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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 r₀. We find that the surface angle θ of the pile reaches its final critical value ( θf) from lower values only at long times. The deviation ( θf-θ) behaves as (t/r₀)^-1/2.
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Dorogovt︠s︡ev et al. (1999) studied this question.
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