Compressible Baker Maps and Their Inverses. A Memoir for Francis Hayin Ree [1936–2020]
Ruby Valley Research Institute
601 Highway Contract 60
Ruby Valley, Nevada 89833
E-mail: hooverwilliam@yahoo.com
Received:
Received: 06 March 2020; accepted: 06 March 2020; published online: 16 March 2020
DOI: 10.12921/cmst.2020.0000007
Abstract:
This memoir is dedicated to the late Francis Hayin Ree, a formative influence shaping my work in statistical mechanics. Between 1963 and 1968 we collaborated on nine papers published in the Journal of Chemical Physics. Those dealt with the virial series, cell models, and computer simulation. All of them were directed toward understanding the statistical thermodynamics of simple model systems. Our last joint work is also the most cited, with over 1000 citations, “Melting Transition and Communal Entropy for Hard Spheres”, submitted 3 May 1968 and published that October. Here I summarize my own most recent work on compressible time-reversible two-dimensional maps. These simplest of model systems are amenable to computer simulation and are providing stimulating and surprising results.
Key words:
Francis Ree, information and Kaplan-Yorke dimensions, maps, reversibility, statistical physics
References:
[1] B.J. Alder, T.E. Wainwright, Molecular Motions, Scientific American 201, 113–126 (1959).
[2] W.G. Hoover, A.G. De Rocco, Sixth and Seventh Virial Coefficients for the Parallel Hard-Cube Model, Journal of Chemical Physics 36, 3141–3162 (1962).
[3] A.G. De Rocco, W.G. Hoover, Second Virial Coefficient for the Spherical Shell Potential, Journal of Chemical Physics 36, 916–926 (1962).
[4] F.H. Ree, T.S. Ree, T. Ree, H. Eyring, Random Walk and Related Physical Problems, [In:] Advances in Chemical Physics 4, 1–66 (1962), ed. I. Prigogine.
[5] A list of 161 of Francis Ree’s publications can be found (in January 2020) on the ResearchGate website. Francis’ LLNL obituary can be found at https://www.llnl.gov/community/retiree-and-employee-resources/in-memoriam/francis-ree.
[6] W.G. Hoover, W.T. Ashurst, Nonequilibrium Molecular Dynamics, Theoretical Chemistry 1, 1–51, Academic, New York (1975).
[7] H.A. Posch, W.G. Hoover, Time-Reversible Dissipative Attractors in Three and Four Phase-Space Dimensions, Physical Review E 55, 6803–6810 (1997).
[8] W.G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Physical Review A 31, 1695–1697 (1985).
[9] W.G. Hoover, B.L. Holian, Kinetic Moments Method for the Canonical Ensemble Distribution, Physics Letters A 211, 253–257 (1996).
[10] J.C. Sprott, W.G. Hoover, C.G. Hoover, Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient, Physical Review E 89, 042914 (2014).
[11] B.L. Holian, W.G. Hoover, H.A. Posch, Resolution of Loschmidt’s Paradox: The Origin of Irreversible Behaviour in Reversible Atomistic Dynamics, Physical Review Letters 59, 10–13 (1987).
[12] W.G. Hoover, H.A. Posch, B.L. Holian, M.J. Gillan, M. Mareschal, C. Massobrio, Dissipative Irreversibility from Nosé’s Reversible Mechanics, Molecular Simulation 1, 79–86 (1987).
[13] Wm.G. Hoover, H.A. Posch, Chaos and Irreversibility in Simple Model Systems, Chaos 8, 366–373 (1998).
[14] J. Kumiˆcák, Irreversibility in a Simple Reversible Model, Physical Review E 71, 016115 (2005).
[15] W.G. Hoover, C.G. Hoover, Aspects of Dynamical Simulations, Emphasizing Nosé and Nosé-Hoover Dynamics and the Compressible Baker Map, Computational Methods in Science and Technology 25, 125–141 (2019).
[16] W.G. Hoover, C.G. Hoover, Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps, Regular and Chaotic Dynamics (submitted January 2020), arXiv:2001.02541.
[17] W.G. Hoover, C.G. Hoover, Random Walk Equivalence to the Compressible Baker Map and the Kaplan-Yorke Approximation to Its Information Dimension, arXiv:1909.04526 (2019).
[18] W.G. Hoover, C.G. Hoover, 2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps, Computational Methods in Science and Technology 25, 153–159 (2019).
This memoir is dedicated to the late Francis Hayin Ree, a formative influence shaping my work in statistical mechanics. Between 1963 and 1968 we collaborated on nine papers published in the Journal of Chemical Physics. Those dealt with the virial series, cell models, and computer simulation. All of them were directed toward understanding the statistical thermodynamics of simple model systems. Our last joint work is also the most cited, with over 1000 citations, “Melting Transition and Communal Entropy for Hard Spheres”, submitted 3 May 1968 and published that October. Here I summarize my own most recent work on compressible time-reversible two-dimensional maps. These simplest of model systems are amenable to computer simulation and are providing stimulating and surprising results.
Key words:
Francis Ree, information and Kaplan-Yorke dimensions, maps, reversibility, statistical physics
References:
[1] B.J. Alder, T.E. Wainwright, Molecular Motions, Scientific American 201, 113–126 (1959).
[2] W.G. Hoover, A.G. De Rocco, Sixth and Seventh Virial Coefficients for the Parallel Hard-Cube Model, Journal of Chemical Physics 36, 3141–3162 (1962).
[3] A.G. De Rocco, W.G. Hoover, Second Virial Coefficient for the Spherical Shell Potential, Journal of Chemical Physics 36, 916–926 (1962).
[4] F.H. Ree, T.S. Ree, T. Ree, H. Eyring, Random Walk and Related Physical Problems, [In:] Advances in Chemical Physics 4, 1–66 (1962), ed. I. Prigogine.
[5] A list of 161 of Francis Ree’s publications can be found (in January 2020) on the ResearchGate website. Francis’ LLNL obituary can be found at https://www.llnl.gov/community/retiree-and-employee-resources/in-memoriam/francis-ree.
[6] W.G. Hoover, W.T. Ashurst, Nonequilibrium Molecular Dynamics, Theoretical Chemistry 1, 1–51, Academic, New York (1975).
[7] H.A. Posch, W.G. Hoover, Time-Reversible Dissipative Attractors in Three and Four Phase-Space Dimensions, Physical Review E 55, 6803–6810 (1997).
[8] W.G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Physical Review A 31, 1695–1697 (1985).
[9] W.G. Hoover, B.L. Holian, Kinetic Moments Method for the Canonical Ensemble Distribution, Physics Letters A 211, 253–257 (1996).
[10] J.C. Sprott, W.G. Hoover, C.G. Hoover, Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient, Physical Review E 89, 042914 (2014).
[11] B.L. Holian, W.G. Hoover, H.A. Posch, Resolution of Loschmidt’s Paradox: The Origin of Irreversible Behaviour in Reversible Atomistic Dynamics, Physical Review Letters 59, 10–13 (1987).
[12] W.G. Hoover, H.A. Posch, B.L. Holian, M.J. Gillan, M. Mareschal, C. Massobrio, Dissipative Irreversibility from Nosé’s Reversible Mechanics, Molecular Simulation 1, 79–86 (1987).
[13] Wm.G. Hoover, H.A. Posch, Chaos and Irreversibility in Simple Model Systems, Chaos 8, 366–373 (1998).
[14] J. Kumiˆcák, Irreversibility in a Simple Reversible Model, Physical Review E 71, 016115 (2005).
[15] W.G. Hoover, C.G. Hoover, Aspects of Dynamical Simulations, Emphasizing Nosé and Nosé-Hoover Dynamics and the Compressible Baker Map, Computational Methods in Science and Technology 25, 125–141 (2019).
[16] W.G. Hoover, C.G. Hoover, Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps, Regular and Chaotic Dynamics (submitted January 2020), arXiv:2001.02541.
[17] W.G. Hoover, C.G. Hoover, Random Walk Equivalence to the Compressible Baker Map and the Kaplan-Yorke Approximation to Its Information Dimension, arXiv:1909.04526 (2019).
[18] W.G. Hoover, C.G. Hoover, 2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps, Computational Methods in Science and Technology 25, 153–159 (2019).
