SIZE EFFECTS OF SLOPE DYNAMICS IN A 2-DIMENSIONAL SANDPILE

We study a two-dimensional sandpile automaton model under the so-calle d critical slope dynamics where the stability depends upon the first d erivative of the sand height, i.e. height difference. For fixed critic al slope we investigate systems of increasing linear dimension L on th e square lattice for both randomly and systematically built piles. Sta tistics are presented for the size and duration of the avalanches prod uced. For excess grains distributed with equal probability to nearest neighbours, the average cluster size tends to a fixed limit which is d ependent on the size of the initial perturbation. Furthermore, stable behaviour appears to be reached for relatively low values of the linea r dimension L approximately 250. The average time taken for avalanches of all sizes to die away stabilizes less readily within the system si zes considered. No evidence is found in support of a scaling law of th e usual type.