# The adsorption-desorption model and its application to vibrated granular materials Source: [The adsorption-desorption model and its application to vibrated granular materials]() Collection index: [llms.txt]() Data updated: 2025-10-24T09:33:00.363Z Authors: J. Talbot, G. Tarjus, P. Viot Published: 1999-10-15T14:50:57.000Z ## Abstract We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model which is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm which is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as $1/t$, a logarithmic one where the density varies as $1/\\ln(t)$, followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by a mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()