Dynamic length scales in athermal, shear-driven, jamming of frictionless disks in two dimensions

Abstract

We carry our numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, $\xi$ and $\ell$, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function, and argue that the more divergent length $\ell$ is a consequence of a dangerous irrelevant scaling variable, and that it is $\xi$ which is the correlation length that determines the divergence of the system viscosity as jamming is approached from below in the liquid phase. We find that $\xi \sim ({\varphi }_J-\varphi {)}^{-\nu }$ diverges with the critical exponent $\nu =1$. We provide evidence that $\xi$ measures the length scale of fluctuations in the rotation of the particle velocity field, while $\ell$ measures the length scale of fluctuations in the divergence of the velocity field.

12 pages, 14 figures; updated to published version

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• Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations
• Relaxation dynamics and long-time tails explain shear-induced diffusion of soft athermal particles near jamming
• Gradient descent dynamics and the jamming transition in infinite dimensions