TY - JOUR

T1 - NVU dynamics. II. Comparing to four other dynamics

AU - Ingebrigtsen, Trond

AU - Toxværd, Søren

AU - Schrøder, Thomas

AU - Dyre, J. C.

N1 - Ingen sidetal...

PY - 2011

Y1 - 2011

N2 - In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, “NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface,” J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nos-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.

AB - In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, “NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface,” J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nos-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.

KW - differential geometry

KW - diffusion

KW - entropy

KW - Lennard-Jones potential

KW - Monte Carlo methods

KW - Newton method

KW - stochastic processes

U2 - 10.1063/1.3623586

DO - 10.1063/1.3623586

M3 - Journal article

SN - 0021-9606

VL - 135

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 10

ER -