title: 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) ~ W(-1/2) with the system's width W, while in square systems it decreases logarithmically vc) ~ 1/lnL with length L. Although derived for asymptotically wide rectangles, our analytical results agree with numerical data for systems as small as W ≈ 10.
authors.affiliation: School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. eialteom@post.tau.ac.il
authors.forename: Eial
authors.initials: E
authors.lastname: Teomy
authors.forename: Yair
authors.initials: Y
authors.lastname: Shokef
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D007700:Kinetics; D008956:Models, Chemical; D008958:Models, Molecular; D010316:Particle Size
chemical_list: D003102:Colloids