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Viscous attractor for the Galton board.

W. G. Hoover1, B. Moran

  • 1Department of Applied Science, University of California at Davis/Livermore and Lawrence Livermore National Laboratory, Livermore, California 94550.

Chaos (Woodbury, N.Y.)
|October 1, 1992
PubMed
Summary

This study analyzes the Galton Board model, revealing multifractal phase-space structures in a nonequilibrium steady state. The findings are accurately described by creeping-flow and Green-Kubo limits depending on system damping.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • The Galton Board, or periodic Lorentz Gas, is a model system for studying particle dynamics.
  • Nonequilibrium steady states arise from driving forces and dissipative interactions.
  • Understanding phase-space structures is crucial for characterizing complex systems.

Purpose of the Study:

  • To analyze the nonequilibrium steady state of a driven Galton Board with linear drag.
  • To investigate the emergent multifractal phase-space structures.
  • To compare results with previous findings using isokinetic equations of motion.

Main Methods:

  • Simulating a point mass scattered by elastic disks under a constant driving field and linear drag.
  • Analyzing long-time-averaged trajectories.
  • Examining the creeping-flow and Green-Kubo linear-response limits.

Main Results:

  • A nonequilibrium steady state emerges, dependent on the dimensionless ratio gtau(2)/sigma.
  • Multifractal phase-space structures are observed, consistent with prior isokinetic studies.
  • The system exhibits distinct behaviors in the highly damped (creeping-flow) and lightly damped (Green-Kubo) regimes.

Conclusions:

  • The Galton Board model with combined driving and damping exhibits complex multifractal dynamics.
  • The system's behavior can be accurately described by different physical limits based on the damping parameter.
  • This work provides insights into nonequilibrium statistical mechanics and complex system dynamics.

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