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Area of Science:

  • Statistical physics
  • Complex systems dynamics
  • Mathematical modeling

Background:

  • Aggregation-fragmentation models exhibit condensate formation in steady states.
  • Understanding coarsening dynamics is crucial for complex systems.
  • Previous studies often focused on steady-state properties.

Purpose of the Study:

  • To investigate the dynamics of coarsening in aggregation-fragmentation models.
  • To analyze the role of local condensates during the coarsening process.
  • To characterize the statistical properties of condensate mass distribution.

Main Methods:

  • Application of extreme value statistics.
  • Analysis of the zero-range process and conserved mass aggregation model.
  • Investigation of condensate mass distribution and scaling behavior.

Main Results:

  • Coarsening dynamics are driven by local condensate formation.
  • A characteristic length scale for condensates grows over time.
  • Condensate mass distribution shows scaling with anomalously large fluctuations.
  • Mean and standard deviation of condensate mass are proportional to the coarsening length.

Conclusions:

  • The preasymptotic state, not the steady state, governs system behavior during coarsening.
  • Strong fluctuations in condensate mass characterize the dynamic preasymptotic regime.
  • Extreme value statistics provide a powerful tool for analyzing such complex dynamics.