title: Scaling behavior of coarsening Faraday heaps.
abstract: When a layer of sand is vertically shaken, the surface spontaneously breaks up in a landscape of small conical "Faraday heaps," which merge into larger ones on an ever increasing time scale. We propose a model for the heap dynamics and show analytically that the mean lifetime of the transient state with N heaps scales as N(-2). When there is an abundance of sand, such that the vibrating plate always remains completely covered, this means that the average diameter of the heaps grows as t(1/2). Otherwise, when the sand is less plentiful and parts of the plate get depleted during the coarsening process, the average diameter of the heaps grows more slowly, namely as t(1/3). This result compares well with experimental observations.
authors.affiliation: Faculty of Science and Technology, University of Twente, NL-7500 AE Enschede, The Netherlands.|National Aerospace Laboratory, P.O. Box 153, NL-8300 AD Emmeloord, The Netherlands.
authors.forename: Henk Jan
authors.initials: HJ
authors.lastname: van Gerner
authors.affiliation: Department of Mathematics, University of Patras, 26500 Patras, Greece.
authors.forename: Ko
authors.initials: K
authors.lastname: van der Weele
authors.affiliation: Faculty of Science and Technology, University of Twente, NL-7500 AE Enschede, The Netherlands.
authors.forename: Devaraj
authors.initials: D
authors.lastname: van der Meer
authors.affiliation: Faculty of Science and Technology, University of Twente, NL-7500 AE Enschede, The Netherlands.
authors.forename: Martin A
authors.initials: MA
authors.lastname: van der Hoef