Modeling of slow time-scale behavior of fast molecular dynamic systems

This paper aims to apply a recently developed numerical scheme towards multi-time scale modeling, which we refer to as ‘Practical Time Averaging’ (PTA), to molecular dynamical (MD) systems. In the first part, we investigate the fine-scale dynamics of a one-dimensional chain of identical particles under cyclic loading. Assuming a double-well interatomic potential among adjacent particles leads to a phase transition between two distinct equilibrium states. Specifically, we study the macroscopic stress-strain behavior of the dynamical chain in three settings, i.e. Newtonian MD, Newtonian MD with viscous dissipation and Newtonian MD with thermostat. Rate-independent high frequency oscillations are observed in Newtonian MD due to an instability that is related to the non-convexity of the strain energy. This is stabilized by adding viscosity or a thermostat, which leads to strong hysteresis that is consistent with quasi-static results (i.e. lattice statics). In the second part, we first define coarse variables as finite time averages of phase functions in MD. Then we apply the technique of PTA developed in Tan, Acharya and Dayal [16] to numerically approximate the coarse dynamics for the time averaged quantities. The tested model problems include a two-dimensional lattice made of stoichiometric Nickel-Manganese undergoing detwinning and a three-dimensional atomic chain made of face-centered cubic (FCC) Nickel under uniaxial tension. The macroscopic features (such as space-time averaged strain/stress) are obtained from coarse dynamics. It is also shown that the time savings become significant when the loading rate is small.