BTW model with probabilistically nonuniform distribution of particles from the unstable sites

Abstract

The two dimensional BTW model of SOC, with probabilistically nonuniform distribution of particles among the nearest neighbouring sites, is studied by computer simulation. When the value of height variable of a particular site reaches the critical value (z c = 4), the value of height variable of that site is reduced by four units by distributing four particles among the four nearest neighbouring sites. In this paper, it is considered that, two particles are distributed equally among the two nearest neighbouring sites along X-axis. However, the distribution of other two particles along Y- axis, is probabilistically nonuniform. The variation of spatial average of the height variable with time is studied. In the SOC state, the distribution of avalanche sizes and durations is obtained. The total number of topplings occured during the stipulated time of evolution is also calculated.