论文标题
与拓扑障碍接触过程中的对数周期振荡的出现
The emergence of Logarithmic-periodic oscillations in Contact process with the topological disorder
论文作者
论文摘要
我们提出了具有几何疾病的Domany-Kinzel细胞自动机的接触过程模型。在1-D模型中，每个站点都连接到两个最近的邻居，这些邻居在左侧或右侧。该系统始终被吸收状态所吸引，其平均密度的代数衰减具有不断变化的复杂指数。对数周期振荡在通常的功率定律之上施加，并且显然是p-> 1。这种效果纯粹是由于潜在的拓扑结构所致，因为所有部位都具有相同的感染概率P，并且感染率没有障碍。该模型向两个和三个维度的扩展会带来相似的结果。我们还研究了一个在一个和二维中具有固定免疫率P0的模型。如果P0> PS，则PS为渗透阈值，则系统始终趋于吸收状态。作为感染率P-> 1，我们观察到具有复杂指数的订单参数的功率定律衰减。这可能是在系统中导致晶格有效碎片化的系统中的共同特征。
We present a model of contact process on Domany-Kinzel cellular automata with a geometrical disorder. In the 1-D model, each site is connected to two nearest neighbors which are either on the left or the right. The system is always attracted to an absorbing state with algebraic decay of average density with a continuously varying complex exponent. The log-periodic oscillations are imposed over and above the usual power law and are clearly evident as p --> 1. This effect is purely due to an underlying topology because all sites have the same infection probability p and there is no disorder in the infection rate. An extension of this model to two and three dimensions leads to similar results. We also study a model with fixed immunization rate p0 in one and two dimensions. If p0 > ps, where ps is percolation threshold, the system always tends to an absorbing state. As infection rate p --> 1, we observe a power law decay of order parameter with complex exponent. This may be a common feature in systems where quenched disorder leads to effective fragmentation of the lattice.
