Ordering According to Size of Disks in a Narrow Channel

¹ Department of Physics, University of Hartford, West Hartford CT 06443, USA
² Fachgruppe Physik, Bergische Universität Wuppertal, 42119 Wuppertal, Germany
³ Department of Physics, University of Rhode Island, Kingston RI 02881, USA

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Published online: 12 September 2025

Abstract

A long and narrow channel confines disks of two sizes. The disks are randomly agitated in a widened channel under moderate pressure, then jammed according to a tunable protocol. We present exact results that characterize jammed macrostates (volume, entropy, jamming patterns). The analysis divides jammed disk sequences into overlapping tiles out of which statistically interacting quasiparticles are constructed. The fractions of small and large disks are controlled by a chemical potential adapted to configurational statistics of granular matter. The results show regimes for the energy parameters (determined by the jamming protocol) that either enhance or suppress the mixing of disk sizes. Size segregation or size alternation driven by steric forces alone are manifestations of a broken symmetry.