Diffusive persistence on disordered lattices and random networks
Diffusive persistence on disordered lattices and random networks
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无序晶格和随机网络上的扩散持久性
DOI：
10.1103/physreve.109.024113
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发表时间：
2024
影响因子：
2.4
通讯作者：
Korniss, Gyorgy
中科院分区：
文献类型：
--
作者：
Malik, Omar;Varga, Melinda;Moussawi, Alaa;Hunt, David;Szymanski, Boleslaw K.;Toroczkai, Zoltan;Korniss, Gyorgy
为了更好地理解网络中随机过程波动的时间特性和生命周期，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分数，对于这些节点，在一个站点（或节点）处的扩散场没有随时间改变符号（或者，一般来说，节点在离散模型中保持活跃或不活跃）。在这里，我们研究无序和随机网络，并表明持久性的行为取决于网络的拓扑结构。在二维（2D）无序网络中，我们发现，以上的逾渗阈值扩散的持久性尺度类似于在原来的二维规则晶格，根据幂律与指数，在大的线性系统的大小的限制。然而，在逾渗阈值，标度指数的变化，作为在逾渗阈值的无序晶格中的扩散持久性和潜在的结构转变的相互作用的结果。此外，我们还研究了渗流阈值及以上的二维晶格的有限尺寸效应，发现在渗流阈值处，长时间渐近值服从幂律，而不是二维规则晶格上通常与有限尺寸效应相关的值。相反，我们观察到，在没有局部规则结构的随机网络中，如Erdens-Rényi网络，在逾渗阈值以上不存在简单的幂律标度行为。
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(or, in general, that the node remained active or 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 lawwith an exponent, in the limit of large linear system size. At the percolation threshold, however, the scaling exponent changes to, 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 lawwithinstead of the value ofnormally 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.