Year: 2012
Type: article
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.
Source: Physical Review E
Authors: Eial Teomy, Yair Shokef
Institution: Tel Aviv University
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1978186624