• Corpus ID: 195584287

Aspects of Nos\'e and Nos\'e-Hoover Dynamics Elucidated

  title={Aspects of Nos\'e and Nos\'e-Hoover Dynamics Elucidated},
  author={Wm. G. Hoover and Carol Griswold Hoover},
  journal={arXiv: Statistical Mechanics},
Some paradoxical aspects of the Nose and Nose-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible, or contracting, as is described here by a variety of three- and four-dimensional phase-space models. These findings illustrate some surprising consequences when Liouville's continuity equation is applied to Hamiltonian flows. 

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Remark on "Some simple chaotic flows"

  • Hoover
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
The Nose-Hoover oscillator system is the simplest mechanical system exhibiting chaos.

Global analysis of a generalized Nosé–Hoover oscillator

Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics

The Nose Hamiltonian is adapted, leading to a derivation of the Nose-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the

Canonical dynamics of the Nosé oscillator: Stability, order, and chaos.

The Nose oscillator is a borderline case, not sufficiently chaotic for a fully statistical description, and it is suggested that the behavior of only slightly more complicated systems is considerably simpler and in accord with statistical mechanics.

The Coexistence of Invariant Tori and Topological Horseshoe in a Generalized Nosé-Hoover Oscillator

Horseshoe chaos can be demonstrated by applying the topological horseshoe theory to a Poincare map defined in a proper cross-section, which further shows the coexistence of infinitely stable periodic trajectories and infinite saddle periodic trajectoryories.

Canonical dynamics: Equilibrium phase-space distributions.

  • Hoover
  • Physics
    Physical review. A, General physics
  • 1985
The dynamical steady-state probability density is found in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilus-dot andZeta act as thermodynamic friction coefficients.

A unified formulation of the constant temperature molecular dynamics methods

Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem.

A molecular dynamics method for simulations in the canonical ensemble

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed.

Qualitative Analysis of the Nosé–Hoover Oscillator

In this paper, we analyze the qualitative behavior of the solution of the Nosé–Hoover oscillator which is a three-dimensional quadratic polynomial system. We show that every invariant set of the