Shock-wave compression and Joule-Thomson expansion.

Structurally stable atomistic one-dimensional shock waves have long been simulated by injecting fresh cool particles and extracting old hot particles at opposite ends of a simulation box. The resulting shock profiles demonstrate tensor temperature, Txx≠Tyy and Maxwell's delayed response, with stress lagging strain rate and heat flux lagging temperature gradient. Here this same geometry, supplemented by a short-ranged external "plug" field, is used to simulate steady Joule-Kelvin throttling flow of hot dense fluid through a porous plug, producing a dilute and cooler product fluid.

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Tensor temperature and shock-wave stability in a strong two-dimensional shock wave.

The anisotropy of temperature is studied here in a strong two-dimensional shock wave, simulated with conventional molecular dynamics. Several forms of the kinetic temperature are considered, corresponding to different choices for the local instantaneous stream velocity. A local particle-based definition omitting any "self"-contribution to the stream velocity gives the best results. The configurational temperature is not useful for this shock-wave problem. The configurational temperature is subject to a shear instability and can give local negative temperatures in the vicinity of the shock front. The decay of sinusoidal shock-front perturbations shows that strong two-dimensional planar shock waves are stable to such perturbations.

Microscopic and macroscopic stress with gravitational and rotational forces.

Many recent papers have questioned Irving and Kirkwood's atomistic expression for stress. In Irving and Kirkwood's approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate (i) a fluid in a gravitational field and (ii) a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.

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.

Nonequilibrium temperature and thermometry in heat-conducting phi4 models.

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We also show in detail, for both two- and three-dimensional systems, that the ideal-gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the phi4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between the kinetic temperature and nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that the kinetic temperature, as modeled and imposed by the Nosé-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.

Hamiltonian dynamics of thermostated systems: two-temperature heat-conducting phi4 chains.

We consider and compare four Hamiltonian formulations of thermostated mechanics, three of them kinetic, and the other one configurational. Though all four approaches "work" at equilibrium, their application to many-body nonequilibrium simulations can fail to provide a proper flow of heat. All the Hamiltonian formulations considered here are applied to the same prototypical two-temperature "phi4" model of a heat-conducting chain. This model incorporates nearest-neighbor Hooke's-Law interactions plus a quartic tethering potential. Physically correct results, obtained with the isokinetic Gaussian and Nose-Hoover thermostats, are compared with two other Hamiltonian results. The latter results, based on constrained Hamiltonian thermostats, fail to model correctly the flow of heat.

Smooth-particle phase stability with generalized density-dependent potentials.

Stable fluid and solid particle phases are essential to the simulation of continuum fluids and solids using smooth particle applied mechanics. We show that density-dependent potentials, such as Phi rho=1/2 Sigma(rho-rho 0)2, along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that special stabilization potentials, with density gradients or curvatures, such as Phi inverted Delta rho=1/2 Sigma(inverted Delta rho)2, not only stabilize crystalline solid phases (or meshes) but also provide a surface tension which is missing in the usual density-dependent-potential approach. We illustrate these ideas for two-dimensional square, triangular, and hexagonal lattices.

Smooth-particle applied mechanics: Conservation of angular momentum with tensile stability and velocity averaging.

Smooth-particle applied mechanics (SPAM) provides several approaches to approximate solutions of the continuum equations for both fluids and solids. Though many of the usual formulations conserve mass, (linear) momentum, and energy, the angular momentum is typically not conserved by SPAM. A second difficulty with the usual formulations is that tensile stress states often exhibit an exponentially fast high-frequency short-wavelength instability, "tensile instability." We discuss these twin defects of SPAM and illustrate them for a rotating elastic body. We formulate ways to conserve angular momentum while at the same time delaying the symptoms of tensile instability for many sound-traversal times. These ideas should prove useful in more general situations.

Smooth-particle boundary conditions.

We study the relative usefulness of static and dynamic boundary conditions as a function of system dimensionality. In one space dimension, dynamic boundaries, with the temperatures and velocities of external mirror-image boundary particles linked directly to temperatures and velocities of interior particles, perform qualitatively better than the simpler static-mirror-image boundary condition with fixed boundary temperatures and velocities. In one space dimension, the Euler-Maclaurin sum formula shows that heat-flux errors with dynamic temperature boundaries vary as h(-4), where h is the range of the smooth-particle weight function w(r

Fractal dimension of steady nonequilibrium flows.

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces. For both kinds of nonequilibrium systems, it is demonstrated numerically that external isothermal boundaries can drive the otherwise purely Newtonian flow onto a multifractal attractor with a phase-space information dimension significantly less than that of the corresponding equilibrium flow. Thus the Gibbs' entropy of such nonequilibrium flows can diverge.

Heat transfer between two degrees of freedom.

A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures T(x) and T(y), is introduced. The two temperatures are maintained by Nose-Hoover canonical-ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.