Olsson Peter, Teitel S
Department of Physics, Umeå University, 901 87 Umeå, Sweden.
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
Phys Rev E. 2020 Oct;102(4-1):042906. doi: 10.1103/PhysRevE.102.042906.
We carry out 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, ξ and ℓ, 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 ℓ is a consequence of a dangerous irrelevant scaling variable and that it is ξ, 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 ξ∼(ϕ_{J}-ϕ)^{-ν} diverges with the critical exponent ν=1. We provide evidence that ξ measures the length scale of fluctuations in the rotation of the particle velocity field, while ℓ measures the length scale of fluctuations in the divergence of the velocity field.
我们对二维热剪切、双分散、无摩擦圆盘进行了数值模拟。从适当定义的速度相关函数出发，我们确定，随着接近堵塞转变，存在两个发散的长度尺度，ξ 和 ℓ。我们使用相关函数的临界标度假设来分析结果，并认为更发散的长度 ℓ 是一个危险的无关标度变量的结果，而 ξ 才是相关长度，它决定了在液相中从下方接近堵塞时系统粘度的发散。我们发现 ξ∼(ϕ_J - ϕ)^(-ν) 以临界指数 ν = 1 发散。我们提供的证据表明，ξ 测量的是粒子速度场旋转波动的长度尺度，而 ℓ 测量的是速度场散度波动的长度尺度。
