NVU dynamics. II. Comparing to four other dynamics

Abstract

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this 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 Gaussian Lennard-Jones 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 then 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 section 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 Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.

References in corpus (14)

• Pressure-energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams
• "Isomorphs" in liquid state diagrams
• Pressure-energy correlations in liquids. I. Results from computer simulations
• Strong pressure-energy correlations in van der Waals liquids
• Pressure-energy correlations in liquids. II. Analysis and consequences
• Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance
• Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
• A repulsive reference potential reproducing the dynamics of a liquid with attractions
• Revisiting the slow dynamics of a silica melt using Monte Carlo simulations
• Feasibility of single-order parameter description of equilibrium viscous liquid dynamics
• Predicting The Effective Temperaure of a Glass
• NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
• Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble
• Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape

Cited by in corpus (12)

• Simplicity of condensed matter at its core: Generic definition of a Roskilde-simple system
• RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles
• Isomorphs, hidden scale invariance, and quasiuniversality
• Impact of size polydispersity on the nature of Lennard-Jones liquids
• NVU perspective on simple liquids' quasiuniversality
• NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
• The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality
• Isomorph theory of physical aging
• NVU dynamics. III. Simulating molecules at constant potential energy
• $NVU$ view on energy polydisperse Lennard-Jones systems
• Interpolating between pair-potential systems
• Viscous liquid dynamics modeled as random walks within overlapping hyperspheres