Tarasevich Yuri Yu, Lebovka Nikolai I, Laptev Valeri V
Astrakhan State University, 20a Tatishchev Street, 414056 Astrakhan, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061116. doi: 10.1103/PhysRevE.86.061116. Epub 2012 Dec 12.
Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear k-mers (also denoted in publications as rigid rods, needles, sticks) on two-dimensional square lattices L × L with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear k-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. A detailed study of the behavior of percolation probability R(L)(p) that a lattice of size L percolates at concentration p in dependence on k, anisotropy, and lattice size L has been performed. A nonmonotonic size dependence for the percolation threshold has been confirmed in the isotropic case. We propose a fitting formula for percolation threshold, p(c) = a/k(α)+blog(10)k+c, where a, b, c, and α are the fitting parameters depending on anisotropy. We predict that for large k-mers (k >/≈ 1.2 × 10(4)) isotropically placed at the lattice, percolation cannot occur, even at jamming concentration.
通过蒙特卡罗方法和有限尺寸标度分析进行了数值模拟，以研究线性k聚体（在出版物中也表示为刚性棒、针、棍）在具有周期性边界条件的二维正方形晶格L×L上的渗流行为。研究了线性k聚体的各向异性弛豫随机顺序吸附的渗流现象。特别地，研究了物体的各向异性放置对渗流阈值的影响。详细研究了尺寸为L的晶格在浓度p下发生渗流的渗流概率R(L)(p)随k、各向异性和晶格尺寸L的变化行为。在各向同性情况下，已证实渗流阈值存在非单调的尺寸依赖性。我们提出了一个渗流阈值的拟合公式，p(c)=a/k(α)+blog(10)k+c，其中a、b、c和α是取决于各向异性的拟合参数。我们预测，对于在晶格上各向同性放置的大k聚体（k>/≈1.2×10(4)），即使在堵塞浓度下也不会发生渗流。
