Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA.
Phys Rev Lett. 2011 Aug 12;107(7):078301. doi: 10.1103/PhysRevLett.107.078301.
Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N→∞) for all compressions Δϕ studied, and at jamming onset Δϕ→0 for all N. We perform fixed energy simulations following perturbations with amplitude δ along eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈δ(c) (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ > δ(c), all discrete modes disappear into a continuous frequency band. <δ(c)> scales with 1/N and Δϕ, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.
许多被堵塞的颗粒体系，如颗粒和胶体材料，通过排斥接触力相互作用。我们发现，在所有研究的压缩率 Δϕ 下，这些体系在大体系极限（N→∞）下没有简谐模式，对于所有的 N，在堵塞起始点 Δϕ→0 时也没有。我们沿着动力学矩阵的本征方向，对具有振幅 δ 的扰动进行固定能量模拟。与线性和弱非线性行为相反，在 δ≈δ(c)（其中一个接触断开）时，波动会突然扩散到所有模式。对于 δ > δ(c)，所有离散模式都会消失在一个连续的频带中。<δ(c)>与 1/N 和 Δϕ 成比例，这将简谐行为限制在仅过压缩系统中。当系统进入非简谐状态时，振动模式的密度与动力学矩阵预测的密度有很大的偏离，这会显著影响其力学和输运性质。
