Multiple scaling in a one-dimensional sandpile

We study the Abelian one-dimensional sandpile model in which the toppling a t a site periodically depends on the number of previous topplings at that s ite with the period T. When T tends to infinity, the redistribution of part icles in unstable states becomes completely stochastic. For finite T, we fo und the probability distribution of avalanche sizes. We show that it is qua litatively similar to a multifractal scaling form obtained earlier for the sandpile model with fixed toppling conditions on decorated one-dimensional chains [A. A. Ali and D. Dhar, Phys. Rev. E 52, 4804 (1995)]. [S1063-651X(9 8)04507-3].