Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

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

Identyfikatory

DOI

10.12921/cmst.2018.0000035

• Języki publikacji: EN

Abstrakty

EN

Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs’ canonical distribution for simple (small) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a quartic oscillator, and even to the “Mexican-Hat” (doublewell) potential problem. We consider here a time-reversible dynamical approach to Gibbs’ “microcanonical” (isoenergetic) distribution for simple systems. To enable isoenergetic ergodicity we add occasional random rotations to the velocities. This idea conserves energy exactly and can be made to cover the entire energy shell with an ergodic dynamics. We entirely avoid the Poincaré-section holes and island chains typical of Hamiltonian chaos. We illustrate this idea for the simplest possible two-dimensional example, a single particle moving in a periodic square-lattice array of scatterers, the “cell model”.

Słowa kluczowe

EN

chaos; ergodicity; Lyapunov exponent; algorithms

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2018
• Tom: Vol. 24, No. 2
• Strony: 155--158
• Opis fizyczny: Bibliogr. 11 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 Molecular Dynamics Method for Simulation in the Canonical Ensemble, Molecular Physics, 52, 255–268 (1984).
• [2] S. Nosé, A Unified Formulation of the Constant-Temperature Molecular Dynamics Methods, Journal of Chemical Physics, 81, 511–519 (1984).
• [3] Wm.G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Physical Review A, 31, 1695–1697 (1985).
• [4] Wm.G. Hoover, B.L. Holian, Kinetic Moments Method for the Canonical Ensemble Distribution, Physics Letters A 211, 253–257 (1996).
• [5] G.J. Martyna, M.L. Klein, M. Tuckerman, Nosé-Hoover Chains: the Canonical Ensemble via Continuous Dynamics, The Journal of Chemical Physics 97, 2635–2643 (1992).
• [6] Wm. G. Hoover, C.G. Hoover, J.C. Sprott, Nonequilibrium Systems: Hard Disks and Harmonic Oscillators Near and Far from Equilibrium, Molecular Simulation, 42, 1300–1316 (2016).
• [7] D. Tapias, A. Bravetti, D.P. Sanders, Ergodicity of One-Dimensional Systems Coupled to the Logistic Thermostat, Computational Methods in Science and Technology 23, 11–18 (2017).
• [8] I. Shimada, T. Nagashima, A Numerical Approach to Ergodic Problems of Dissipative Dynamical Systems, Progress of Theoretical Physics 61, 1605–1616 (1979).
• [9] G. Benettin, L. Galgani, A. Giorgilli, J.-M. Strelcyn, Lyapunov Characteristic Exponents for Smooth Dynamics Systems and for Hamiltonian Systems; a Method for Computing All of Them, Parts I and II: Theory and Numerical Application, Meccanica 15, 9-20 and 21-30 (1980).
• [10] F. Ricci-Tersenghi, The Solution to the Challenge in ‘Time-Reversible Random Number Generators’ ar¬iv:1305.1805 (2013).
• [11] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics 21, 1087-1092 (1953).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).