GENERALISATION OF BTW MODEL WITH NEXT NEAREST NEIGHBOUR

The two-dimensional BTW model of self-organised criticality (SOC) with critical height, z(c) = 8, is studied by computer simulation in the following two different cases. When the value of height variable of a particular site reaches the critical value, z(c) = 8, the value of height variable of that site is reduced by eight units: (i) by distributing eight particles among the four nearest neighbouring sites and four next nearest neighbouring sites, each receiving one particle at a time; (ii) by distributing eight particles among the four nearest neighbouring sites, each receiving two particles at a time. It is observed that in the SOC state, the average (spatial) value of height variable, (z) over bar, in the BTW model with next nearest neighbour is less than that in the BTW model with only nearest neighbour. But in the SOC state, the distributions of avalanche sizes and durations are identical in both the cases. The distribution of the size of clusters for different values of height variable have been studied in both the cases of BTW model.