Time-reversal symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium.

@article{Bosetti2010TimereversalSA,
  title={Time-reversal symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium.},
  author={Hadrien Bosetti and Harald A. Posch and Christoph Dellago and William Graham Hoover},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2010},
  volume={82 4 Pt 2},
  pages={
          046218
        }
}
  • H. Bosetti, H. Posch, +1 author W. G. Hoover
  • Published 26 April 2010
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a simple model representing a harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the… 
Symmetry properties of orthogonal and covariant Lyapunov vectors and their exponents
Lyapunov exponents are indicators for the chaotic properties of a classical dynamical system. They are most naturally defined in terms of the time evolution of a set of so-called covariant vectors,
Local Gram–Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems
We compare the Gram–Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively.
Why Instantaneous Values of the "Covariant" Lyapunov Exponents Depend upon the Chosen State-Space Scale
We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations
Covariant Lyapunov vectors
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of
Orthogonal versus covariant Lyapunov vectors for rough hard disk systems
The Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this
A review of the hydrodynamic Lyapunov modes of hard disk systems
A review of the results obtained for hard disk fluids confined to a quasi-one-dimensional (QOD) system is presented. One of the main achievements in recent years has been determining the hydrodynamic
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the
Periodic Eigendecomposition and Its Application to Kuramoto-Sivashinsky System
TLDR
The periodic Schur decomposition is incorporated to the computation of dynamical Floquet vectors, compared with other methods, and it is shown that the method can yield the full Floquet spectrum of a periodic orbit at every point along the orbit to high accuracy.
Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited
The stability analysis introduced by Lyapunov and extended by Oseledec provides an excellent tool to describe the character of nonlinear n-dimensional flows by n global exponents if these flows are
Estimating Hyperbolicity of Chaotic Bidimensional Maps
TLDR
This work applies to bidimensional chaotic maps the numerical method proposed by Ginelli et al.
...
1
2
...

References

SHOWING 1-10 OF 59 REFERENCES
Characterizing dynamics with covariant Lyapunov vectors.
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of
DYNAMICAL INSTABILITIES, MANIFOLDS, AND LOCAL LYAPUNOV SPECTRA FAR FROM EQUILIBRIUM
We consider an harmonic oscillator in a thermal gradient far from equilibrium. The motion is made ergodic and fully time-reversible through the use of two thermostat variables. The equations of
Symmetry-breaking in local Lyapunov exponents
Abstract:Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time
Covariant Lyapunov vectors for rigid disk systems
TLDR
Detailed computer simulations are carried out to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions and the stable and unstable manifolds are transverse to each other and the system is hyperbolic.
Fluctuations and asymmetry via local Lyapunov instability in the time-reversible doubly thermostated harmonic oscillator
Forward and backward trajectories from time-symmetric equations of motion can have time-asymmetric stability properties, and exhibit time-asymmetric fluctuations. Away from equilibrium this symmetry
Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices.
TLDR
This work performs a detailed study of the scaling properties of Lyapunov vectors for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ^{4} models and calculates characteristic LVs in large systems thanks to a "bit reversible" algorithm, which completely obviates computer memory limitations.
Determining Lyapunov exponents from a time series
We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative
Lyapunov Instability of Classical Many-Body Systems
In this paper we are concerned with the instability of the phase-space trajectory for particle models resembling classical fluids with short-range interactions. Recently, the application of dynamical
Are local Lyapunov exponents continuous in phase space
Local expansion rates of small displacements in phase space are calculated for two simple ergodic model systems, one with hard elastic collisions, the other with smooth forces. We find that the local
Lyapunov instability of dense Lennard-Jones fluids.
  • Posch, Hoover
  • Physics, Medicine
    Physical review. A, General physics
  • 1988
TLDR
Nose-Hoover mechanics, ofmore » which Gauss's isokinetic mechanics is a special case, resolves the reversibility paradox first stated by J. Loschmidt (Sitzungsber.
...
1
2
3
4
5
...