Jammed disks of two sizes and weights in a narrow channel

Jammed disk models are often studied for the properties of granular materials. Here we introduce our approach to the models of jammed disks of two sizes and weights in a long narrow channel. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations subject to moderate pressure, gravity, and random agitations. Disk sizes and channel width are such that underjamming no disk remains loose and all disks touch one wall. Based on a generalized Pauli Principle and configuration statistics, we calculate the models where the two types of disks are in alternating and random sequences. The exact results for the characterization of jammed macrostates including volume and entropy are presented.