Resumen:
A simple method to estimate percolation thresholds pc in lattice models is presented. The technique is based on the calculation of the probabilities RXL(p) for finding a percolating cluster of type X [X could be horizontal (H), vertical (V), average (A), intersection (I), or union (U)] on a finite lattice of side length L at concentration p of occupied sites. The functions RXL(p) are obtained by numerical simulations. Then, (1) effective percolation thresholds pXc ,r (L) are estimated from the condition RXL (p) = r (where r is a parameter ranging between 0 and 1); and (2) the percolation threshold in the ther-modynamic limit is determined by extrapolating the effective percolation thresholds to infinite L.The methodology presented herein contains and extends the classical scheme developed by Yonezawa, Sakamoto and Hori, offering a more complete and versatile theoretical/simulation framework to calculate percolation thresholds. The approach is validated by successfully comparing with well-known results obtained for the problem of random site percolation on square lattices. Taking advantage of the behavior of the curves of pX,r c (L) for different values of the parameter r, more general scaling relations are proposed for the effective percolation thresholds. Finally, the technique is applied to model experimental data of clogging transitions in a two-dimensional silo with a vibrated base. & COPY; 2023 Elsevier B.V. All rights reserved.
