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Related Experiment Videos

Balls-in-boxes condensation on networks.

L Bogacz1, Z Burda, W Janke

  • 1Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Kraków, Poland. bogacz@th.if.uj.edu.pl

Chaos (Woodbury, N.Y.)
|July 7, 2007
PubMed
Summary
This summary is machine-generated.

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Condensate formation in networks differs between regular and irregular structures. Irregular networks show exponential melting time increases with system size, unlike regular networks

Area of Science:

  • Statistical Physics
  • Network Theory
  • Complex Systems

Background:

  • Condensate formation is a key phenomenon in statistical physics.
  • Zero-range processes model particle systems on networks.
  • Network structure significantly impacts system dynamics.

Purpose of the Study:

  • To investigate condensate formation in two distinct network regimes: q-regular and minimally irregular.
  • To analyze the influence of network irregularity on condensation statics and dynamics.
  • To compare the condensate melting behavior in regular versus irregular networks.

Main Methods:

  • Theoretical analysis of zero-range processes on networks.
  • Introduction of a single node with higher degree (Q node) to create minimal irregularity.

Related Experiment Videos

  • Mathematical modeling to derive scaling laws for condensation dynamics.

    • Main Results:

    • Condensate formation on q-regular networks arises from spontaneous symmetry breaking.
    • On irregular networks, condensation is driven by explicit symmetry breaking, controlled by alpha = ln(Q/q).
    • Condensate melting time on the irregular Q node scales exponentially with system size N, unlike the power-law scaling on q-regular networks.

    Conclusions:

    • Network irregularity fundamentally alters condensate formation and stability.
    • The parameter alpha quantifies the impact of minimal irregularity on particle distribution and condensate lifetime.
    • Findings highlight the critical role of network topology in determining macroscopic system behavior.