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CONTACT PROCESS ON FRACTAL CLUSTERS SIMULATED BY GENERALIZED DIFFUSION-LIMITED AGGREGATION (g-DLA) MODEL
Fractals ( IF 4.7 ) Pub Date : 2020-08-22 , DOI: 10.1142/s0218348x20501376
ASHWINI V. MAHAJAN 1 , ABHAY V. LIMAYE 1 , ARUN G. BANPURKAR 1 , PRASHANT M. GADE 2
Affiliation  

The spread of infectious disease, virus epidemic, fashion, religion and rumors is strongly affected by the nearest neighbor hence underlying morphologies of the colonies are crucial. Likewise, the morphology of naturally grown patterns ranges from fractal to compact with lacunarity. We analyze the contact process on the fractal clusters simulated by generalized Diffusion-limited Aggregation (g-DLA) model. In g-DLA model, randomly walking particle is added to the cluster with sticking probability [Formula: see text] depending on the local density of occupied sites in the neighborhood of radius [Formula: see text] from the center of active site. It takes values [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) for highly dense, moderately dense and sparsely occupied regions, respectively. The corresponding morphology varies from fractal to compact as [Formula: see text] varies from [Formula: see text] to [Formula: see text]. Interestingly, the contact process on the g-DLA clusters shows clear transition from active phase to absorbing phase and the exponent values fall between 1-d and 2-d in directed percolation (DP) universality class. The local persistence exponents at transition are studied and are found to be much smaller than that for 1-d and 2-d DP cases. We conjecture that infection in the fractal cluster does not easily reach far-flung or remote areas at the periphery of the cluster.

中文翻译:

广义扩散限制聚合(g-DLA)模型模拟​​分形簇的接触过程

传染病、病毒流行、时尚、宗教和谣言的传播受到最近邻国的强烈影响,因此殖民地的基本形态至关重要。同样,自然生长的图案的形态范围从分形到带有空隙的紧凑型。我们分析了广义扩散限制聚集(g-DLA)模型模拟​​的分形簇上的接触过程。在g-DLA模型中,随机游走的粒子被添加到具有粘附概率[公式:见文本]的簇中,这取决于从活动站点中心半径[公式:见文本]附近的占据站点的局部密度。它分别为高密度、中等密度和稀疏占用区域取值 [公式:见文本]、[公式:见文本] 和 [公式:见文本]([公式:见文本])。相应的形态从分形到紧凑变化,因为 [公式:参见文本] 从 [公式:参见文本] 到 [公式:参见文本]。有趣的是,g-DLA 簇上的接触过程显示出从活性阶段到吸收阶段的明显转变,并且指数值在定向渗透(DP)普遍性类中介于 1-d 和 2-d 之间。研究了过渡时的局部持久性指数,发现它比一维和二维 DP 情况下的要小得多。我们推测分形集群中的感染不会轻易到达集群外围的偏远或偏远地区。g-DLA 簇上的接触过程显示出从活性阶段到吸收阶段的明显转变,并且指数值在定向渗透(DP)普遍性类中介于 1-d 和 2-d 之间。研究了过渡时的局部持久性指数,发现它比一维和二维 DP 情况下的要小得多。我们推测分形集群中的感染不会轻易到达集群外围的偏远或偏远地区。g-DLA 簇上的接触过程显示出从活性阶段到吸收阶段的明显转变,并且指数值在定向渗透(DP)普遍性类中介于 1-d 和 2-d 之间。研究了过渡时的局部持久性指数,发现它比一维和二维 DP 情况下的要小得多。我们推测分形集群中的感染不会轻易到达集群外围的偏远或偏远地区。
更新日期:2020-08-22
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