Multiple scaling in a one-dimensional sandpile

We study the Abelian one-dimensional sandpile model in which the toppling at a site periodically depends on the number of previous topplings at that site with the period T. When T tends to infinity, the redistribution of particles in unstable states becomes completely stochastic. For finite T, we found the probability distribution of avalanche sizes. We show that it is qualitatively 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(98)04507-3].