Title: Jamming and percolation of parallel squares in single-cluster growth model
Author(s):

	I.A. Kriuchevskyi (Taras Shevchenko Kiev National University, Department of Physics, 2 Academician Glushkov Avenue, 031127 Kyiv, Ukraine) ,
	L.A. Bulavin (Taras Shevchenko Kiev National University, Department of Physics, 2 Academician Glushkov Avenue, 031127 Kyiv, Ukraine) ,
	Yu.Yu. Tarasevich (Astrakhan State University, 20a Tatishchev St., 414056 Astrakhan, Russia) ,
	N.I. Lebovka (Institute of Biocolloidal Chemistry named after F.D. Ovcharenko of the National Academy of Sciences of Ukraine, 42 Academician Vernadsky Boulevard, 03142 Kiev, Ukraine)

This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size k x k squares (E-problem) or a mixture of k x k and m x m (m ≤ k) squares (M-problem). The larger k x k squares were assumed to be active (conductive) and the smaller m x m squares were assumed to be blocked (non-conductive). For equal size k x k squares (E-problem) the value of p_j = 0.638 ± 0.001 was obtained for the jamming concentration in the limit of k →∞. This value was noticeably larger than that previously reported for a random sequential adsorption model, p_j = 0.564 ± 0.002. It was observed that the value of percolation threshold p_c (i.e., the ratio of the area of active k x k squares and the total area of k x k squares in the percolation point) increased with an increase of k. For mixture of k x k and m x m squares (M-problem), the value of p_c noticeably increased with an increase of k at a fixed value of m and approached 1 at k ≥ 10 m. This reflects that percolation of larger active squares in M-problem can be effectively suppressed in the presence of smaller blocked squares.

Key words: jamming, percolation, squares, disordered systems, Monte Carlo methods, Leath-Alexandrowicz method
PACS: 02.70.Uu, 05.65.+b, 36.40.Mr, 61.46.Bc, 64.60.ah

Full text [pdf]

<< List of papers