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NASA NTRS1978

Two-scale-factor universality near the critical point of fluids

Thermodynamic data from interferometric density profile studies and light-scattering experiments near the critical isochore of Xe, CO2 and SF6 provide a basis for examining the hypothesized two-scale-factor universality for the correlation function of fluids near the gas-liquid critical point. For the investigation, three-scale-factor universality is assumed, with Ising-like critical exponent values obtained through the renormalization group technique. The two thermodynamic scale factors are found from the density profiles, while the scale factor for the correlation length is obtained from the light-scattering data.

Sengers, J. V.↗

NASA NTRS1980

Modified radiative transfer theory for a two-layer random medium

Modified radiative transfer (MRT) equations appropriate for electromagnetic wave propagation in bounded random media are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The MRT equations are then solved with the first-order renormalization approximation to obtain analytical results for the backscattering cross sections of a two-layer random medium with arbitrary three-dimensional correlation functions. The coherent effects of the MRT theory are illustrated and comparisons are made with backscattering cross sections obtained with the first Born approximation to the wave equation.

Zuniga, M. A.↗

NASA NTRS1981

Scattering of electromagnetic waves from random media with strong permittivity fluctuations

By taking into account the singularity of the dyadic Green's function in the renormalization method, a theory is derived for vector electromagnetic wave propagation in a random medium with large permittivity fluctuations and with anisotropic correlation function. The strong fluctuation theory is then applied to a discrete scatterer problem in which the permittivity can assume only two values. The results are found to be consistent with those derived from discrete scatterer theory for all values of dielectric constants of the scatterers.

Tsang, L.↗

NASA NTRS1982

Ice sheet surface features in southwestern Greenland from satellite radio altimetry

Fourteen SEASAT and ten GEOS-3 satellite radar altimeter groundtracks across a 1 deg x 2.5 deg study area in southwestern Greenland have yielded 3,328 ice sheet surface elevations. The surface elevations derived from SEASAT were recalculated based on a waveform retracking algorithm. The elevations have been utilized to develop a surface profile, a three dimensional surface representation, and surface contours. Analysis of the elevations reveals the presence of surface terraces, some greater than 100 km in length; each terrace is at a discrete elevation. Renormalized SEASAT AGC values are shown to be correlated with the surface slope. The ice surface undulations caused frequent altimeter losses-of-lock. Future satellite radar altimeters could significantly contribute to ice sheet mapping in the next decade, particularly if they incorporate tracking systems with more frequent updates.

Brooks, R. L.↗

NASA NTRS1983

Discovery of s-process Nd in Allende residue

New interpretation is given to the isotopic anomalies detected by Lugmair et al. (1983) in an acid-resistant residue of the Allende meteorite. If the Nd-142 excess is due to Sm-146 decay, as the discoverers proposed, it is argued that the decay has occurred in interstellar grains, so that the conclusion that Sm-146 (1.03 x 10 to the 8th yr) was alive in the solar system is premature. It is shown by renormalizing their data that the discovery is likely to be s-process Nd, confirming the survival of red-giant stardust in carbonaceous interstellar dust.

Clayton, D. D.↗

NASA NTRS1984

The rheology of icy satellites

High-temperature creep in orthoenstatite under conditions of controlled oxygen fugacity was studied. It was found that creep was conttrolled by the extremely thin layer of SiO2 which wetted the grain boundaries. Slight reduction of the (Mg, Fe)SiO3 enstatite during hot pressing produced microscopic particles of Fe and the thin film of intergranular SiO2. This result highlights another complication in determining the flow properties of iron bearing silicates which constitute the bulk of terrestrial planets and moons. The Phenomenon may be important in the ductile formation of any extraterrestrial body which is formed in a reducing environment. The rheology of dirty ice was studied. This involves micromechanical modeling of hardening phenomena due to contamination by a cosmic distribution of silicate particles. The larger particles are modeled by suspension theory. In order to handle the distribution of particles sizes, the hardening is readed as a critical phenomenon, and real space renormalization group techniques are used. Smaller particles interact directly with the dislocations. The particulate hardening effect was studied in metals. The magnitude of such hardening in ice and the defect chemistry of ice are studied to assess the effects of chemical contamination by methane, ammonia, or other likely contaminants.

Sammis, C. G.↗

NASA NTRS1984

Boron cosmochemistry

The assumption that boron is a moderately volatile element is examined. It was demonstrated that interior pieces of chondrites contain significantly less boron than had been thought to be indigenous to this type of meteorite. The mean and range of boron abundances in 16 internal pieces of 10 chondrites were significantly smaller than in 126 pieces of 40 chondrites with unknown terrestrial histories. A new value of the cosmic abundance of boron was determined using the geometric average of the results from interior pieces of 10 chondrites. Based upon the thermodynamic assessment of the cosmochemical properties of boron by Cameron, et al. Anders and Ebihara assumed that boron was a moderately volatile element. They renormalized the data of Curtis et al. to a chondrule free basis and thus inferred that the cosmic abundance of boron was about 3 times greater than that proposed by Curtis, et al. To resolve these differences in data, the relative abundances of several elements including boron were measured in 38 carefully prepared interior pieces of 26 different chondrites. Correlation between boron and sulfur abundances, indicate that, contrary to the conclusions of Cameron, et al., boron is not a moderately volatile element.

Curtis, D. B.↗

NASA NTRS1985

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

Chapman, G. T.↗

NASA NTRS1985

Diffusion and localization of a particle in a periodic potential coupled to a dissipative environment

The phase diagram of a Hamiltonian which describes a particle moving in a periodic potential and coupled to an external heat bath has been analyzed in detail. By renormalization-group methods, it is proved that this system exhibits an unusual transition between diffusive behavior and a self-trapped phase. The dynamics along the transition line is shown to be integrable and the order parameter, the mobility, is computed exactly.

Guinea, F.↗

NASA NTRS1985

Anderson localization and the theory of dirty superconductors

A study is made of the effect of Anderson localization in dirty superconductors. The scale dependence of the diffusion in the vicinity of the mobility edge results in a strong renormalization of the zero-temperature coherence length. This implies the breakdown of the Ginzburg criterion close to the metal-insulator transition and thus the importance of fluctuations in this regime. The upper critical field is calculated, and possible experiments are also discussed.

Kapitulnik, A.↗

NASA NTRS1985

On the relative scattering of P- and S-waves

Using a single-scattering approximation, equations for the scattering attenuation coefficients of P-body and S-body waves are derived. The results are discussed in the light of the energy-renormalization approaches of Wu (1980, 1982) and Sato (1982) to seismic wave scattering. Practical methods for calculating the scattering attenuation coefficients for various earth models are emphasized. The conversions of P-waves to S-waves and S-waves to P-waves are included in the theory. The earth models are assumed to be randomly inhomogeneous, with their properties known only through their average-wavenumber power spectra. The power spectra are approximated with piecewise constant functions, each segment of which contributes to the net frequency-dependent scattering attenuation coefficient. The smallest and largest wavenumbers of a segment can be plotted along with the wavevectors of the incident and scattered waves on a wavenumber diagram. This diagram gives a geometric interpretation for the frequency behavior associated with each spectral segment, including a transition peak that is due entirely to the wavenumber limits of the segment. For regions of the earth where the inhomogeneity spectra are concentrated in a band of wavenumbers, it should be possible to observe such a peak in the apparent attenuation of seismic waves. Both the frequency and distance limits on the accuracy of the theoretical results are given.

Malin, P. E.↗

NASA NTRS1984

Ice sheet surface features from satellite radar altimetry

Fourteen SEASAT and ten GEOS-3 satellite radar altimeter groundtracks across a 1 deg x 2.5 deg study area in southwestern Greenland have yielded 3,328 ice sheet surface eievations. The surface elevations derived from SEASAT were recalculated based on a waveform retracking algorithm. The elevations have been utilized to develop a surface profile, a three dimensional surface representation, and surface contours. Analysis of the elevations reveals the presence of surface terraces, some greater than 100 km in length; each terrace is at a discrete elevation. Renormalized SEASAT AGC values are shown to be correlated with the surface slope. The ice surface undulations caused frequent altimeter losses-of-lock. Future satellite radar altimeters could significantly contribute to ice sheet mapping in the next decade, particularly if they incorporate tracking systems with more frequent updates.

Brooks, R. L.↗

NASA NTRS1985

Critical Transport Phenomena in Fluid Helium Under Low Gravity

The feasibility of carrying out measurements of certain critical transport properties of pure fluid under conditions of low gravity was studied. These properties are the thermal conductivity, kappa, the shear viscosity zeta and the diffusive relaxation time tau, which are predicted to diverge (tend to infinity) as the liquid-vapor critical point is approached. However, in this critical region, the Earth's gravity effect becomes very important. As the critical point is approached, the gravity effects increasingly distort the results. The reason for this is that the compressibility of the fluid also diverges and under the influence of gravity causes a vertical density gradient in the fluid, which is significant even when very thin fluid layers (typically 1 mm high) are being used. The result is that the temperature dependence of kappa, zeta, and tau tends to flatten off as T sub c is approached instead of continuing to increase, and therefore the predictions from the renormalization group and mode coupling theories cannot be subjected to a satisfactory test.

Meyer, H.↗

NASA NTRS1984

High accuracy heat capacity measurements through the lambda transition of helium with very high temperature resolution

A measurement of the heat capacity singularity of helium at the lambda transition was performed with the aim of improving tests of the Renormalization Group (RG) predictions for the static thermodynamic behavior near the singularity. The goal was to approach as closely as possible to the lambda-point while making heat capacity measurements of high accuracy. To do this, a new temperature sensor capable of unprecedented resolution near the lambda-point, and two thermal control systems were used. A short description of the theoretical background and motivation is given. The initial apparatus and results are also described.

Fairbanks, W. M.↗

NASA NTRS1985

Oscillation-center autocorrelation time

It is shown that, within the quasi-linear regime, a recently proposed flux-minimization principle for optimizing canonical representations of nonintegrable systems also maximizes the generalized force-force autocorrelation time as seen in the new representation. Using a renormalized canonical perturbation theory, the optimum autocorrelation time is shown to be of the order of the Liapunov time.

Dewar, R. L.↗

NASA NTRS1986

Microwave remote sensing: Active and passive. Volume 3 - From theory to applications

Aspects of volume scattering and emission theory are discussed, taking into account a weakly scattering medium, the Born approximation, first-order renormalization, the radiative transfer method, and the matrix-doubling method. Other topics explored are related to scatterometers and probing systems, the passive microwave sensing of the atmosphere, the passive microwave sensing of the ocean, the passive microwave sensing of land, the active microwave sensing of land, and radar remote sensing applications. Attention is given to inversion techniques, atmospheric attenuation and emission, a temperature profile retrieval from ground-based observations, mapping rainfall rates, the apparent temperature of the sea, the emission behavior of bare soil surfaces, the emission behavior of vegetation canopies, the emission behavior of snow, wind-vector radar scatterometry, radar measurements of sea ice, and the back-scattering behavior of cultural vegetation canopies.

Ulaby, F. T.↗

NASA NTRS1986

Statistical properties and correlation functions for drift waves

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Horton, W.↗

NASA NTRS1986

Universal amplitude ratios and the interfacial tension near consolute points of binary liquid mixtures

The interfacial tension of the binary liquid mixtures triethylamine/heavy water, triethylamine/water, and cyclohexane/methanol near their consolute temperatures is determined experimentally by measuring the densities of the phases and the capillary lengths. The results are presented in tables and graphs and compared with published data obtained by other methods and with theoretical predictions. The findings are shown to be in good agreement with previous experiments, confirming the discrepancy between temperature-independent universal amplitude ratios calculated from such data and those predicted by renormalization-group calculations or Monte Carlo simulations of Ising models.

Moldover, M. R.↗