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A thermodynamic-like approach to the characterization of product state distributions is outlined. A moment analysis of the surprisal and the entropy deficiency is presented from a statistical mechanical viewpoint. The role of reactant state selection is discussed using the 'state function' property of the entropy.
Turbulent Couette flow between parallel plates was studied from a statistical mechanics approach utilizing a model equation, similar to the Boltzmann equation of kinetic theory, which was proposed by Lundgren from the velocity distribution of fluid elements. Solutions to this equation are obtained numerically, employing the discrete ordinate method and finite differences. Two types of boundary conditions on the distribution function are considered, and the results of the calculations are compared to available experimental data. The research establishes that Lundgren's equation provides a very good description of turbulence for the flow situation considered and that it offers an analytical tool for further study of more complex turbulent flows. The present work also indicates that modelling of the boundary conditions is an area where further study is required.
The subject of satellite disintegration is examined in detail. Elements of the orbits of individual fragments, determined by DOD space surveillance systems, are used to accurately predict the time and place of fragmentation. Dual time independent and time dependent analyses are performed for simulated and real breakups. Methods of statistical mechanics are used to study the evolution of the fragment clouds. The fragments are treated as an ensemble of non-interacting particles. A solution of Liouville's equation is obtained which enables the spatial density to be calculated as a function of position, time and initial velocity distribution.
A specific heat anomaly in PdH and PdD has been observed by Aston et al. (1957) close to 55 K. Its position was found to be independent of hydrogen concentration and its magnitude to be linear in hydrogen concentration. Ferguson's (1965) and Brodowsky's (1972) explanations of the anomaly are shown to be unsatisfactory. This is true also for the detailed mechanical statistical model proposed by Staford and McLellan (1974) for interstitial solid solutions of hydrogen in transition metals. It is shown that Gopal's (1966) simple Schottky model of specific heat anomaly, which considers a system of several levels with Boltzmann statistics, provides much better agreement with experiment than the more elaborate models, both in magnitude and in predicting a linear dependence on hydrogen concentration.
Articles are grouped under four headings: (1) dynamics and control of satellites; (2) satellite mission analysis; (3) Aeros-B and Symphonie satellite engineering problems; (4) optimization and control techniques applied to solar space heating and cooling of buildings. Topics covered include: communications and earth survey satellite systems, a system of two counter-orbiting satellites measuring GRT-predicted nodal drag, statistical mechanics studies of the spatial density function of orbiting space junk, attitude control of satellites, nutation dampers, low thrust inertial guidance and ascent inertial guidance, a shuttle-launched multi-comet intercept mission, preflight and in-flight analysis of the Atmosphere Explorer (AE-C) satellite, and launch-encounter strategy for the Mariner 1977 Jupiter-Saturn mission. Individual items are announced in this issue.
It is shown that the Kubo formulation leads to an expression for bulk viscosity involving the differences of the trace equilibrium and nonequilibrium hydrodynamic tensors just as in the Boltzmann formulation. It is argued that, if a dense system is represented by a quantum field, the field-theoretic energy-momentum tensor and, therefore, the hydrodynamic tensor should always have a vanishing trace in the limit of high energies. This bulk viscosity should vanish in the same limit. Finally, it is noted that the explicit use of well-known statistical mechanical formulation can be considered as a justification of Weinberg's intuitive argument from a fundamental point of view.
A simplified model of an electromagnetic filamentation instability that arises when two counterstreaming electron beams pass through a uniform ion background is treated by statistical mechanical techniques borrowed from fluid turbulence theory. Accumulation of magnetic energy at long wavelengths is predicted, as observed in the numerical simulations of Lee and Lampe.
The 1986 apparition of Halley's comet will be the subject of numerous space probes, planned to determine the chemical nature and physical structure of comet nuclei, atmospheres, and ionospheres, as well as comet tails. The problems of cometary origin remain inconclusive, with theories ranging from a purely interstellar origin to their being ejecta from the Galilean satellites of Jupiter. Comets can be grouped into one of two classes, depending on their periodicity, and statistical mechanics of the entire Jovian family of comets can be examined under the equilibrium hypothesis. Comet anatomy estimations have been determined, and there is speculation that comet chemistry may have been a factor in the origin of life on earth. Halley's comet was first noted using Newton's dynamical methods, and Brady (1972) attempted to use the comet as a gravitational probe in search of a trans-Plutonian planet. Halley's orbit is calculated by combination of ancient observations and modern scientific methods.
The evaluation of the thermodynamic properties of a gas mixture can be performed using a generalized correlation which makes use of the second virial coefficient. This coefficient is based on statistical mechanics and is a function of temperature and composition, but not of pressure. The method provides results accurate to within 3 percent for gases which are nonpolar or only slightly polar. When applied to highly polar gases, errors of 5 to 10 percent may result. For gases which associate, even larger errors are possible. The sequences of calculations can be routinely programmed for a digital computer. The thermodynamic properties of a mixture of neon, argon and ethane were calculated by such a program. The result will be used for the design of the gas replenishment system for the Energetic Gamma Ray Experiment Telescope.
Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.
The understanding of the surface tension of liquid metals and alloys from as close to first principles as possible is discussed. The two ingredients which are combined in these calculations are: the electron theory of metals, and the classical theory of liquids, as worked out within the framework of statistical mechanics. The results are a new theory of surface tensions and surface density profiles from knowledge purely of the bulk properties of the coexisting liquid and vapor phases. It is found that the method works well for the pure liquid metals on which it was tested; work is extended to mixtures of liquid metals, interfaces between immiscible liquid metals, and to the temperature derivative of the surface tension.
The present state of MHD turbulence theory as a possible solar wind research tool is surveyed. The theory is statistical, and does not make statements about individual events. The ensembles considered typically have individual realizations which differ qualitatively, unlike equilibrium statistical mechanics. Most of the theory deals with highly symmetric situations; most of these symmetries have yet to be tested in the solar wind. The applicability of MHD itself to solar wind parameters is highly questionable; yet it has no competitors, as a potentially comprehensive dynamical description. The purpose of solar wind research require sharper articulation. If they are to understand radial turbulent plasma flows from spheres, laboratory experiments and numerical solution of equations of motion may be cheap alternative to spacecraft. If "real life" information is demanded, multiple spacecraft with variable separation may be necessary to go further. The principal emphasis in the theory so far has been on spectral behavior for spatial covariances in wave number space. There is no respectable theory of these for highly anisotropic situations. A rather slow development of theory acts as a brake on justifiable measurement, at this point.
The following topics were discussed: surface state of Titan; statistical mechanical treatment of clathrate hydrates; planetary dynamos; formation of the giant planets; the e-ring; Uranian satellites and atmosphere; 10 sulfur lakes; episodic tidal evolution; resurfacing of Ganymede; and the origin of the Moon.
The thermodynamic stability of clathrate hydrate is calculated to predict the formation conditions corresponding to a range of solar system parameters. The calculations were performed using the statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data concerning clathrate hydrate and its components. Dissociation pressures and partition functions (Langmuir constants) are predicted at low pressure for CO clathrate (hydrate) using the properties of chemicals similar to CO. It is argued that nonsolar but well constrained noble gas abundances may be measurable by the Galileo spacecraft in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances of the Jovian satellite Titan are predicted, assuming that most of the methane in Titan is accreted as clathrate. It is suggested that under thermodynamically appropriate conditions, complete clathration of water ice could have occurred in high-pressure nebulas around giant planets, but probably not in the outer solar nebula. The stability of clathrate in other pressure ranges is also discussed.
A study is conducted of an extension of Levy flight to include self-repulsion in the path of the walk. The extension is called node-avoiding Levy flight and its equivalence to the n approaches 0 limit of a statistical mechanical model for a magnetic system with long-range interactions between the spins is shown. By use of this equivalence it is possible to make a detailed comparison beween the results of the epsilon expansion for the magnetic model, a Monte Carlo simulation of the Levy flight model, and the results of a Flory-type argument. This is the first comparison of the epsilon expansion for epsilon much less than 1 with a numerical simulation for any model. Some speculations are made on applications of the model of node-avoiding Levy flight.
A major goal of this project is to understand the surface tension and other thermophysical properties of liquid metals and alloys from a fundamental viewpoint. The approach is to calculate these quantities by a first principles technique which combines the statistical-mechanical theory of the liquid state with an electronic pseudopotential theory of electrons in metals. The inhomogeneity of the surface is treated using an ionic-density-functional formalism developed with the support of NASA. Of particular interest are the variation of surface tension with temperature and impurity concentration: such variations strongly influence the types of convection which make take place in a low-gravity environment. Some progress has already been achieved in computing the reduction of surface tension due to the presence of low-surface-tension impurities, and the corresponding surface segregation of such impurities. In the coming year, it is planned to concentrate on the surface properties of materials of particular interest to the MSA program: Si, Ga and GaSn alloys. An additional goal is to gain some theoretical understanding of the high temperature thermophysical properties of liquid metals, particularly high melting point materials which have not been studied extensively from a theoretical viewpoint.
In situ measurements of stratospheric ozone and laboratory studies of ozone production in electric discharge through oxygen have shown previously that ozone containing heavy isotopes of oxygen (O-17, O-18) may be formed preferentially. In order to assess the relevance of thee latter experiment to the stratospheric measurements, detailed understanding of the effect of isotopic substitution on the O3 formation reaction O + O2 + M yields O3 + M and on the O atom exchange reaction O + O2 + O yields O2 + O is necessary. In this work, an estimate of the effect of isotopic substitution on the recombination rate is made by us of approximate dynamical theories and statistical mechanics. The results indicate the possibility of isotope effects on the O + O2 recombination rate of the order of several percent at stratospheric temperatures. In general, recombination reactions involving heavy (mass 49, 50) O3 formation are found to be slower than the reaction leading to normal (mass 48) O3 formation. The calculated isotope effects are sufficiently small that the uncertainties in the model input and the approximations in the dynamical theories will probably make the quantitative nature of these results subject to considerable uncertainty. This isotope effect should not be observable in the atmosphere given the precision of the current measurements but may be crucial in the understanding of the laboratory experiments, where observed enhancements are only of the order of several percent. Possible reasons for this discrepancy between the observed enhancement and predicted depletion are presented.
The thermodynamic stability of clathrate hydrate is calculated to predict the formation conditions corresponding to a range of solar system parameters. The calculations were performed using the statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data concerning clathrate hydrate and its components. Dissociation pressures and partition functions (Langmuir constants) are predicted at low pressure for CO clathrate (hydrate) using the properties of chemicals similar to CO. It is argued that nonsolar but well constrained noble gas abundances may be measurable by the Galileo spacecraft in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances of the Jovian satellite Titan are predicted, assuming that most of the methane in Titan is accreted as clathrate. It is suggested that under thermodynamically appropriate conditions, complete clathration of water ice could have occurred in high-pressure nebulas around giant planets, but probably not in the outer solar nebula. The stability of clathrate in other pressure ranges is also discussed.