The calculation of thermal conductivities by perturbed molecular dynamics simulation

Nonequilibrium molecular dynamics method based on coarse-graining formalism: Application to a nonuniform temperature field system

A nonequilibrium molecular dynamics method is proposed to produce nonequilibrium states flexibly. In this method, virtual points are set in a simulation box, and coarse-grained physical quantities at these points are constrained using Gauss's principle of least constraint. The coarse-grained physical quantities are evaluated by averaging microscopic quantities with an appropriate weight. To obtain the weight to evaluate the coarse-grained physical quantities, a shape function matrix is initially constructed from the particle configuration. This matrix expresses an interpolation of the physical quantities at particle positions from the coarse-grained quantities at the virtual points. Then, a matrix form of the weight is calculated as the Moore-Penrose pseudoinverse matrix for the shape function matrix. This method is applied to constrain the coarse-grained kinetic energy and produce a nonuniform temperature field in the system. The temperature profile at a nonequilibrium steady state depends on the method for constructing the shape function matrix. In particular, a local temperature coincides with the coarse-grained temperature when the shape function matrix is constructed based on a higher-order interpolation.

From hard spheres and cubes to nonequilibrium maps with thirty-some years of thermostatted molecular dynamics

This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models that best achieve reproducibility and promote understanding. Few-body models with pair forces have led to today's "realistic" simulations with billions of atoms and molecules. Rapid advances in computer technology have led to change. Theoretical formalisms have largely been replaced by simulations incorporating ingenious algorithm development. We choose to study particularly simple, yet relevant, models directed toward understanding general principles. Simplicity remains a worthy goal, as does relevance. We discuss hard-particle virial series, melting, thermostatted oscillators with and without heat conduction, chaotic dynamics, fractals, the connection of Lyapunov spectra to thermodynamics, and finally simple linear maps. Along the way, we mention directions in which additional modeling could provide more clarity and yet more interesting developments in the future.

Thermal conductivity of ionic systems from equilibrium molecular dynamics

Thermal conductivities of ionic compounds (NaCl, MgO, Mg(2)SiO(4)) are calculated from equilibrium molecular dynamics simulations using the Green-Kubo method. Transferable interaction potentials including many-body polarization effects are employed. Various physical conditions (solid and liquid states, high temperatures, high pressures) relevant to the study of the heat transport in the Earth's mantle are investigated, for which experimental measures are very challenging. By introducing a frequency-dependent thermal conductivity, we show that important coupled thermoelectric effects occur in the energy conduction mechanism in the case of liquid systems.

Simulation of two- and three-dimensional dense-fluid shear flows via nonequilibrium molecular dynamics: comparison of time-and-space-averaged stresses from homogeneous Doll's and Sllod shear algorithms with those from boundary-driven shear

Homogeneous shear flows (with constant strainrate dv(x)/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear normal-stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, Pxx-Pyy, depend on both the thermostat type and the chosen shearflow algorithm. The Doll's and Sllod algorithms predict opposite signs for this normal-stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures: Txx > Tzz > Tyy.

Equilibrium and nonequilibrium molecular dynamics simulations of the thermal conductivity of molten alkali halides

The thermal conductivity of molten NaCl and KCl was calculated through the Evans-Gillan nonequilibrium molecular dynamics (NEMD) algorithm and Green-Kubo equilibrium molecular dynamics (EMD) simulations. The EMD simulations were performed for a "binary" ionic mixture and the NEMD simulations assumed a pure system for reasons discussed in this work. The cross thermoelectric coefficient obtained from Green-Kubo EMD simulations is discussed in terms of the homogeneous thermoelectric power or Seebeck coefficient of these materials. The thermal conductivity obtained from NEMD simulations is found to be in very good agreement with that obtained through Green-Kubo EMD simulations for a binary ionic mixture. This result points to a possible cancellation between the neglected "partial enthalpy" contribution to the heat flux associated with the interdiffusion of one species through the other and that part of the thermal conductivity related to the coupled fluxes of charge and heat in "binary" ionic mixtures.

Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.

Statistical mechanical theory for steady state systems. IV. Transition probability and simulation algorithm demonstrated for heat flow

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results.