Relaxation dynamics of non-Brownian spheres below jamming

Abstract

We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless spheres below jamming in spatial dimensions $d=2$, $3$, $4$, and $8$, and in the mean-field Mari-Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite $d$ logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all $d$ in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.

11 pages, 8 figures

References in corpus (11)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Microfluidic rheology of soft colloids above and below jamming
• Jamming versus Glass Transitions
• Universal microstructure and mechanical stability of jammed packings
• Jamming Criticality Revealed by Removing Localized Buckling Excitations
• Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
• Dynamic criticality at the jamming transition
• Critical Scaling of Shearing Rheology at the Jamming Transition of Soft Core Frictionless Disks
• Diverging viscosity and soft granular rheology in non-Brownian suspensions
• Growing length and time scales in a suspension of athermal particles
• Note: Relaxation time below jamming

Cited by in corpus (10)

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• Correlation of plastic events with local structure in jammed packings across spatial dimensions
• Strain-controlled critical slowing down in the rheology of disordered networks
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Jamming, relaxation, and memory in a structureless glass former
• Critical Scaling of Compression-Driven Jamming of Athermal Frictionless Spheres in Suspension
• Non-Affine Displacements Below Jamming under Athermal Quasi-Static Compression
• Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression
• Gradient descent dynamics and the jamming transition in infinite dimensions
• Relaxation dynamics and long-time tails explain shear-induced diffusion of soft athermal particles near jamming