#### Event Title

#### Description

When Molecular Dynamics (MD) was originally conceived, the trajectories of atoms are determined by numerically solving the Newton’s equations for a system under equilibrium condition. However, to study the multifunctionalities of advanced nanomaterial, such as piezoelectricity or thermoelectricity, the nonequilibrium MD should be considered and further developed to incorporate the multiphysics phenomena, i.e., thermo-mechanical-electromagnetic coupling effects. For the temperature simulation, 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 non-equilibrium 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 non-equilibrium MD with suitable algorithmic thermostat for local temperature regulation. Inspired by Nosé–Hoover thermostat, this study 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 simulated and 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 correct (reasonable and logical) temperature distributions across the specimens after the steady state arrives for long time duration until the steady state arrives. Yet, the results from the original Nosé–Hoover thermostat cannot reach yield the steady state solution. In addition, 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. By following this conclusion, we can proceed to calculate the thermal conductivity of MgO material system, which fits the experimental results very well. To incorporate the electromagnetic effect, the Lorentz force is rigorously derived based on the Maxwell’s equations at atomic scale. This allows us to unveil the resonance phenomena at nanoscale, which resemble the relationship between the frequency and response in classical mechanical vibration. Moreover, the coupling effects, including the temperature variation induced by electromagnetic field, and the electromagnetic quantities induced by mechanical input, will be discussed in detail.

#### Recommended Citation

Li, J.,
&
Lee, J.
(2014).
Molecular dynamics simulation of multiphysics.
In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.).
*
Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014
*,
West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014.
http://docs.lib.purdue.edu/ses2014/mss/mechnano/4

Molecular dynamics simulation of multiphysics

When Molecular Dynamics (MD) was originally conceived, the trajectories of atoms are determined by numerically solving the Newton’s equations for a system under equilibrium condition. However, to study the multifunctionalities of advanced nanomaterial, such as piezoelectricity or thermoelectricity, the nonequilibrium MD should be considered and further developed to incorporate the multiphysics phenomena, i.e., thermo-mechanical-electromagnetic coupling effects. For the temperature simulation, 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 non-equilibrium 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 non-equilibrium MD with suitable algorithmic thermostat for local temperature regulation. Inspired by Nosé–Hoover thermostat, this study 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 simulated and 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 correct (reasonable and logical) temperature distributions across the specimens after the steady state arrives for long time duration until the steady state arrives. Yet, the results from the original Nosé–Hoover thermostat cannot reach yield the steady state solution. In addition, 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. By following this conclusion, we can proceed to calculate the thermal conductivity of MgO material system, which fits the experimental results very well. To incorporate the electromagnetic effect, the Lorentz force is rigorously derived based on the Maxwell’s equations at atomic scale. This allows us to unveil the resonance phenomena at nanoscale, which resemble the relationship between the frequency and response in classical mechanical vibration. Moreover, the coupling effects, including the temperature variation induced by electromagnetic field, and the electromagnetic quantities induced by mechanical input, will be discussed in detail.