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Related Experiment Videos

Critical phase in nonconserving zero-range processes and rewiring networks.

A G Angel1, M R Evans, E Levine

  • 1SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

This study introduces a generalized model for zero-range processes and network rewiring, achieving sustained criticality and scale-free properties without parameter tuning. This offers a new perspective on complex systems dynamics.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Zero-range processes involve particle hopping on lattices, related to network rewiring dynamics.
  • Both systems can exhibit condensation transitions, leading to macroscopic occupation or connectivity.
  • Criticality, marked by scale-free distributions, typically occurs only at specific transition points.

Purpose of the Study:

  • To propose a generalized model for zero-range processes and network rewiring.
  • To achieve criticality and scale-free distributions across an entire phase, not just at a transition point.
  • To eliminate the need for fine-tuned parameters to obtain scale-free properties.

Main Methods:

  • Generalization of existing zero-range process and network rewiring models.

Related Experiment Videos

  • Analysis of dynamical rules and phase transitions.
  • Characterization of emergent scale-free distributions.

    • Main Results:

    • The generalized model yields criticality throughout a continuous phase.
    • Scale-free distributions emerge independently of specific parameter values.
    • This contrasts with traditional models requiring precise parameter tuning for criticality.

    Conclusions:

    • A novel framework for generating scale-free complex systems is presented.
    • The model offers a robust mechanism for achieving criticality in dynamic systems.
    • This work provides insights into the fundamental properties of complex networks and statistical physics models.