How Sandpiles Spill: Sandpile Problem in a Thick Flow Regime

S. N. Dorogovtsev; J. F. F. Mendes

doi:10.1103/PhysRevLett.83.2946

How Sandpiles Spill: Sandpile Problem in a Thick Flow Regime

S. N. Dorogovtsev and J. F. F. Mendes

Phys. Rev. Lett. 83, 2946 – Published 11 October 1999

Abstract

We obtain an analytical solution of a one-dimensional sandpile problem in a thick flow regime, when it can be formulated in terms of linear equations. It is shown that a space periodicity takes place during the sandpile evolution even for a sandpile of only one type of particle. Similar periodicity was observed previously for many component sandpiles. Space periods are proportional to an input flow of particles $r_{0}$ . We find that the surface angle $θ$ of the pile reaches its final critical value ( $θ_{f}$ ) from lower values only at long times. The deviation ( $θ_{f} - θ$ ) behaves as $(t / r_{0})^{- 1 / 2}$ .

Received 4 May 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.2946

Authors & Affiliations

S. N. Dorogovtsev^1,2,* and J. F. F. Mendes^1,†

¹Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
²A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia

^*Electronic address: sdorogov@fc.up.pt
^†Electronic address: jfmendes@fc.up.pt