Lyapunov Modes in Hard-Disk Systems

Abstract

We consider simulations of a 2-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated ``eigen-directions'', called Lyapunov modes. We carefully analyze these modes and show how they are naturally associated with vector fields over the container. We also show that the Lyapunov exponents, and the coupled dynamics of the modes (where it exists) follow linear laws, whose coefficients only depend on the density of the gas, but not on aspect ratio and very little on the boundary conditions.

Animated pictures are available at http://theory.physics.unige.ch/modes/ Second revised version

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Cited by in corpus (14)

• Characterizing dynamics with covariant Lyapunov vectors
• Covariant Lyapunov vectors
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• Covariant Lyapunov vectors for rigid disk systems
• Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium
• What does dynamical systems theory teach us about fluids?
• Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems
• Lyapunov Modes for a Nonequilibrium System with a Heat Flux
• Lyapunov Mode Dynamics in Hard-Disk Systems
• From Lyapunov modes to the exponents for hard disk systems
• Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems
• Backward and covariant Lyapunov vectors and exponents for hard disk systems with a steady heat current
• Radius of curvature approach to the Kolmogorov-Sinai entropy of dilute hard particles in equilibrium
• Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems