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Related Experiment Videos

Exactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces.

S Torquato1, F H Stillinger

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. torquato@electron.princeton.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2006
PubMed
Summary

We introduce a solvable disordered sphere packing model. This model suggests high-dimensional packings may be disordered, exceeding old density bounds.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Materials science

Background:

  • Sphere packing problems are fundamental in various scientific fields.
  • Existing models often lack analytical solvability in higher dimensions.
  • Minkowski's bound provides a lower limit for periodic lattice packings.

Purpose of the Study:

  • To introduce a generalized random sequential addition (RSA) model for hard spheres.
  • To analytically solve the n-particle correlation functions for a specific RSA packing limit.
  • To investigate the density limits of disordered sphere packings in arbitrary dimensions.

Main Methods:

  • Generalization of the random sequential addition (RSA) process.
  • Analytical derivation of n-particle correlation functions in the "ghost" RSA packing limit.

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  • Analysis of packing density in d-dimensional Euclidean space (Rd).

    • Main Results:

    • The "ghost" RSA packing model is exactly solvable for all densities and dimensions.
    • The maximal density of ghost RSA packing is 1/2d.
    • A conjectural lower bound on density suggests exponential improvement over Minkowski's bound.

    Conclusions:

    • Disordered sphere packings can exceed traditional density bounds in high dimensions.
    • The densest packings in high dimensions might be disordered, not periodic.
    • This implies the existence of disordered classical ground states for certain continuous potentials.