堵塞的微粒系统本质上是非谐波的
Jammed particulate systems are inherently nonharmonic
摘要：
堵塞的颗粒系统，如颗粒介质，胶体和泡沫，通过单侧力相互作用，只有当颗粒重叠时才不为零。我们发现，系统具有单侧排斥相互作用具有不具有线性响应制度的大系统极限（$N\rightarrow \infty$）的所有压力$p$（或压缩$Δϕ$），并为所有$N$附近的堵塞开始$p\rightarrow 0$。我们进行模拟的2D无摩擦双分散机械稳定的磁盘填料在一个范围内的包装分数$Δϕ= ϕ-ϕ_J$以上的干扰开始$ϕ_J$。我们将幅度为$δ$的扰动应用于动力学矩阵沿每个本征方向的填充，并确定以恒定能量演化的系统的响应是否保持在扰动的原始本征模式中。对于$δ> δ_c$，我们计算分析，一个单一的接触中断和波动突然蔓延到所有的谐波模式。随着$δ$的进一步增加，所有离散的谐波模式都消失在连续的频带中。我们发现，$<δ_c >\sim Δϕ/N^λ$，其中$1 > λ> 0.5$，因此堵塞的颗粒系统是固有的非谐波与没有线性振动响应制度的$N\rightarrow \infty$在整个范围内的$Δϕ$，并作为$Δϕ\rightarrow 0$在任何$N$。
英文摘要：
Jammed particulate systems, such as granular media, colloids, and foams, interact via one-sided forces that are nonzero only when particles overlap. We find that systems with one-sided repulsive interactions possess no linear response regime in the large system limit ($N\rightarrow \infty$) for all pressures $p$ (or compressions $Δϕ$), and for all $N$ near jamming onset $p\rightarrow 0$. We perform simulations on 2D frictionless bidisperse mechanically stable disk packings over a range of packing fractions $Δϕ= ϕ-ϕ_J$ above jamming onset $ϕ_J$. We apply perturbations with amplitude $δ$ to the packings along each eigen-direction from the dynamical matrix and determine whether the response of the system evolving at constant energy remains in the original eigenmode of the perturbation. For $δ> δ_c$, which we calculate analytically, a single contact breaks and fluctuations abruptly spread to all harmonic modes. As $δ$ increases further all discrete harmonic modes disappear into a continuous frequency band. We find that $<δ_c >\sim Δϕ/N^λ$, where $1 > λ> 0.5$, and thus jammed particulate systems are inherently nonharmonic with no linear vibrational response regime as $N\rightarrow \infty$ over the full range of $Δϕ$, and as $Δϕ\rightarrow 0$ at any $N$.
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