各种纳米颗粒复合材料的膨胀诱导的传输特性有新的激增（参见。RSC Nanoscience & Nanotechnology Series，Paul O 'Brien主编）。我们特别注意到一个广泛的兴趣，在纳米复合材料表现出尖锐的电性能增益及以上的逾渗阈值，这促使我们重新审视经典的设置中的随机电阻网络的逾渗，但从多尺度的角度来看。对于阈值以上的随机电阻网络的每个实现，我们使用网络图表示和相关算法来识别和限制的干扰分量，从而通过过滤{ \it先验}零载流键在大小和精度上预处理网络。然后，我们模拟了许多实现每键密度和分析缩放行为的完整的电流分布上支持的封装组件。我们首先确认了著名的幂律分布的小电流在渗流阈值，第二，我们确认结果的最大电流在网络中的缩放与骨干的集群。然后将这些属性与电流分布的全局特征放在一起，特别是与材料科学应用最相关的大电流尾部的主导作用。我们确定了一个强大的，指数大电流尾：1。持续高于阈值; 2.以小电流尾部中消失的幂律缩放为代价，在电流分布上广泛扩展并占主导地位;以及3.采用二阶矩，再现了实验观察到的体电导率在阈值以上的幂律标度。
英文摘要：
There is a renewed surge in percolation-induced transport properties of diverse nano-particle composites (cf. RSC Nanoscience & Nanotechnology Series, Paul O'Brien Editor-in-Chief). We note in particular a broad interest in nano-composites exhibiting sharp electrical property gains at and above percolation threshold, which motivated us to revisit the classical setting of percolation in random resistor networks but from a multiscale perspective. For each realization of random resistor networks above threshold, we use network graph representations and associated algorithms to identify and restrict to the percolating component, thereby preconditioning the network both in size and accuracy by filtering {\it a priori} zero current-carrying bonds. We then simulate many realizations per bond density and analyze scaling behavior of the complete current distribution supported on the percolating component. We first confirm the celebrated power-law distribution of small currents at the percolation threshold, and second we confirm results on scaling of the maximum current in the network that is associated with the backbone of the percolating cluster. These properties are then placed in context with global features of the current distribution, and in particular the dominant role of the large current tail that is most relevant for material science applications. We identify a robust, exponential large current tail that: 1. persists above threshold; 2. expands broadly over and dominates the current distribution at the expense of the vanishing power law scaling in the small current tail; and 3. by taking second moments, reproduces the experimentally observed power law scaling of bulk conductivity above threshold.
Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons
Institute of Physics, Humboldt University（柏林洪堡大学物理研究所）；School of Physics and Astronomy, Yunnan University（云南大学物理与天文学院）；Princeton University（普林斯顿大学）；BCCN, Humboldt University（柏林洪堡大学神经中心）
无限重尾幂律随机网络上的键渗流缺乏适当的相变;或者可以说，在{ \em零渗流概率}处存在相变。然而，可以定义有限尺寸的逾渗阈值$q_c(N)$，其中$N$是网络尺寸。对于这种重尾网络，可以选择一个渗流概率$q(N)=ρq_c(N)$，使得$\displaystyle \lim_{N\to \infty}(q-q_c(N)) =0$和$ρ$任意大（对于具有非零渗流阈值的网络，这种情况不存在）。我们发现，随机幂律网络的临界行为是最好的描述$ρ$作为序参量，而不是$q$。本文提出了$ρ=1$中最大连通分支尺寸相变的概念。特别地，使用基于生成函数的方法，我们表明，对于$ρ>1$和幂律指数$2\leq τ<3$，最大连通分量的尺度为$\sim N^{1-1/τ}$，而对于$0<ρ<1$，尺度至多为$\sim N^{\frac{2-τ}τ}$ ;这里，任何节点的最大度，$k_{max}$，已假定缩放为N^{1/τ} $. In general, our approach yields that for large $ N $, $ ρ \gg 1 $, $ 2 \leq τ<3 $, and $ k_{max} \sim N^{1/τ} $, the largest connected component scales as $ \sim ρ^{1/（3-τ）}N^{1-1/τ} $.Thus…
