Disks in a narrow channel jammed by gravity and centrifuge: profiles of pressure, mass density and entropy density

Abstract

This work investigates jammed granular matter under conditions that produce heterogeneous mass distributions on a mesoscopic scale. We consider a system of identical disks that are confined to a narrow channel, open at one end and closed off at the other end. The disks are jammed by the local pressure in a gravitational field or centrifuge. All surfaces are hard and frictionless. We calculate the profiles of pressure, mass density, and entropy density on a mesoscopic length scale under the assumption that the jammed states are produced by random agitations of uniform intensity along the channel. These profiles exhibit trends and features governed by the balancing of position-dependent forces and potential energies. The analysis employs a method of configurational statistics that uses interlinking two-disk tiles as the fundamental degrees of freedom. Configurational statistics weighs the probabilities of tiles according to competing potential energies associated with gravity and centrifugation. Amendments account for the effects of the marginal stability of some tiles due to competing forces.

20 pages, 10 figures

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