Reformulation of Nosé-Hoover Thermostat for Heat Conduction Simulation at Nanoscale
Jiaoyan Li (The George Washington University), James Lee (George Washington University)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Mon 10:45 - 12:15
MacMillan 117
When Molecular Dynamics was originally conceived, the trajectories of atoms are determined by numerically solving the Newton's equations for a system under equilibrium condition. The revolutionary Nosé-Hoover dynamics, modified Newtonian dynamics so as to reproduce canonical and isobaric-isothermal ensemble equilibrium systems. However, there is an increasing interest in conducting MD simulation for a nonequilibrium system whose temperature varies spatially and temporally during the simulation with the imposition of a temperature gradient. Clearly, this is a heat conduction problem and requires Nonequilibrium Molecular Dynamics with suitable algorithmic thermostat for local temperature regulation. Inspired by Nosé-Hoover thermostat, this paper reformulates the feedback force caused by the temperature control, aiming at (i) controlling the temperature locally at several distinct spots, and (ii) eliminating the rigid-body translation and rotation which are irrationally introduced into the system due to the temperature force. This reformulation will generate accurate and rigorous trajectories of atoms and thus the heat conduction can be performed successfully at nanoscale. Correspondingly, the definition of temperature is modified; the expression of Hamiltonian is upgraded. To demonstrate the capability and feasibility of this new algorithm, we studied heat conduction phenomena in a beam-like and a ring-like finite size specimen by using our in-house developed computer code. The results from the reformulated Nosé-Hoover thermostat show the temperature distributions across the specimens for long time duration until the steady state arrives. Yet, the results from the original Nosé-Hoover thermostat cannot yield the steady state solution. Also, it reaches the conclusion that the heat conduction at nanoscale exhibits the same feature of Fourier's law at macroscopic scale if the temperature is averaged over a sufficiently large time interval and spatial region.