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Biased random organization (BRO) models random close packing (RCP) in dimensions 3-5. This dynamical model suggests RCP may not exist in lower dimensions, with an upper-critical dimension of 4.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Random close packing (RCP) describes the densest possible disordered arrangements of particles.
  • Understanding RCP's existence and properties across different dimensions is a fundamental challenge in statistical mechanics.

Purpose of the Study:

  • To investigate the dynamical model of biased random organization (BRO) as a method for generating random close packing configurations.
  • To determine the existence and characteristics of RCP in various dimensions (d=1-5) using the BRO model.
  • To classify the dynamical phase transitions of the BRO model within existing universality classes.

Main Methods:

  • Simulating the biased random organization (BRO) model in dimensions d=1-5.
  • Analyzing the densest critical points generated by BRO dynamics.
  • Measuring critical exponents related to steady-state activity and density fluctuations.
  • Examining the distribution of inter-particle gaps (near contacts).

Main Results:

  • The BRO model generates configurations consistent with random close packing (RCP) at its densest critical point in d=3.
  • RCP configurations are conjectured to be produced by BRO in all dimensions, implying RCP does not exist in d=1-2.
  • In dimensions d=3-5, BRO yields isostatic configurations with specific volume fractions (0.64, 0.46, 0.30).
  • BRO dynamics belong to the Manna universality class for dynamical phase transitions across dimensions d=2-5.
  • Near-contact distributions align with theoretical RCP treatments in dimensions d≥4.
  • The upper-critical dimension for RCP is found to be consistent with the Manna class, d_uc=4.

Conclusions:

  • The biased random organization (BRO) model provides a viable dynamical pathway to achieving random close packing (RCP) configurations.
  • The study suggests a dimensional limitation for the existence of RCP, with an upper-critical dimension of 4.
  • BRO's classification within the Manna universality class offers insights into the nature of dynamical phase transitions in disordered systems.