Jammed disks in narrow channel: criticality and ordering tendencies

Abstract

A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and perpendicular to the axis of the channel. We employ a method of configurational statistics that interprets jammed states as configurations of floating particles with structure. The particles interlink according to set rules. The two jammed microstates with smallest volume act as pseudo-vacuum. The placement of particles is subject to a generalized Pauli principle. Jammed macrostates are generated by random agitations and specified by two control variables. One is a measure of the intensity of random agitations at given pressure. The other is a measure of the change in gravitational potential energy in units of compression work when one particle is excited. In this two-dimensional space of variables there exists a critical point. The jammed macrostate realized at the critical point depends on the path of approach. We describe all jammed macrostates by volume and entropy. Both are functions of the average population densities of particles. Approaching the critical point in an extended space of control variables generates two types of jammed macrostates: states with random heterogeneities in mass density and states with domains of uniform mass density.

16 pages, 6 figures, 3 tables, new revised version due to publication

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• The Jamming Transition in Granular Systems
• Universal microstructure and mechanical stability of jammed packings
• Phase transition in a static granular system
• Critical scaling and aging in cooling systems near the jamming transition
• Jammed disks in narrow channel: criticality and ordering tendencies
• Statistically interacting quasiparticles in Ising chains

Cited by in corpus (9)

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• Free-energy landscapes and insertion pathways for peptides in membrane environment
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