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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Dense random packings are ubiquitous in nature and technology.
  • Understanding their correlation properties is crucial for predicting material behavior.
  • Disks with power-law size distributions present unique challenges in modeling.

Purpose of the Study:

  • To investigate the correlation properties of dense random packings of disks with power-law size distributions.
  • To determine if these packings exhibit fractal characteristics.
  • To derive a structure factor applicable to small-angle scattering.

Main Methods:

  • Theoretical analysis in 1D.
  • Numerical simulations in 1D and 2D.
  • Analysis of structure factor, mass-radius relation, and pair distribution function.

Main Results:

  • Dense disk packings with power-law radii show fractal properties.
  • The exponent of the power-law distribution and the fractal dimension were found to be equal.
  • An approximate structure factor formula was derived for arbitrary dimensions.

Conclusions:

  • The fractal nature of these packings is confirmed.
  • The derived structure factor can be used for analyzing scattering data.
  • Findings are relevant for diverse systems like concrete, emulsions, and biological tissues.