标题： 无序非热网络中的位移相关性 显示英文标题

标题： Displacement correlations in disordered athermal networks

摘要： 我们推导了近晶体无热系统中位移场$\{ \delta \vec{r} \} \equiv \{ \delta r_{\mu = x,y} \}$的关联的精确结果。 我们分析了由不同类型的微观无序产生的位移关联，并表明微观尺度的无序会导致与系统尺寸$L$相关的长程关联，其关系为$\langle \delta r_{\mu} \delta r_{\nu} \rangle \sim c_{\mu \nu}(r/L,\theta)$。 此外，我们表明组分粒子尺寸的多分散性和随机键无序会导致对数系统尺寸标度，其中$c_{\mu \nu}(\rho,\theta) \sim \text{const}_{\mu\nu} - \text{a}_{\mu\nu}(\theta)\log \rho + \text{b}_{\mu\nu}(\theta) \rho^{2} $对于$\rho~(=r/L) \to 0$。 这种标度对于由每个网络顶点处的随机外部力产生的位移关联情况是不同的，其表达式为$c^{f}_{\mu \nu}(\rho,\theta) \sim \text{const}^{f}_{\mu \nu} -( \text{a}^{f}_{\mu \nu}(\theta) + \text{b}^{f}_{\mu \nu}(\theta) \log \rho ) \rho^2 $。 此外，我们发现由多分散性产生的关联和由键刚度无序产生的关联在对称性特性上有所不同。 最后，我们还预测了受外部固定力作用的多分散软盘模型的位移关联，该模型涉及两种不同类型的微观无序。 我们通过二维随机弹簧接触的多分散软盘的数值模拟验证了我们的理论预测。 显示英文摘要

摘要： We derive exact results for correlations in the displacement fields $\{ \delta \vec{r} \} \equiv \{ \delta r_{\mu = x,y} \}$ in near-crystalline athermal systems in two dimensions. We analyze the displacement correlations produced by different types of microscopic disorder, and show that disorder at the microscopic scale gives rise to long-range correlations with a dependence on the system size $L$ given by $\langle \delta r_{\mu} \delta r_{\nu} \rangle \sim c_{\mu \nu}(r/L,\theta)$. In addition, we show that polydispersity in the constituent particle sizes and random bond disorder give rise to a logarithmic system size scaling, with $c_{\mu \nu}(\rho,\theta) \sim \text{const}_{\mu\nu} - \text{a}_{\mu\nu}(\theta)\log \rho + \text{b}_{\mu\nu}(\theta) \rho^{2} $ for $\rho~(=r/L) \to 0$. This scaling is different for the case of displacement correlations produced by random external forces at each vertex of the network, given by $c^{f}_{\mu \nu}(\rho,\theta) \sim \text{const}^{f}_{\mu \nu} -( \text{a}^{f}_{\mu \nu}(\theta) + \text{b}^{f}_{\mu \nu}(\theta) \log \rho ) \rho^2 $. Additionally, we find that correlations produced by polydispersity and the correlations produced by disorder in bond stiffness differ in their symmetry properties. Finally, we also predict the displacement correlations for a model of polydispersed soft disks subject to external pinning forces, that involve two different types of microscopic disorder. We verify our theoretical predictions using numerical simulations of polydispersed soft disks with random spring contacts in two dimensions.