论文标题
在无序晶格和随机网络上的扩散持久性
Diffusive Persistence on Disordered Lattices and Random Networks
论文作者
论文摘要
为了更好地了解网络随机过程中波动的时间特征和寿命，我们研究了各种图中的扩散持久性。全局扩散持久性被定义为节点的比例，该节点（或节点）在该节点（或节点）的扩散字段尚未更改为$ t $（或一般而言，该节点在离散模型中保持活性/不活动）。在这里，我们研究了无序和随机网络，并表明持久性的行为取决于网络的拓扑。在二维（2D）无序网络中，我们发现，根据Power Law $ P（t，t，l）\ sim t^{ - t^{ - θ} $，具有指数$θ\ simeq 0.186 $，在大型linear system system $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $ l $。然而，在渗透阈值时，由于扩散持久性的相互作用以及在渗透阈值处的无序晶格中的基本结构过渡，缩放指数变为$θ\ simeq 0.141 $。 Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power-law $P(t,L)\sim L^{-zθ}$ with $z\simeq 2.86$ instead of the value of $z=2$ normally associated with finite-size effects on 2D regular lattices.相比之下，我们观察到，在没有局部规则结构的随机网络中，例如ERDőS-Rényi网络，渗透阈值以上没有简单的幂律缩放行为。
To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time $t$ (or in general, that the node remained active/inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law $P(t,L)\sim t^{-θ}$ with an exponent $θ\simeq 0.186$, in the limit of large linear system size $L$. At the percolation threshold, however, the scaling exponent changes to $θ\simeq 0.141$, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power-law $P(t,L)\sim L^{-zθ}$ with $z\simeq 2.86$ instead of the value of $z=2$ normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdős-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.
