterns can be readily observed in an extensive range of systems at various scales in nature [1][2][3][4][5][6][7][8]. Recently, hyperuniformity has been utilised as a framework to describe glassy states of jammed granular materials [2-4, 6, 8] giving us a deeper understanding of their out-of-equilibrium structures while being maximally disordered yet mechanically rigid.…”

Irreversibility and rate dependence in sheared adhesive suspensions

“…Moreover, we reveal that this rheological behavior in OS is accompanied by enhanced particle diffusivities and cluster formations below a critical shear rate, thus the onset of rate dependence when reducing γ 0 is closely related to the threshold for irreversibility. A deeper understanding of self-organization and dynamical phase transition in suspensions is not only of fundamental interest [12][13][14][15], but has also attracted practical attention due to its applications in hyperuniform photonic materials or suspension flow control [16][17][18]. This letter shows that a physical ingredient up to now neglected, i.e.…”

“…Particularly, in OS, the threshold for irreversibility was found to be gauged by a φ-dependent critical strain amplitude γ c 0 (φ): for γ 0 > γ c 0 , suspensions are irreversible with non-vanishing effective diffusivities, D i = (∆ i /a) 2 /2γ tot (∆ i denotes the particle displacement in any spatial direction i at integer-period intervals); for γ 0 < γ c 0 , the dynamics evolve towards absorbing states with D i ≈ 0 in finite time. The system undergoes a continuous phase transition (likely conserved directed percolation [15]) at γ 0 = γ c 0 , indicated by a nonzero order parameter f ∞ a based on the mean fraction of actively colliding particles. This theoretical framework [2] applies to a remarkable variety of situations, see e.g.…”