Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis, CONICET, Ejército de Los Andes 950, D5700HHW San Luis, San Luis, Argentina.
Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
Phys Rev E. 2019 Nov;100(5-1):052114. doi: 10.1103/PhysRevE.100.052114.
Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal, and random lattices is studied. The adsorption process is modeled by using random sequential adsorption algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension d between 1 and 2, and on Erdős-Rényi random graphs. The number of sites is M=L^{d} for Euclidean and fractal lattices, where L is a characteristic length of the system. In the case of random graphs, such a characteristic length does not exist, and the substrate can be characterized by a fixed set of M vertices (sites) and an average connectivity (or degree) g. This paper concentrates on measuring (i) the probability W_{L(M)}(θ) that a lattice composed of L^{d}(M) elements reaches a coverage θ and (ii) the exponent ν_{j} characterizing the so-called jamming transition. The results obtained for Euclidean, fractal, and random lattices indicate that the quantities derived from the jamming probability W_{L(M)}(θ), such as (dW_{L}/dθ){max} and the inverse of the standard deviation Δ{L}, behave asymptotically as M^{1/2}. In the case of Euclidean and fractal lattices, where L and d can be defined, the asymptotic behavior can be written as M^{1/2}=L^{d/2}=L^{1/ν_{j}}, with ν_{j}=2/d.
研究了不同形状和大小的物体在欧几里得、分形和随机晶格上不可逆吸附的情况。吸附过程通过随机顺序吸附算法进行建模。物体被吸附在一维、二维和三维欧几里得晶格上，在维度在 1 到 2 之间的 Sierpinski 地毯上，以及在 Erdős-Rényi 随机图上。对于欧几里得和分形晶格，晶格的站点数为 M=L^{d}，其中 L 是系统的特征长度。对于随机图，不存在这样的特征长度，并且可以通过固定的 M 个顶点（站点）和平均连接度（或度数）g 来描述基底。本文集中测量（i）由 L^{d}(M)个元素组成的晶格达到覆盖率θ的概率 W_{L(M)}(θ)和（ii）表征所谓的堵塞转变的指数 ν_{j}。在欧几里得、分形和随机晶格上得到的结果表明，从堵塞概率 W_{L(M)}(θ)中得出的量，如(dW_{L}/dθ){max}和标准偏差 Δ{L}的倒数，作为 M^{1/2}的量级表现出渐近行为。在可以定义 L 和 d 的欧几里得和分形晶格的情况下，渐近行为可以写成 M^{1/2}=L^{d/2}=L^{1/ν_{j}}，其中 ν_{j}=2/d。
