Abstract
Traditionally, settling of powders under mechanical vibration has been a subject of soil mechanics and powder technology [1]. In recent years a large body of literature has emerged on the physics of vibrated granular media. A wide range of fascinating phenomena have been studied; vibration-induced size-segregation [2,3], slow relaxation to a steady state density [4, 16], convection rolls [5], vibration history dependence of density [6], large density fluctuations about the steady state [7] and crystallization under horizontal shaking [8], to name but a few. A typical granular material is a system with a large number of individual grains and therefore it has a huge number of degrees of freedom. Grains interact with each other via contact forces which are determined by friction, gravitational loading and amplitude of an exernal force if the system is perturbed. Therefore one needs to invent a formalism that would allow us to calculate macroscopic averages in terms of microscopic (i.e. of individual grains) properties of the system. If we assume that it may be characterised by a
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