William W. Wood

Flow Calculations for Pulsating One‐Dimensional Detonations

The nature of the long‐time flow in an idealized one‐dimensional, piston‐supported detonation is investigated by numerical solution of the time‐dependent hydrodynamic equations. The method of characteristics is used, with shocks treated as jump discontinuities. The fluid is an ideal gas of constant heat capacity undergoing an exothermic, irreversible, unimolecular reaction A → B obeying an Arrhenius rate law. The results are consistent with Erpenbecks linearized analysis of the stability of the steady detonation, which revealed some cases in which the usual steady‐state solution is unstable to infinitesimal longitudinal perturbations. In a typical flow of this type, the shock pressure is found to oscillate about the steady‐solution value with a peak pressure nearly 50% higher and with a period of about 9 steady‐solution half‐reaction times.

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V0 to 1.6V0, whereV0 is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratkys value for the fifth virial coefficientB5 and choosingB6 andB7, to obtain a least-squares fit. The resulting values ofB6 andB7 lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB8,B9, andB10 predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.

Structure of a Steady‐State Plane Detonation Wave with Finite Reaction Rate

An analytical elaboration of von Neumanns model of the detonation wave is presented. A hydrodynamic argument for the well‐known Chapman‐Jouguet condition is advanced, and the sound speed to be used therein is identified as that obtained with frozen chemical equilibrium, in agreement with a recent result of Brinkley and Richardson. Possible situations in which the classical Chapman‐Jouguet hypothesis might be incorrect are very briefly discussed.

Molecular dynamics calculations of shear viscosity time-correlation functions for hard spheres

The time-correlation function for shear viscosity is evaluated for hard spheres at volumes of 1.6 and 3 times the close-packed volume by a Monte Carlomolecular dynamics technique. At both densities, the kinetic part of the timecorrelation function is consistent, within its rather large statistical uncertainty, with the long-timet−3/2 tail predicted by the mode-coupling theory. However, at the higher density, the time-correlation function is dominated by the cross and potential terms out to 25 mean free times, whereas the mode-coupling theory predicts that these are asymptotically negligible compared to the kinetic part. The total time-correlation function decays roughly asαt−3/2, withα much larger than the mode-coupling value, similar to the recent observations by Evans in his nonequilibrium simulations of argon and methane. The exact value of the exponent is, however, not very precisely determined. By analogy with the case of the velocity autocorrelation function, for which results are also presented at these densities, it is argued that it is quite possible that at high density the asymptotic behavior is not established until times substantially longer than those attainable in the present work. At the lower density, the cross and potential terms are of the same magnitude as the kinetic part, and all are consistent with the mode-coupling predictions within the relatively large statistical uncertainties.

Shock Hugoniots for Liquid Argon

Shock Hugoniots for liquid argon are calculated using equations‐of‐state obtained from the Monte Carlo method and the Lennard‐Jones‐Devonshire cell theory, using an experimentally determined pair potential. Agreement with presently available experimental data is poor.

A Detonation‐Product Equation of State Obtained from Hydrodynamic Data

A recent experimental measurement of the Chapman‐Jouguet isentrope of the solid explosive Composition B, together with the experimental detonation velocity vs initial density curve, give considerable information about the equation of state of the detonation products. With the aid of some thermodynamic assumptions, a simple explicit form is obtained for the energy as a function of pressure and volume.

Investigation of the Chapman‐Jouguet Hypothesis by the ``Inverse Method''

Generalizing a particular case studied by Jones, Stanyukovich, and Manson have given general equations connecting (1) the Chapman‐Jouguet detonation pressure; (2) the derivative α = p(∂v/∂E)p of the equation of state E(p, v) of the product gases; (3) the derivatives of the detonation velocity D with respect to the thermodynamic variables defining the initial state of the explosive, such as the initial density ρ0; (4) the variables D and ρ0 themselves.After presenting a careful derivation of this result, it is pointed out that in conjunction with experimental observations of (a) the unsupported detonation‐wave pressure p and velocity D and (b) the derivatives of D with respect to two independent initial variables (e.g., ρ0 and E0), it permits an experimental test of the basic assumptions of detonation theory, namely the assumption of laminar flow and the Chapman‐Jouguet hypothesis. Several experimental possibilities are suggested for condensed explosives, where direct experimental observations (such as Whi...

On the linearity of the self-diffusion process

Formal arguments are given that the self-diffusion process, understood as the mutual diffusion process in a system which consists of two mechanically similar species of particles, and which is at total equilibrium if the species labels are ignored, is an inherently linear, but nonlocal, transport process. There are no nonlinear Burnett effects, and the nonlocal diffusion coefficient is independent of the composition of the mixture. The present state of knowledge, from theory and from computer experiments, concerning the various quantities which appear in the formal analysis is summarized for both fluid and Lorentz systems.

A Brief History of the Use of the Metropolis Method at LANL in the 1950s

A personal view of the use of the Metropolis Algorithm in statistical mechanics calculations at Los Alamos during the 1950s will be presented, based on [1] and [2].