Jamming transition of kinetically-constrained models in rectangular systems

Abstract

We theoretically calculate the average fraction of frozen particles in rectangular systems of arbitrary dimensions for the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models. We find the aspect ratio of the rectangle's length to width, which distinguishes short, square-like rectangles from long, tunnel-like rectangles, and show how changing it can effect the jamming transition. We find how the critical vacancy density converges to zero in infinite systems for different aspect ratios: for long and wide channels it decreases algebraically $v_c\sim W^{-1/2}$ with the system's width W, while in square systems it decreases logarithmically $v_c\sim 1/\ln L$ with length L. Although derived for asymptotically wide rectangles, our analytical results agree with numerical data for systems as small as $W\approx 10$.

20 pages, 15 figures

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• Jamming Percolation in Three Dimensions
• Hydrodynamics in kinetically-constrained lattice-gas models
• The relation between the structure of blocked clusters and the relaxation dynamics in kinetically-constrained models
• Jamming by Shape in Kinetically-Constrained Models
• Jamming vs. Caging in Three Dimensional Jamming Percolation
• Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models
• Kinetically constrained model for gravity-driven granular flow and clogging
• Constraint relaxation leads to jamming