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Scaling theory for migration-driven aggregate growth.

F Leyvraz1, S Redner

  • 1Centro de Ciencias Físicas, Avenida Universidad s/n, Colonia Chamilpa, Cuernavaca, Morelos, Mexico.

Physical Review Letters
|February 28, 2002
PubMed
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This study describes irreversible aggregate growth driven by monomer migration. Aggregate size distribution and mean size evolution depend on migration rate scaling, applicable to population dynamics and economic models.

Area of Science:

  • Physical Chemistry
  • Statistical Mechanics
  • Complex Systems

Background:

  • Aggregate formation and growth are fundamental processes in various scientific domains.
  • Understanding the dynamics of aggregate size distribution is crucial for predicting system evolution.
  • Previous models often simplify the migration rates between aggregates of different sizes.

Purpose of the Study:

  • To provide a comprehensive theoretical description of irreversible aggregate growth.
  • To analyze how the scaling properties of monomer migration rates influence aggregate size distribution and mean size.
  • To establish the applicability of the developed theory to diverse real-world phenomena.

Main Methods:

  • Development of a theoretical framework for aggregate growth based on monomer migration.

Related Experiment Videos

  • Analysis of homogeneous migration rates, K(i;j), where K(ai;aj) is proportional to a(lambda)K(i;j).
  • Derivation of the time evolution of mean aggregate size and the aggregate size distribution.

    • Main Results:

    • The mean aggregate size grows with time as t(1/(2-lambda)) for lambda<2.
    • The aggregate size distribution exhibits distinct regimes controlled by the scaling properties of the migration rate.
    • The theory provides a unified approach to understanding size distributions in various systems.

    Conclusions:

    • The scaling of monomer migration rates is a key determinant of aggregate growth dynamics.
    • The theoretical model accurately describes irreversible aggregate growth and size distribution.
    • The findings have broad implications for understanding city population distributions, material science coarsening, and wealth exchange models.