In this paper we briefly review few self-organized critical (SOC) models of the phenomenon of earthquakes. For example, the two-dimensional non-conservative SOC model of Olami, Feder and Christensen (OFC) has been described. It is known that the effect of the fixed boundary on this model is very...

The generic phase transition from a phase of freely flowing traffic of electronic data packets to a congested phase is studied in a very simple model. Here the network is an oriented square lattice. Packets are randomly introduced at the nodes located at one boundary with a certain posting rate,...

The culling process in bootstrap percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap percolation threshold in two dimension which takes L2...

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the...

On a simple cubic lattie, which is initially occupied randomly with concentration p, a site is emptied if it does not have at least four of its six neighbors occupied. The threshold concentration, below which all sites are emptied after sufficiently many iterations, is found to vary...

We study here a space filling tiling generated by random non-overlapping packing of discs. To place the nth disc we randomly choose a point in the empty pore space of the n−1 discs and place a disc with the centre at this point and touching the nearest disc. We measure the fractal dimension of...

We study numerically the outflow of a two-dimensional sandpile cellular automation. Motivated by recent experiments we calculated the correlations in the sizes of the outflow avalanches and obtained for short times exponential decay. For long times a quasiperiodic behavior was observed with the...

The growth of the average size 〈smax〉 of the largest component at the percolation threshold pc(N) on a graph of size N has been defined as 〈smax(pc(N),N)〉∼Nχ. Here we argue that the precise value of the ‘growth exponent’ χ indicates the nature of percolation transition; χ1 or...

We study the properties of two-dimensional unentangled polymer chains in a dense environment of many other cross-linked polymer molecules incorporating the excluded volume effect. A kinetic random-walk model is introduced in which the different possible directions of a step are chosen...

We study the restructuring process of diagenesis in sedimentary rocks using a geometrical model of percolation theory. The competing processes of cementation and dissolution of diagenesis are modelled by growth of vacant sites and culling of occupied sites in a percolation model depending on a...