The effect of the number of dissipative sites on a sandpile model

In this paper we investigate the effect of the number of dissipative sites in an Abelian sandpile model. The dissipative sites are considered to be in the bulk rather than in the boundary. In such systems, statistics of avalanches smaller than a certain size obey a power law. We have seen that the exponents associated with these power law behaviors change slightly as the number of dissipative sites is decreased. We have found that the zero dissipation limits of these exponents are independent of size. Therefore we suggest that the previously-seen dependence of the exponent on the system size is because of the number of dissipative sites rather than the system size. Also it is observed that exponents associated with the waves of toppling show the same dependence on dissipation rate, which shows that the scaling exponents found by direct measurement produce results that are just as poor for waves as for avalanches. (paper)