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Kinetics of migration-driven aggregation processes on scale-free networks.

Jianhong Ke1, Xiaoshuang Chen, Zhenquan Lin

  • 1School of Physics and Electronic Information, Wenzhou University, Wenzhou 325027, China. kejianhong@yahoo.com.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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We developed a model for aggregate growth on networks, finding that migration dynamics can lead to infinite growth or gelation transitions. Our findings align with U.S. population data over the last century.

Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Aggregate growth models are crucial for understanding complex systems.
  • Scale-free networks exhibit unique properties influencing system dynamics.
  • Migration processes can significantly alter aggregate formation and evolution.

Purpose of the Study:

  • To propose and analyze a solvable model for migration-driven aggregate growth on scale-free networks.
  • To investigate the influence of different rate kernels on system evolution.
  • To compare model predictions with real-world population data.

Main Methods:

  • Development of a reversible migration system with generalized rate kernels.
  • Introduction of a simplified model with independent monomer gain/loss rates.

Related Experiment Videos

  • Analytical derivation of aggregate size distribution and growth dynamics.
  • Validation of theoretical results using U.S. county population data.

    • Main Results:

    • System evolution critically depends on the rate kernel details.
    • Aggregate size distribution can approach a scaling form with infinite growth or exhibit a gelation transition.
    • Models show distinct aggregate evolution behavior compared to normal space systems.
    • Analytical predictions show good agreement with historical U.S. population data.

    Conclusions:

    • Migration dynamics play a pivotal role in aggregate growth on scale-free networks.
    • The proposed models offer a framework for understanding complex aggregation phenomena.
    • The study highlights the applicability of network models to real-world demographic trends.