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Packing-limited growth.

Peter Sheridan Dodds1, Joshua S Weitz

  • 1Columbia Earth Institute, Columbia University, New York, New York 10027, USA. dodds@ldeo.columbia.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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This study explores sphere growth models, revealing a universal exponent in sphere radius distributions and linking fractal structure to pore space decay. These findings are confirmed through theoretical and simulation-based packing studies.

Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Growing spheres seeded randomly in space and time.
  • Growth cessation occurs upon sphere contact, leading to a jammed state.

Purpose of the Study:

  • Investigate the statistics of growth-limited packing in d dimensions.
  • Analyze the relationship between fractal structure and pore space decay in these models.
  • Determine the universal exponent governing sphere radius distributions.

Main Methods:

  • Theoretical analysis in d dimensions.
  • Numerical simulations in 2, 3, and 4 dimensions.
  • Construction and validation of a scaling theory.

Main Results:

Related Experiment Videos

  • A broad class of models exhibit sphere radius distributions with a universal exponent.
  • The scaling theory accurately relates fractal structure to pore space decay.
  • Numerical simulations confirm the scaling theory's predictions, especially in 4 dimensions.

Conclusions:

  • The study establishes a universal exponent in sphere packing models.
  • A validated scaling theory connects geometric properties (fractal structure, pore space) to growth dynamics.
  • The findings have implications for understanding jammed states and disordered systems.