No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
2.S. Gallot, D. Hulin, and J. Lafontaine, Riemannian Geometry, 3rd ed. (Springer, Berlin, 2004).
3. N. J. Hicks, Notes on Differential Geometry (van Nostrand Reinhold, New York, 1965);
4. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972);
4.L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 5th ed. (Pergamon, London, 1975).
10. R. M. J. Cotterill and J. U. Madsen, Phys. Rev. B 33, 262 (1986);
10.R. M. J. Cotterill and J. U. Madsen, in Characterizing Complex Systems, edited by H. Bohr (World Scientific, Singapore, 1990), p. 177;
12. V. Caselles, R. Kimmel, and G. Sapiro, Int. J. Comput. Vis. 22, 61 (1997);
12.J. A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge University Press, Cambridge, England, 1999);
15. J. E. Marsden and M. West, Acta Numerica 10, 357 (2001);
15.A. Lew, “Variational time integrators in computational solid mechanics,” Ph.D. dissertation, California Institute of Technology, 2003;
15.M. West, “Variational integrators,” Ph.D. dissertation, California Institute of Technology, 2004;
15.E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration - Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. (Springer, Berlin, 2006);
16.A. Stein and M. Desbrun, in Discrete Differential Geometry: An Applied Introduction, edited by M. Desbrun, P. Schroeder, and M. Wardetzky (Columbia University, New York, 2008), p. 95.
All simulations were performed using a molecular dynamics code optimized for NVIDIA
graphics cards, which is available as open source code at http://rumd.org
18. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford Science, Oxford, 1987);
18.D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, New York, 2002).
Article metrics loading...
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to “entropic drift” of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.
Full text loading...
Most read this month