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Space-filling percolation.

Abhijit Chakraborty1, S S Manna1

  • 1Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700098, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 16, 2014
PubMed
Summary
This summary is machine-generated.

This study investigates percolation in randomly grown disks, revealing a sharp yet continuous transition. The findings suggest a space-filling limit and scale-free networks at critical points, offering insights into complex system dynamics.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Materials Science

Background:

  • Percolation theory describes the formation of connected clusters in random systems.
  • Growing disk models are used to simulate spatial patterns and phase transitions.
  • Understanding transitions in random geometric systems is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the percolation properties of randomly grown circular disks with slight overlaps.
  • To characterize the nature of the transition (discontinuous vs. continuous) as a function of disk growth rate.
  • To determine critical parameters and properties, such as fractal dimension and network structure.

Main Methods:

  • Numerical simulations of randomly growing circular disks in a 2D space.
  • Analysis of percolation properties, including order parameter, cluster size distribution, and area coverage.
  • Investigation of the system's behavior in the limit of vanishing growth rate (δ→0).

Main Results:

  • Evidence for a sharp but continuous transition, exhibiting characteristics of both discontinuous and continuous percolation.
  • Observation that the order parameter jumps discontinuously, while cluster size distribution follows a power-law decay.
  • In the limit of vanishing growth rate (δ→0), the system approaches a space-filling configuration with a fractal dimension of 1.42(10) for pore space and a scale-free contact network.

Conclusions:

  • The study identifies a novel 'sharp but continuous' transition in growing disk percolation, analogous to explosive percolation.
  • The findings suggest that as the growth rate approaches zero, the system becomes space-filling and exhibits scale-free network properties.
  • This research contributes to the understanding of phase transitions in random geometric systems and their emergent network structures.