Sand Density As Sandpile Descriptor

We investigate a collection of one-parametric families of isotropic sandpile models. The models involve the square lattice slowly accumulating the grains and quickly transferring them as the local piles become over-critical. The paper groups the sand-piles with respect to two features influencing the model dynamics. They are the value of the local transfer's stochasticity and the number of the transferred grains. Every pair generates one-parametric family of the sand-piles. The parameter reflects the relative height of an over-critical pile with respect to the incoming flow of sand. If the stochasticity disappears with the growth of the parameter, the families with thefixednumber of the transferred grains have much in common with Baket al.'s sand-pile [Phys. Rev. Lett.59, 381 (1987)], while the families, whose over-critical piles losealltheir grains, tend to the Zhang sand-pile [Phys. Rev. Lett.63, 470 (1989)]. The families with non-disappearing variance give rise to new properties described in terms of the probability distribution of the pile heights.