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Random Close Packing as a Dynamical Phase Transition.

Sam Wilken1, Rodrigo E Guerra1, Dov Levine2

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This summary is machine-generated.

We introduce a biased random organization (BRO) model that simulates sphere packing. Our model

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Sphere packing is a fundamental problem in physics and materials science.
  • The densest known packing is face-centered cubic (FCC) with a space-filling fraction of ~0.74.
  • The densest random packing (RCP) is ill-defined but experimentally and computationally estimated at ~0.64.

Purpose of the Study:

  • To introduce a novel absorbing-state model for sphere packing.
  • To investigate the densest critical point of this model and its relation to random close packing (RCP).
  • To determine if the model's configurations are structurally identical to RCP.

Main Methods:

  • Development of a simple absorbing-state model termed biased random organization (BRO).
  • Analysis of the model's dynamical phase transition between absorbing and active states.
  • Comparison of critical configurations from the BRO model with known RCP configurations.

Main Results:

  • The BRO model exhibits a Manna class dynamical phase transition.
  • The densest critical point of the BRO model is approximately 0.64, matching the estimated density of RCP.
  • Configurations generated by the BRO model are structurally identical to those found in RCP.

Conclusions:

  • The biased random organization (BRO) model provides a new framework for studying sphere packing.
  • The model's critical state successfully reproduces the structural characteristics of random close packing (RCP).
  • This suggests that the densest absorbing state in BRO models may define RCP configurations.