Aspects of Dynamical Simulations, Emphasizing Nosé and Nosé-Hoover Dynamics and the Compressible Baker Map

• Autorzy: Hoover W. G. , Hoover C. G.

Identyfikatory

DOI

10.12921/cmst.2019.0000035

• Języki publikacji: EN

Abstrakty

EN

Aspects of the Nosé and Nosé-Hoover dynamics developed in 1983–1984 along with Dettmann’s closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville’s Theorem. Our account is pedagogical, focused on the harmonic oscillator for simplicity, though exactly the same ideas can be, and have been, applied to manybody systems. Nosé, Nosé-Hoover, and Dettmann flows were all developed in order to access Gibbs’ canonical ensemble directly from molecular dynamics. Unlike Monte Carlo algorithms dynamical flow models are often not ergodic and so can fail to reproduce Gibbs’ ensembles. Accordingly we include a discussion of ergodicity, the visiting of all relevant microstates corresponding to the desired ensemble. We consider Lyapunov instability too, the usual mechanism for phasespace mixing. We show that thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible, or contracting, depending upon the chosen “phase space”. The fractal nature of nonequilibrium flows is also illustrated for two simple two-dimensional models, the hard-disk-based Galton Board and the time-reversible Baker Map. The simultaneous treatment of flows as one-dimensional and many-dimensional suggests some interesting topological problems for future investigations.

Słowa kluczowe

EN

Nosé oscillator; Nosé-Hoover oscillator; Dettmann oscillator; nonlinear dynamics; Galton Board; Baker Map

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2019
• Tom: Vol. 25, No. 3
• Strony: 125--141
• Opis fizyczny: Bibliogr. 39 poz., rys.

Twórcy

autor

Hoover W. G.

• Ruby Valley Research Institute 601 Highway Contract 60 Ruby Valley, Nevada 89833

autor

Hoover C. G.

• Ruby Valley Research Institute 601 Highway Contract 60 Ruby Valley, Nevada 89833

Bibliografia

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