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Updated: Jan 29, 2026

Measuring the Complete-arch Distortion of an Optical Dental Impression
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Percolation in a distorted square lattice.

Sayantan Mitra1, Dipa Saha1, Ankur Sensharma1

  • 1Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India.

Physical Review. E
|February 21, 2019
PubMed
Summary
This summary is machine-generated.

This study explores percolation on distorted square lattices. Increasing lattice distortion raises the percolation threshold, while a higher connection threshold facilitates percolation, suggesting a link to ordinary percolation universality classes.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Percolation theory models connectivity in disordered systems.
  • Real-world systems often exhibit imperfections and distortions, deviating from ideal lattices.
  • Understanding percolation in non-ideal structures is crucial for various applications.

Purpose of the Study:

  • Investigate percolation phenomena in a distorted square lattice model.
  • Analyze the impact of lattice distortion (parameter α) and connection threshold (d) on percolation.
  • Determine critical exponents and fractal dimensions to classify the universality class.

Main Methods:

  • Monte Carlo simulations were employed to study the distorted square lattice.
  • Lattice site positions were systematically shifted using a tunable parameter α.
  • Connectivity was defined by a connection threshold d between neighboring occupied sites.

Main Results:

  • Percolation threshold (p_c) increases with lattice distortion (α), making spanning more difficult.
  • An increased connection threshold (d) facilitates percolation.
  • Scaling behavior and fractal dimension (d_f) suggest the model belongs to the ordinary percolation universality class.

Conclusions:

  • Distorted lattices present unique percolation behaviors compared to regular lattices.
  • The model provides a framework for studying percolation in more realistic, imperfect systems.
  • Findings have implications for understanding phase transitions and connectivity in disordered materials.