Avalanche mixing of granular solids in a rotating 2D drum and discrete mapping

Evolution of mixing of granular solids in a slowly rotated 2D drum is considered as a discrete mapping. The rotation is around the axis of the upright drum which is filled partially, and the mixing occurs only at a free surface of a material. The most simple cases that demonstrate clearly the essence of such a type of mixing are studied analytically. We calculate the characteristic time of the mixing and the distribution of the mixed material over the drum.