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Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.

G Zhang1, S Torquato2

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
PubMed
Summary
This summary is machine-generated.

Researchers developed a precise algorithm for random sequential addition (RSA) packing of hyperspheres, revealing how disorder increases with dimension and enhancing understanding of condensed matter systems.

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Area of Science:

  • Statistical mechanics
  • Condensed matter theory
  • Computational physics

Background:

  • Packing of hard hyperspheres is a fundamental problem in statistical mechanics.
  • Dense packings are ordered in low dimensions but may be disordered in high dimensions.
  • Random sequential addition (RSA) models disorder in high-dimensional packing.

Purpose of the Study:

  • To refine an algorithm for generating precise random sequential addition (RSA) packings of hyperspheres.
  • To study the saturation density and properties of RSA packings in high dimensions (2 to 8).
  • To investigate the impact of dimension on particle correlations and hyperuniformity.

Main Methods:

  • Refinement of a previously developed algorithm for RSA packing.
  • Generation of RSA packings in large simulation boxes across dimensions 2 to 8.
  • Calculation of packing/covering densities, pair correlation function g(2)(r), and structure factor S(k).
  • Computation of void exclusion probability and quantizer error.

Main Results:

  • Achieved heretofore unattained precision in RSA packing simulations.
  • Observed diminishing pair correlations and increasing hyperuniformity with increasing spatial dimension.
  • Calculated key statistical properties of saturated RSA configurations.

Conclusions:

  • The refined algorithm enables precise simulation of RSA packings in high dimensions.
  • Increasing dimension leads to decorrelation and enhanced hyperuniformity in hypersphere packings.
  • The method is generalizable to nonspherical particles.