• NEWS
  • CURRENT ISSUE
  • CONTACT
GET_pdf

Volume 23 (4) 2017, 299–303

Bit-Reversible Version of Milne’s Fourth-Order Time-Reversible Integrator for Molecular Dynamics

Hoover Wm.G. , Hoover C.G.

Ruby Valley Research Institute
Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA
E-mail: hooverwilliam@yahoo.com

Received:

Received: 28 June 2017; accepted: 29 June 2017; published online: 17 August 2017

DOI:   10.12921/cmst.2017.0000031

Abstract:

We point out that two of Milne’s fourth-order integrators are well-suited to bit-reversible simulations. The fourth-order method improves on the accuracy of Levesque and Verlet’s algorithm and simplifies the definition of the velocity v and energy e = (q2 + v2 )/2. (We use this one-dimensional oscillator problem as an illustration throughout this paper). Milne’s integrator is particularly useful for the analysis of Lyapunov (exponential) instability in dynamical systems, including manybody molecular dynamics. We include the details necessary to the implementation of Milne’s Algorithms.

Key words:

bit-reversible molecular dynamics, chaotic dynamical systems, Lyapunov instability

References:

[1] W. E. Milne, Numerical Calculus – Approximations, Interpo-
lation, Finite Differences, Numerical Integration, and Curve
Fitting (Princeton University Press, 1949 and 2015).
[2] D. Levesque and L. Verlet, Molecular Dynamics and Time Re-
versibility, Journal of Statistical Physics 72, 519-537 (1993).
[3] L. Verlet, ‘Computer Experiments’ on Classical Fluids. I.
Thermodynamical Properties of Lennard-Jones Molecules,
Physical Review 159, 98-103 (1967).
[4] H. A. Posch and W. G. Hoover, Large-System Phase-Space
Dimensionality Loss in Stationary Heat Flows, Physica D 187,
281-293 (2004).
[5] O. Kum and Wm. G. Hoover, Time-Reversible Continuum Me-
chanics, Journal of Statistical Physics 76, 1075-1081 (1994).
[6] B. L. Holian, Wm. G. Hoover, and H. A. Posch, Resolution of
Loschmidt’s Paradox: The Origin of Irreversible Behavior in
Reversible Atomistic Dynamics, Physical Review Letters 59,
10-13 (1987).
[7] C. Grebogi, E. Ott, and J. A. Yorke, Roundoff-Induced Peri-
odicity and the Correlation Dimension of Chaotic Attractors,
Physical Review A 38, 3688-3692 (1988).
[8] C. Dellago and Wm. G. Hoover, Finite-Precision Stationary
States At and Away from Equilibrium, Physical Review E 62,
6275-6281 (2000).
[9] M. Romero-Bastida, D. Pazó, J. M. Lopéz, and M. A. Ro-
driguez, Structure of Characteristic Lyapunov Vectors in
Anharmonic Hamiltonian Lattices, Physical Review E 82,
036205 (2010).
[10] Wm. G. Hoover and Carol G. Hoover, Time-Symmetry Break-
ing in Hamiltonian Mechanics, Computational Methods in
Science and Technology 19, 77-87 (2013).
[11] Wm. G. Hoover and C. G. Hoover, The Kharagpur Lectures
(World Scientific, Singapore, 2018, in preparation).

  • JOURNAL MENU

    • AIMS AND SCOPE
    • EDITORS
    • EDITORIAL BOARD
    • NOTES FOR AUTHORS
    • CONTACT
    • IAN SNOOK PRIZES 2015
    • IAN SNOOK PRIZES 2016
    • IAN SNOOK PRIZES 2017
  • GALLERY

    vol_19_04_2013
    vol_19_03_2013
    volume_19_2_2013
    volume_19_1_2013
    vol_sp_2_2010
    vol_sp_2006
    vol_sp_1_2010
    vol_16_01_2010
    vol_18_2_2012
    vol_18_01_2012
    vol_17_01_02_2011
    vol_16_02_2010
    vol_15_02_2009
    vol_15_01_2009
    vol_14_02_2008
    vol_14_01_2008
    vol_13_02_2007
    vol_13_01_2007
    vol_12_02_2006
    vol_12_01_2006
    vol_11_02_2005
    vol_11_01_2005
  • CURRENT ISSUE

  • MANUSCRIPT SUBMISSION

    • SUBMIT A MANUSCRIPT
  • FUTURE ISSUES

    • ACCEPTED PAPERS
  • ALL ISSUES

    • 2018
      • Volume 24 (4)
      • Volume 24 (3)
      • Volume 24 (2)
      • Volume 24 (1)
    • 2017
      • Volume 23 (4)
      • Volume 23 (3)
      • Volume 23 (2)
      • Volume 23 (1)
    • 2016
      • Volume 22 (4)
      • Volume 22 (3)
      • Volume 22 (2)
      • Volume 22 (1)
    • 2015
      • Volume 21 (4)
      • Volume 21 (3)
      • Volume 21 (2)
      • Volume 21 (1)
    • 2014
      • Volume 20 (4)
      • Volume 20 (3)
      • Volume 20 (2)
      • Volume 20 (1)
    • 2013
      • Volume 19 (4)
      • Volume 19 (3)
      • Volume 19 (2)
      • Volume 19 (1)
    • 2012
      • Volume 18 (2)
      • Volume 18 (1)
    • 2011
      • Volume 17 (1-2)
    • 2010
      • Volume SI (2)
      • Volume SI (1)
      • Volume 16 (2)
      • Volume 16 (1)
    • 2009
      • Volume 15 (2)
      • Volume 15 (1)
    • 2008
      • Volume 14 (2)
      • Volume 14 (1)
    • 2007
      • Volume 13 (2)
      • Volume 13 (1)
    • 2006
      • Volume SI (1)
      • Volume 12 (2)
      • Volume 12 (1)
    • 2005
      • Volume 11 (2)
      • Volume 11 (1)
    • 2004
      • Volume 10 (2)
      • Volume 10 (1)
    • 2003
      • Volume 9 (1)
    • 2002
      • Volume 8 (2)
      • Volume 8 (1)
    • 2001
      • Volume 7 (2)
      • Volume 7 (1)
    • 2000
      • Volume 6 (1)
    • 1999
      • Volume 5 (1)
    • 1998
      • Volume 4 (1)
    • 1997
      • Volume 3 (1)
    • 1996
      • Volume 2 (1)
      • Volume 1 (1)
    • OLDER ISSUES
  • DATABASES

    • ARTICLES BASE
    • AUTHORS BASE
  • NEWS
  • CURRENT ISSUE
  • CONTACT

Institute of Bioorganic Chemistry Polish Academy of Sciences
Poznań Supercomputing and Networking Center

61-704 Poznań, Z. Noskowskiego 12/14
phone: (+48 61) 858-20-03
fax: (+48 61) 858-21-51