Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics

• Published in: Journal of the mechanics and physics of solids 2014-02, Vol.63, p.94-112
• Main Authors: Kim, W.K., Luskin, M., Perez, D., Voter, A.F., Tadmor, E.B.
• Format: Article
• Language: English
• Subjects: Accessibility; Computer simulation; Constitutive behavior; Dynamical systems; Dynamics; Finite elements; Fracture; Mathematical models; Metastable state; Multiscale methods; Probability and statistics; Quality control
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2013.10.001

The quasicontinuum (QC) method is a spatial multiscale method that extends the length scales accessible to fully atomistic simulations (like molecular dynamics (MD)) by several orders of magnitude. While the recent development of the so-called “hot-QC method” enables dynamic simulations at finite temperature, the times accessible to these simulations remain limited to the sub-microsecond time scale due to the small time step required for stability of the numerical integration. To address this limitation, we develop a novel finite-temperature QC method that can treat much longer time scales by coupling the hot-QC method with hyperdynamics—a method for accelerating time in MD simulations. We refer to the new approach as “hyper-QC”. As in the original hyperdynamics method, hyper-QC is targeted at dynamical systems that exhibit a separation of time scales between short atomic vibration periods and long waiting times in metastable states. Acceleration is achieved by modifying the hot-QC potential energy to reduce the energy barriers between metastable states in a manner that ensures that the characteristic dynamics of the system are preserved. First, the high accuracy of hot-QC in reproducing rare event kinetics is demonstrated. Then, the hyper-QC methodology is validated by comparing hyper-QC results with those of hot-QC and full MD for a one-dimensional chain of atoms interacting via a Lennard–Jones potential.