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Nonextensive Supercluster States in Aggregation with Fragmentation.

Nikolai V Brilliantov1,2, Wendy Otieno2, P L Krapivsky1,3,4

  • 1Skolkovo Institute of Science and Technology, 143026 Moscow, Russia.

Physical Review Letters
|January 14, 2022
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Summary
This summary is machine-generated.

Systems can enter a supercluster state (SCS) resembling gelling but governed by critical fluctuations. This nonextensive state, distinct from equilibrium and jamming, requires novel scaling approaches for characterization.

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Area of Science:

  • Complex systems
  • Statistical physics

Background:

  • Systems evolving via aggregation and fragmentation can exhibit unique states.
  • The supercluster state (SCS) is characterized by large clusters, resembling a gelling state.
  • SCS formation is influenced by fluctuations, similar to critical phenomena.

Purpose of the Study:

  • To investigate the properties of the supercluster state (SCS) in evolving systems.
  • To differentiate the SCS from equilibrium and jamming states.
  • To develop a theoretical framework for describing the SCS.

Main Methods:

  • Proposed a scaling approach with critical exponents to characterize the SCS.
  • Utilized theoretical analysis, noting the failure of conventional methods like van Kampen expansion.
  • Validated theoretical findings with numerical simulations.

Main Results:

  • The SCS is a nonextensive state where cluster number scales sublinearly with system size.
  • The SCS occupies a distinct region in the parameter space, separating equilibrium and jamming (extensive) states.
  • The proposed scaling approach successfully described the SCS.

Conclusions:

  • The supercluster state (SCS) is a novel, non-gelling, non-jamming state in evolving systems.
  • A scaling theory with critical exponents is effective for characterizing the SCS.
  • The findings offer new insights into the behavior of complex systems near criticality.