Bill Moran

Diffusion in a periodic Lorentz gas

We use a constant “driving force”Fd together with a Gaussian thermostatting “constraint force”Fd to simulate a nonequilibrium steady-state current (particle velocity) in a periodic, two-dimensional, classical Lorentz gas. The ratio of the average particle velocity to the driving force (field strength) is the Lorentz-gas conductivity. A regular “Galton-board” lattice of fixed particles is arranged in a dense triangular-lattice structure. The moving scatterer particle travels through the lattice at constant kinetic energy, making elastic hard-disk collisions with the fixed particles. At low field strengths the nonequilibrium conductivity is statistically indistinguishable from the equilibrium Green-Kubo estimate of Machta and Zwanzig. The low-field conductivity varies smoothly, but in a complicated way, with field strength. For moderate fields the conductivity generally decreases nearly linearly with field, but is nearly discontinuous at certain values where interesting stable cycles of collisions occur. As the field is increased, the phase-space probability density drops in apparent fractal dimensionality from 3 to 1. We compare the nonlinear conductivity with similar zero-density results from the two-particle Boltzmann equation. We also tabulate the variation of the kinetic pressure as a function of the field strength,

Corresponding states for thermal conductivities via nonequilibrium molecular dynamics

We follow Rosenfeld in comparing fluid‐phase thermal conductivities for several simple pair potentials. Within about ten percent these (nonelectronic) conductivities satisfy a corresponding states relation involving the equilibrium entropy. This corresponding states relation, deduced directly from the results of computer simulations, is also suggested by hard‐sphere perturbation theory and by the quasiharmonic cell‐model approach. The conductivity‐entropy relation should be useful for estimating transport coefficients from the equation of state of monatomic fluids with arbitrary pair potentials.

Pressure‐volume work exercises illustrating the first and second laws

We present two exercises involving rapid compression and expansion of ideal gases. The exercises are useful teaching tools and illustrate the first and second laws of thermodynamics. The first problem involves the conversion of gravitational energy into heat through mechanical work. The second involves the mutual interaction of two gases through an adiabatic piston. Both local and global versions of the second law can be applied to this second exercise. Both problems are also treated by numerical fluid dynamics.

Analytic and numerical surface dynamics of the triangular lattice

The high‐frequency surface waves discovered by Allen, Alldredge, and de Wette, in numerical studies of three‐dimensional fcc crystals, have two‐dimensional analogs. Analytic solutions of the equations of motion for two‐dimensional close‐packed lattices reveal a high‐frequency surface‐mode branch linking together the high‐frequency and low‐frequency bulk‐mode bands. The dispersion relation for this branch is used to estimate the surface entropy. The estimate agrees well with Carman and Huckaby’s recent cell‐cluster calculation. Both the dispersion‐relation and cell‐cluster surface entropy estimates lie slightly below an accurate value we obtain here by extrapolating small‐crystal entropies to the thermodynamic limit.

Irreversible Processes from Reversible Mechanics

We describe and illustrate methods for treating many-body irreversible processes using time-reversible deterministic Nose-Hoover thermostats. In phase space, Lyapunov-unstable multifractal strange attractors are the common feature representing any of these nonequilibrium flows, be they steady, periodic, or transient. This generic behavior is illustrated here for three prototypical one-body problems: steady field-driven diffusive flow in a Galton Board, time-periodic boundary-driven viscous flow of a Lorentz gas, and transient, but time-periodic, compressible flow characterizing a one-dimensional free expansion followed by compression and thermalization.