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Jamming transition of kinetically constrained models in rectangular systems.

Eial Teomy1, Yair Shokef

  • 1School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. eialteom@post.tau.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

The study reveals how system shape influences particle freezing in complex models. Aspect ratio critically affects the jamming transition, with different convergence rates for wide channels versus square systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Kinetically constrained models (KCMs) like Kob-Andersen (KA) and Fredrickson-Andersen (FA) are crucial for understanding glassy dynamics.
  • The behavior of these models in confined geometries is less understood, particularly concerning jamming transitions.

Purpose of the Study:

  • To theoretically investigate the average fraction of frozen particles in rectangular systems for KA and FA models.
  • To analyze the impact of system aspect ratio on the jamming transition.
  • To determine the critical vacancy density convergence in infinite systems with varying aspect ratios.

Main Methods:

  • Theoretical calculations of particle dynamics in rectangular geometries.
  • Analysis of system aspect ratio (length-to-width) and its effect on jamming.
  • Derivation of critical vacancy density convergence rates for different dimensionalities.

Main Results:

  • The aspect ratio distinguishes between square-like and tunnel-like rectangular systems.
  • Changing the aspect ratio significantly affects the jamming transition.
  • Critical vacancy density converges to zero algebraically in wide channels (v(c) ~ W(-1/2)) and logarithmically in square systems (v(c) ~ 1/lnL).
  • Analytical results show good agreement with numerical data for relatively small system widths (W ≈ 10).

Conclusions:

  • System geometry, specifically aspect ratio, plays a fundamental role in the freezing and jamming behavior of kinetically constrained models.
  • The convergence of critical vacancy density depends strongly on the dimensionality and shape of the confinement.
  • These findings provide valuable insights into the physics of glassy systems in confined environments.