Equilibrium and nonequilibrium Lyapunov spectra for dense fluids and solids
作者： Harald A. Posch , William G. Hoover
关键词: Statistical physics 、 Curse of dimensionality 、 Reynolds number 、 Physics 、 Hypersphere 、 Attractor 、 Phase space 、 Lyapunov function 、 Non-equilibrium thermodynamics 、 Lyapunov exponent
摘要: The Lyapunov exponents describe the time-averaged rates of expansion and contraction a Lagrangian hypersphere made up comoving phase-space points. principal axes such grow, or shrink, exponentially fast with time. corresponding set growth decay is called ''Lyapunov spectrum.'' spectra are determined here for variety two- three-dimensional fluids solids, both at equilibrium in nonequilibrium steady states. states all boundary-driven shear flows, which single boundary degree freedom maintained constant temperature, using Nose-Hoover thermostat. Even far-from-equilibrium deviate logarithmically from ones. Our spectra, to planar-Couette-flow Reynolds numbers ranging 13 84, resemble some recent approximate model calculations based on Navier-Stokes hydrodynamics. We calculate Kaplan-Yorke fractal dimensionality flows associated our strange attractors. may exceed number additional dimensions required time dependence shear-flow boundary.
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