Second Virial Coefficient for the Spherical Shell Potential

Values of the second virial coefficient for the three‐parameter spherical shell potential are tabulated over wide ranges of temperature and shell size. The potential, which is not new, results from the interaction of two spherical surfaces having uniform distributions of Lennard‐Jones (6–12) sites.An objective comparison is made between the tabulated values and the literature values for second virial coefficients, from which the potential parameters for twenty compounds are determined. Generally, the spherical shell potential generates a better fit than does the parent Lennard‐Jones potential. The potential parameters found are in good agreement with expectations based upon density and interatomic distance data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69851/2/JCPSA6-36-4-916-1.pd

Sixth Virial Coefficients for Gases of Parallel Hard Lines, Hard Squares, and Hard Cubes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71214/2/JCPSA6-34-3-1059-1.pd

Sixth and Seventh Virial Coefficients for the Parallel Hard‐Cube Model

A procedure for calculating virial coefficients for parallel hard lines, squares, and cubes is outlined, and the sixth and seventh virial coefficients are computed for these models. The essential step in the evaluation of the star integrals lies in the recognition of the fact that only a few ``subintegrals'' contribute to each virial coefficient, relative to the total number of labeled star integrals. Both the sixth and seventh virial coefficients are negative for hard cubes, a fact interesting from the point of view of phase transitions. Approximations to the excess entropy are given for squares and cubes.The procedure for the star integrals is extended to the calculation of approximations to the pair distribution function and the potential of the mean force. These functions are calculated through the fourth approximation for hard lines, squares, and cubes.The topological graphs needed for the above investigations, together with the values of the related integrals in one dimension, are displayed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70209/2/JCPSA6-36-12-3141-1.pd

Nonequilibrium molecular dynamics: The first 25 years

Equilibrium Molecular Dynamics has been generalized to simulate Nonequilibrium systems by adding sources of thermodynamic heat and work. This generalization incorporates microscopic mechanical definitions of macroscopic thermodynamic and hydrodynamic variables, such as temperature and stress, and augments atomistic forces with special boundary, constraint, and driving forces capable of doing work on, and exchanging heat with, an otherwise Newtonian system. The underlying Lyapunov instability of these nonequilibrium equations of motion links microscopic time-reversible deterministic trajectories to macroscopic time-irreversible hydrodynamic behavior as described by the Second Law of Thermodynamics. Green-Kubo linear-response theory has been checked. Nonlinear plastic deformation, intense heat conduction, shockwave propagation, and nonequilibrium phase transformation have all been simulated. The nonequilibrium techniques, coupled with qualitative improvements in parallel computer hardware, are enabling simulations to approximate real-world microscale and nanoscale experiments

Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models, including an harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201