随机Delaunay三角剖分上的流行病爆发
Epidemic Outbreaks on Random Delaunay Triangulations
摘要：
我们研究流行病爆发的随机Delaunay三角剖分应用异步SIR（易感染的删除）模型动力学蒙特卡罗动力学耦合到格子提取的三角剖分。为了研究模型的临界行为，我们通过使用Newman-Ziff算法获得团簇尺寸分布，允许模拟随机非均匀晶格并测量任何所需的可观察到的渗流。我们数值计算的序参量，定义为包裹集群密度，平均集群大小，和Binder累积量比定义的渗流，以估计的流行阈值。我们的研究结果表明，该系统属于二维动态渗流普适类和猝灭的随机无序是无关紧要的，与经典渗流的结果。
英文摘要：
We study epidemic outbreaks on random Delaunay triangulations by applying Asynchronous SIR (susceptible-infected-removed) model kinetic Monte Carlo dynamics coupled to lattices extracted from the triangulations. In order to investigate the critical behavior of the model, we obtain the cluster size distribution by using Newman-Ziff algorithm, allowing to simulate random inhomogeneous lattices and measure any desired percolation observable. We numerically calculate the order parameter, defined as the wrapping cluster density, the mean cluster size, and Binder cumulant ratio defined for percolation in order to estimate the epidemic threshold. Our findings suggest that the system falls into two-dimensional dynamic percolation universality class and the quenched random disorder is irrelevant, in agreement with results for classical percolation.
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