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Percolation and jamming in random bond deposition.

G Kondrat1, A Pekalski

  • 1Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204 Wroclaw, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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We studied how needle length affects jamming and percolation on a square lattice. Shorter needles percolate then jam, while longer needles jam without percolating, revealing a critical transition point.

Area of Science:

  • Statistical Physics
  • Materials Science

Background:

  • Percolation and jamming are critical phenomena studied in various physical systems.
  • Understanding these phenomena is crucial for predicting material properties and system behavior.

Purpose of the Study:

  • To investigate the impact of linear segment (needle) length on percolation and jamming thresholds in a square lattice model.
  • To differentiate this model from standard site deposition problems and identify critical transitions.

Main Methods:

  • A computational model was developed to simulate random placement of linear segments of varying lengths on a square lattice.
  • Analysis focused on determining percolation and jamming thresholds as a function of needle length.
  • The Fisher exponent was calculated to compare with standard percolation theory.

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Main Results:

  • A distinct transition in system behavior was observed at a needle length of a=6.
  • For shorter needles (a<6), the system percolates before jamming.
  • For longer needles (a>6), the lattice jams but does not exhibit percolation, attributed to differing needle clustering.

Conclusions:

  • Needle length significantly influences percolation and jamming dynamics, demonstrating a critical transition at a=6.
  • The observed transition is linked to distinct clustering behaviors of short versus long needles.
  • The study confirms the universality of the Fisher exponent, aligning with standard 2D percolation theory.