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

References in corpus (13)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Glassy dynamics of kinetically constrained models
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Microfluidic rheology of soft colloids above and below jamming
• Energy transport in jammed sphere packings
• Glass Transition in Confined Geometry
• Finite-temperature critical point of a glass transition
• Helical Packings and Phase Transformations of Soft Spheres in Cylinders
• Asymmetric exclusion processes with constrained dynamics
• Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System
• An exactly solvable model for driven dissipative systems
• Driving kinetically constrained models into non-equilibrium steady states: structural and slow transport properties
• Out of equilibrium dynamics of the spiral model