We perform numerical simulation of a lattice model for the compaction of a granular
material based on the idea of reversible random sequential adsorption. Reversible random
sequential adsorption of objects of various shapes on a two−dimensional triangular lattice is studied
numerically by means of Monte Carlo simulations. The growth of the coverage ρ(t) above the
jamming limit to its steady−state value ρ∞ is described by a pattern ρ (t) = ρ∞ − ρEβ[−(t/τ)β],
where Eβ denotes the Mittag−Leffler function of order β ∈ (0, 1). For the first time, the parameter τ
is found to decay with the desorption probability P− according to a power law τ = A P−
−γ. Exponent
γ is the same for all shapes, γ = 1.29 ± 0.01, but parameter A depends only on the order of symmetry
axis of the shape. Finally, we present the possible relevance of the model to the compaction of
granular objects of various shapes.
Exact steady-state velocity of ratchets driven by random sequential adsorption