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Simple dynamical models for hierarchical bunching.

Hidetsugu Sakaguchi1, Norio Fujimoto

  • 1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

Hierarchical bunching models show that uniform states become unstable, forming clusters that merge into larger ones. This coarsening process follows a power law dependent on long-range forces, similar to spinodal decomposition.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Uniform particle distributions can be unstable.
  • Cluster formation and coarsening are observed in various physical systems.

Purpose of the Study:

  • To propose and analyze simple one-dimensional models for hierarchical bunching.
  • To investigate the dynamics of cluster merging and coarsening.
  • To explore the relationship between long-range forces and coarsening exponents.

Main Methods:

  • Development of simple one-dimensional lattice models for hierarchical bunching.
  • Linear stability analysis of uniform states.
  • Analysis of cluster merging and coarsening dynamics.
  • Study of a continuum model with linear repulsive forces.

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Main Results:

  • Uniform states are linearly unstable, leading to the formation of bunching clusters.
  • These clusters merge into larger structures through a coarsening process.
  • The coarsening dynamics obey a power law related to long-range forces.
  • The continuum model exhibits behavior analogous to spinodal decomposition and Ostwald ripening.

Conclusions:

  • Hierarchical bunching is a robust phenomenon driven by instabilities in uniform states.
  • The coarsening process is governed by long-range forces, with exponents dependent on their nature.
  • The studied models provide insights into pattern formation and coarsening dynamics in one dimension.