Singly-Thermostated Ergodicity in Gibbs’ Canonical Ensemble and the 2016 Ian Snook Prize Award

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

Identyfikatory

DOI

10.12921/cmst.2017.0000005

• Języki publikacji: EN

Abstrakty

EN

The 2016 Snook Prize has been awarded to Diego Tapias, Alessandro Bravetti, and David Sanders for their paper “Ergodicity of One-Dimensional Systems Coupled to the Logistic Thermostat”. They introduced a relatively-stiff hyperbolic tangent thermostat force and successfully tested its ability to reproduce Gibbs’ canonical distribution for three one-dimensional problems, the harmonic oscillator, the quartic oscillator, and the Mexican Hat potentials: {(q2=2); (q4=4); (q4=4) 􀀀 (q2=2)}. Their work constitutes an effective response to the 2016 Ian Snook Prize Award goal, “finding ergodic algorithms for Gibbs’ canonical ensemble using a single thermostat”. We confirm their work here and highlight an interesting feature of the Mexican Hat problem when it is solved with an adaptive integrator.

Słowa kluczowe

EN

ergodicity; chaos; algorithms; dynamical systems

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2017
• Tom: Vol. 23, No. 1
• Strony: 5--8
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Hoover W. G.

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

autor

Hoover C. G.

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

Bibliografia

• [1] S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, Journal of Chemical Physics 81, 511–519 (1984).
• [2] S. Nosé, Constant Temperature Molecular Dynamics Methods, Progress in Theoretical Physics Supplement 103, 1–46 (1991).
• [3] Wm.G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Physical Review A 31, 1695–1697 (1985).
• [4] D. Kusnezov, A. Bulgac, W. Bauer, Canonical Ensembles from Chaos, Annals of Physics 204, 155–185 (1990).
• [5] D. Kusnezov, A. Bulgac, Canonical Ensembles from Chaos: Constrained Dynamical Systems, Annals of Physics 214, 180–218 (1992).
• [6] Wm.G. Hoover, B.L. Holian, Kinetic Moments Method for the Canonical Ensemble Distribution, Physics Letters A 211, 253–257 (1996).
• [7] Wm.G. Hoover, C.G. Hoover, Singly-Thermostated Ergodicity in Gibbs’ Canonical Ensemble and the 2016 Ian Snook Prize, Computational Methods in Science and Technology 22, 127–131 (2016).
• [8] D. Tapias, A. Bravetti, D.P. Sanders, Ergodicity of One-Dimensional Systems Coupled to the Logistic Thermostat, Computational Methods in Science and Technology (in press, 2017) = arXiv 1611.05090.
• [9] Wm.G. Hoover, C.G. Hoover, Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators, Computational Methods in Science and Technology 21, 109–116 (2015).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).