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Fractal dimension of steady nonequilibrium flows
William G. Hoover1, Harald A. Posch, Carol G. Hoover
1Department of Applied Science, Post Office Box 808, University of California at Davis-Livermore, California 94550Institute for Experimental Physics, Boltzmanngasse 5, University of Vienna, Vienna A-1090, AustriaMethods Development Group, Mechanical Engineering Department, Lawrence Livermore National Laboratory, Livermore, California 94550.
Chaos (Woodbury, N.Y.)
|April 1, 1992
Summary
External isothermal boundaries can drive nonequilibrium many-body flows onto multifractal attractors. This reduces the phase-space information dimension compared to equilibrium flows, potentially causing diverging Gibbs
Area of Science:
- Statistical Mechanics
- Non-Equilibrium Thermodynamics
- Computational Physics
Background:
- Understanding the behavior of many-body systems under steady nonequilibrium conditions is crucial.
- Characterizing the phase-space dynamics of such systems is a key challenge.
- The role of external boundaries in influencing system dynamics needs further investigation.
Purpose of the Study:
- To evaluate the Kaplan-Yorke information dimension of phase-space attractors for two types of steady nonequilibrium many-body flows.
- To investigate the impact of external isothermal boundaries on the attractor dimension.
- To compare the dimensionality of nonequilibrium attractors with corresponding equilibrium flows.
Main Methods:
- Numerical evaluation of the Kaplan-Yorke information dimension.
- Simulation of Newtonian particle systems interacting with boundary particles.
- Application of Nose-Hoover thermostat forces to impose time-averaged boundary temperatures.
Main Results:
- External isothermal boundaries drive Newtonian flows onto multifractal attractors.
- The phase-space information dimension of these nonequilibrium attractors is significantly lower than that of equilibrium flows.
- This reduction in dimension suggests potential divergence of Gibbs' entropy for these nonequilibrium flows.
Conclusions:
- External isothermal boundaries can induce complex multifractal dynamics in nonequilibrium many-body flows.
- The reduced phase-space information dimension highlights a fundamental difference between equilibrium and nonequilibrium systems.
- The findings have implications for understanding entropy production and thermodynamic properties in driven systems.