Evolution of a sandpile in a thick-flow regime

We solve a one-dimensional sandpile problem analytically in a thick flow re gime when the pile evolution may be described by a set of linear equations. We demonstrate that, if an income flow is constant, a space periodicity ta kes place while the sandpile evolves even for a pile of only one type of pa rticles. Hence, grains are piling layer by layer. The thickness of the laye rs is proportional to the input flow of particles ro and coincides with the thickness of stratified layers in a two-component sandpile problem, which were observed recently. We find that the surface angle theta of the pile re aches its final critical value ( Bf) only at long times after a complicated relaxation process. The deviation (theta(f) - theta) behaves asymptoticall y as (t/r(0))(-1/2). It appears that the pile evolution depends on initial conditions. We consider two cases: (i) grains are absent at the initial mom ent, and (ii) there is already a pile with a critical slope initially. Alth ough at long times the behavior appears to be similar in both cases, some d ifferences are observed for the different initial conditions are observed. We show that the periodicity disappears if the input flow increases with ti me.