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Related Experiment Videos

Complete condensation in a zero range process on scale-free networks.

Jae Dong Noh1, G M Shim, Hoyun Lee

  • 1Department of Physics, Chungnam National University, Daejeon, Korea.

Physical Review Letters
|August 11, 2005
PubMed
Summary

Particle dynamics on scale-free networks exhibit complete condensation when the hopping rate parameter delta is below a critical value. This phenomenon concentrates particles on high-degree nodes, impacting network behavior.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • The zero-range process models particle movement on networks.
  • Scale-free networks possess unique structural properties influencing dynamics.
  • Understanding particle distribution is key to network function.

Purpose of the Study:

  • Investigate particle dynamics on scale-free networks.
  • Analyze the influence of network structure on the zero-range process.
  • Determine conditions for particle condensation.

Main Methods:

  • Analytical derivation of condensation conditions.
  • Numerical simulations of the zero-range process.
  • Analysis of power-law scaling for relaxation time.

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Main Results:

  • Complete condensation occurs when delta <= 1/(gamma-1).
  • High-degree nodes accumulate macroscopic particle numbers in condensation.
  • Relaxation time scales as tau ~ L^z in the condensed phase.

Conclusions:

  • Network topology significantly impacts particle condensation in zero-range processes.
  • The identified critical threshold governs the transition to a condensed state.
  • Dynamic exponent z characterizes relaxation in condensed scale-free networks.