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Hawaii Ocean Mixing Experiment: Program Summary

It is becoming apparent that insufficient mixing occurs in the pelagic ocean to maintain the large scale thermohaline circulation. Observed mixing rates fall a factor of ten short of classical indices such as Munk's "Abyssal Recipe." The growing suspicion is that most of the mixing in the sea occurs near topography. Exciting recent observations by Polzin et al., among others, fuel this speculation. If topographic mixing is indeed important, it must be acknowledged that its geographic distribution, both laterally and vertically, is presently unknown. The vertical distribution of mixing plays a critical role in the Stommel Arons model of the ocean interior circulation. In recent numerical studies, Samelson demonstrates the extreme sensitivity of flow in the abyssal ocean to the spatial distribution of mixing. We propose to study the topographic mixing problem through an integrated program of modeling and observation. We focus on tidally forced mixing as the global energetics of this process have received (and are receiving) considerable study. Also, the well defined frequency of the forcing and the unique geometry of tidal scattering serve to focus the experiment design. The Hawaiian Ridge is selected as a study site. Strong interaction between the barotropic tide and the Ridge is known to take place. The goals of the Hawaiian Ocean Mixing Experiment (HOME) are to quantify the rate of tidal energy loss to mixing at the Ridge and to identify the mechanisms by which energy is lost and mixing generated. We are challenged to develop a sufficiently comprehensive picture that results can be generalized from Hawaii to the global ocean. To achieve these goals, investigators from five institutions have designed HOME, a program of historic data analysis, modeling and field observation. The Analysis and Modeling efforts support the design of the field experiments. As the program progresses, a global model of the barotropic (depth independent) tide, and two models of the baroclinic (depth varying) tide, all validated with near-Ridge data, will be applied, to reveal the mechanisms of tidal energy conversion along the Ridge, and allow spatial and temporal integration of the rate of conversion. Field experiments include a survey to identify "hot spots" of enhanced mixing and barotropic to baroclinic conversion, a Nearfield study identifying the dominant mechanisms responsible for topographic mixing, and a Farfield program which quantifies the barotropic energy flux convergence at the Ridge and the flux divergence associated with low mode baroclinic waves radiation. The difference is a measure of the tidal power available for mixing at the Ridge. Field work is planned from years 2000 through 2002, with analysis and modeling efforts extending through early 2006. If successful, HOME will yield an understanding of the dominant topographic mixing processes applicable throughout the global ocean. It will advance understanding of two central problems in ocean science, the maintenance of the abyssal stratification, and the dissipation of the tides. HOME data will be used to improve the parameterization of dissipation in models which presently assimilate TOPEX-POSEIDON observations. The improved understanding of the dynamics and spatial distribution of mixing processes will benefit future long-term programs such as CLIVAR.

Ray, Richard D.↗

Exclusive Reactions Involving Pions and Nucleons

The HZETRN code requires inclusive cross sections as input. One of the methods used to calculate these cross sections requires knowledge of all exclusive processes contributing to the inclusive reaction. Conservation laws are used to determine all possible exclusive reactions involving strong interactions between pions and nucleons. Inclusive particle masses are subsequently determined and are needed in cross-section calculations for inclusive pion production.

Norbury, John W.↗

Calculation of Supersonic Combustion Using Implicit Schemes

One of the technology goals of NASA for advanced space transportation is to develop highly efficient propulsion systems to reduce the cost of payload for space missions. Developments of rockets for the second generation Reusable Launch Vehicle (RLV) in the past several years have been focused on low-cost versions of conventional engines. However, recent changes in the Integrated Space Transportation Program to build a crew transportation vehicle to extend the life of the Space Shuttle fleet might suggest that air-breathing rockets could reemerge as a possible propulsion system for the third generation RLV to replace the Space Shuttle after 2015. The weight of the oxygen tank exceeds thirty percent of the total weight of the Space Shuttle at launch while the payload is only one percent of the total weight. The air-breathing rocket propulsion systems, which consume oxygen in the air, offer clear advantages by making vehicles lighter and more efficient. Experience in the National Aerospace Plane Program in the late 1980s indicates that scramjet engines can achieve high specific impulse for low hypersonic vehicle speeds. Whether taking a form of Rocket Based Combined Cycle (RBCC) or Turbine Based Combined Cycle (TBCC), the scramjet is an essential mode of operation for air-breathing rockets. It is well known that fuel-air mixing and rapid combustion are of crucial importance for the success of scramjet engines since the spreading rate of the supersonic mixing layer decreases as the Mach number increases. A factored form of the Gauss-Seidel relaxation method has been widely used in hypersonic flow research since its first application to non-equilibrium flows. However, difficulties in stability and convergence have been encountered when there is strong interaction between fluid motion and chemical reaction, such as multiple fuel injection problems. The present paper reports the results from investigation of the effect of modifications to the original algorithm on the performance for multiple injectors.

Yoon, Seokkwan↗

Development of Numerical Codes for Modeling Electromagnetic Behavior at High Frequencies Near Large Objects

A study into the problem of determining electromagnetic solutions at high frequencies for problems involving complex geometries, large sizes and multiple sources (e.g. antennas) has been initiated. Typical applications include the behavior of antennas (and radiators) installed on complex conducting structures (e.g. ships, aircrafts, etc..) with strong interactions between antennas, the radiation patterns, and electromagnetic signals is of great interest for electromagnetic compatibility control. This includes the overall performance evaluation and control of all on-board radiating systems, electromagnetic interference, and personnel radiation hazards. Electromagnetic computational capability exists at NASA LaRC, and many of the codes developed are based on the Moment Method (MM). However, the MM is computationally intensive, and this places a limit on the size of objects and structures that can be modeled. Here, two approaches are proposed: (i) a current-based hybrid scheme that combines the MM with Physical optics, and (ii) an Alternating Direction Implicit-Finite Difference Time Domain (ADI-FDTD) method. The essence of a hybrid technique is to split the overall scattering surface(s) into two regions: (a) a MM zone (MMZ) which can be used over any part of the given geometry, but is most essential over irregular and "non-smooth" geometries, and (b) a PO sub-region (POSR). Currents induced on the scattering and reflecting surfaces can then be computed in two ways depending on whether the region belonged to the MMZ or was part of the POSR. For the MMZ, the current calculations proceed in terms of basis functions with undetermined coefficients (as in the usual MM method), and the answer obtained by solving a system of linear equations. Over the POSR, conduction is obtained as a superposition of two contributions: (i) currents due to the incident magnetic field, and (ii) currents produced by the mutual induction from conduction within the MMZ. This effectively leads to a reduction in the size of linear equations from N to N - Npo with N being the total number of segments for the entire surface and Npo the number of segments over the POSR. The scheme would be appropriate for relatively large, flat surfaces, and at high frequencies. The ADI-FDTD scheme provides for both transient and steady state analyses. The restrictive Courant-Friedrich-Levy (CFL) condition on the time-step is removed, and so large time steps can be chosen even though the spatial grids are small. This report includes the problem definition, a detailed discussion of both the numerical techniques, and numerical implementations for simple surface geometries. Numerical solutions have been derived for a few simple situations.

Joshi, R. P.↗

Cross section parameterizations for cosmic-ray nuclei. II. Double nucleon removal

Parameterizations of double nucleon removal from the electromagnetic and strong interactions of cosmic rays with nuclei are presented. These parameterizations are an extension of previous single nucleon removal parameterizations and combined they represent the dominant part of the electromagnetic dissociation encountered by a cosmic ray on its traversal through matter. Such parameterizations should be very useful in studying cosmic-ray transport through the interstellar medium, the Earth's atmosphere, spacecraft walls, and extraterrestrial matter.

NASA Discipline Radiation Health↗

Modeling Compressibility Effects in High-Speed Turbulent Flows

Man has strived to make objects fly faster, first from subsonic to supersonic and then to hypersonic speeds. Spacecraft and high-speed missiles routinely fly at hypersonic Mach numbers, M greater than 5. In defense applications, aircraft reach hypersonic speeds at high altitude and so may civilian aircraft in the future. Hypersonic flight, while presenting opportunities, has formidable challenges that have spurred vigorous research and development, mainly by NASA and the Air Force in the USA. Although NASP, the premier hypersonic concept of the eighties and early nineties, did not lead to flight demonstration, much basic research and technology development was possible. There is renewed interest in supersonic and hypersonic flight with the HyTech program of the Air Force and the Hyper-X program at NASA being examples of current thrusts in the field. At high-subsonic to supersonic speeds, fluid compressibility becomes increasingly important in the turbulent boundary layers and shear layers associated with the flow around aerospace vehicles. Changes in thermodynamic variables: density, temperature and pressure, interact strongly with the underlying vortical, turbulent flow. The ensuing changes to the flow may be qualitative such as shocks which have no incompressible counterpart, or quantitative such as the reduction of skin friction with Mach number, large heat transfer rates due to viscous heating, and the dramatic reduction of fuel/oxidant mixing at high convective Mach number. The peculiarities of compressible turbulence, so-called compressibility effects, have been reviewed by Fernholz and Finley. Predictions of aerodynamic performance in high-speed applications require accurate computational modeling of these "compressibility effects" on turbulence. During the course of the project we have made fundamental advances in modeling the pressure-strain correlation and developed a code to evaluate alternate turbulence models in the compressible shear layer.

Sarkar, S.↗

The effects of bone on proton NMR relaxation times of surrounding liquids

Preliminary attempts by our group at UCSF to assess fat content of vertebral marrow in the lumbar spine using relaxation time information demonstrated that the presence of trabecular bone affects relaxation times. The objective of this work was a thorough study of the effects of bone on NMR relaxation characteristics of surrounding liquids. Trabecular bone from autopsy specimens was ground up and sifted into a series of powders with graded densities ranging from 0.3 gm/cc to 0.8 gm/cc. Each powder was placed first in n-saline and then in cottonseed oil. With spectroscopy, spin-lattice relaxation times (T1) and effective spin-spin relaxation times (T2*) were measured for each liquid in each bone powder. As bone density and surface to volume ratio increased, T1 decreased faster for saline than for oil. T2* decreased significantly for both water and oil as the surface to volume ratio increased. It was concluded that effects of water on T1 could be explained by a surface interaction at the bone/liquid interface, which restricted rotational and translational motion of nearby molecules. The T1s of oil were not affected since oil molecules are nonpolar, do not participate in significant intermolecular hydrogen bonding, and therefore would not be expected to interact strongly with the bone surface. Effects on T2* could be explained by local magnetic field inhomogeneities created by discontinuous magnetic susceptibility near the bone surface. These preliminary results suggest that water in contact with trabecular bone in vivo will exhibit shortened relaxation times.

NASA Discipline Musculoskeletal↗

Laboratory Infrared Spectra of Polycyclic Aromatic Nitrogen Heterocycles: Quinoline, and Phenanthridine in Solid Argon and H2O

Polycyclic aromatic hydrocarbons (PAHs) are common throughout the universe. Their detection and identification are based on telescopic infrared (IR) spectra compared with laboratory data. Polycyclic Aromatic Nitrogen Heterocycles (PANHs) are heterocyclic aromatics i.e., PAHs with carbon atoms replaced by a nitrogen atom. These molecules should be present in the interstellar medium, but have received relatively little attention. We present mid-IR spectra of two PANHs, quinoline (C9H7N), and phenanthridine (C13H9N) isolated in solid argon and frozen in solid H2O at 12 K, conditions yielding data directly comparable to astronomical observations. In contrast to simple PAHs, that do not interact strongly with solid H2O, the nitrogen atoms in PANHs are potentially capable of hydrogen bonding with H2O. Whereas the IR spectrum of phenanthridine in H2O is similar to that of the same compound isolated in an argon matrix, quinoline absorptions shift up to 16 cm(sup -1) (0.072 mm) between argon and H2O. Thus, astronomers will not always be able to rely on IR band positions of matrix isolated PANHs to correctly interpret the absorptions of PANHs frozen in H2O ice grains. Furthermore, our data suggest that relative band areas also vary, so determining column densities to better than a factor of 3 will require knowledge of the matrix in which the PANH is embedded and laboratory studies of relevant samples.

Bernstein, M. P.↗

Nucleobases in Space: Laboratory Studies of Polycyclic Aromatic Nitrogen Heterocycles

Polycyclic Aromatic Nitrogen Heterocycles (PANHs) are heterocyclic aromatics Le., PAHs with carbon atoms replaced by a nitrogen atom. These molecules have been detected in meteorite extracts, and in general these nitrogen heterocycles are of astrobiological interest since this class of molecules include nucleobases, basic components of our nucleic acids. These compounds are predicted to be present in the interstellar medium and in Titan tholin, but have received relatively little attention. We will present spectra and reactions of PANHs, frozen in solid H2O at 12 K, conditions germane to astronomical observations. In contrast to simple PAHs, that do not interact strongly with solid H2O, the nitrogen atoms in PANHs are potentially capable of hydrogen bonding with H20 changing their spectra, complicating their remote detection on the surfaces of icy bodies. Moreover, we have studied the photo-chemistry of these interesting compounds under astrophysical conditions and will use our lab studies to assess a potential interstellar heritage of these compounds in carbonaceous chondrites.

Elsila, Jamie↗

Coupled Monte Carlo Probability Density Function/ SPRAY/CFD Code Developed for Modeling Gas-Turbine Combustor Flows

The success of any solution methodology for studying gas-turbine combustor flows depends a great deal on how well it can model various complex, rate-controlling processes associated with turbulent transport, mixing, chemical kinetics, evaporation and spreading rates of the spray, convective and radiative heat transfer, and other phenomena. These phenomena often strongly interact with each other at disparate time and length scales. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. Turbulence manifests its influence in a diffusion flame in several forms depending on how turbulence interacts with various flame scales. These forms range from the so-called wrinkled, or stretched, flamelets regime, to the distributed combustion regime. Conventional turbulence closure models have difficulty in treating highly nonlinear reaction rates. A solution procedure based on the joint composition probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices such as extinction, blowoff limits, and emissions predictions because it can handle the nonlinear chemical reaction rates without any approximation. In this approach, mean and turbulence gas-phase velocity fields are determined from a standard turbulence model; the joint composition field of species and enthalpy are determined from the solution of a modeled PDF transport equation; and a Lagrangian-based dilute spray model is used for the liquid-phase representation with appropriate consideration of the exchanges of mass, momentum, and energy between the two phases. The PDF transport equation is solved by a Monte Carlo method, and existing state-of-the-art numerical representations are used to solve the mean gasphase velocity and turbulence fields together with the liquid-phase equations. The joint composition PDF approach was extended in our previous work to the study of compressible reacting flows. The application of this method to several supersonic diffusion flames associated with scramjet combustor flow fields provided favorable comparisons with the available experimental data. A further extension of this approach to spray flames, three-dimensional computations, and parallel computing was reported in a recent paper. The recently developed PDF/SPRAY/computational fluid dynamics (CFD) module combines the novelty of the joint composition PDF approach with the ability to run on parallel architectures. This algorithm was implemented on the NASA Lewis Research Center's Cray T3D, a massively parallel computer with an aggregate of 64 processor elements. The calculation procedure was applied to predict the flow properties of both open and confined swirl-stabilized spray flames.

Source record↗

EUPDF: Eulerian Monte Carlo Probability Density Function Solver for Applications With Parallel Computing, Unstructured Grids, and Sprays

The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic-diffusion flames and spray flames. The EUPDF source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, M. S.↗

Creep Resistance of ZrO2 Ceramic Improved by the Addition of a Small Amount of Er2O3

Zirconia (ZrO2) has great technological importance in structural, electrical, and chemical applications. It is the crucial component for state-of-the art thermal barrier coatings and an enabling component as a solid electrolyte for solid-oxide fuel cell systems. Pure ZrO2 is of limited use for industrial applications because of the phase transformations that occur. Upon the addition of stabilizers, cubic (c-ZrO2) and tetragonal (t-ZrO2) forms can be preserved. It is the stabilized and partially stabilized forms of zirconia that function as thermal barrier coatings, solid electrolytes, and oxygen sensors and that have numerous applications in the electrochemical industry. The cubic form of ZrO2 is typically stabilized through Y2O3 additions. However, Y2O3-stabilized zirconia is susceptible to deformation at high temperatures (greater than 900 C) because of the large number of slip systems and the high oxygen diffusion rates, which result in high creep rates at high temperatures. Successful use of ZrO2 at high temperatures requires that new dopant additives be found that will retain or enhance the desirable properties of cubic ZrO2 and yet produce a material with lower creep rates. At the NASA Glenn Research Center, erbium oxide (Er2O3) was identified as a promising dopant for improving the creep resistance of. ZrO2. The selection of Er2O3 was based on the strong interactions of point defects and dislocations. Single crystals of 5 mol% Er2O3- doped ZrO2 rods (4 mm in diameter) and monofilaments (200 to 300 mm in diameter and 30 cm long) were grown using the laser-heated float zone technique, and their creep behavior was measured as a function of temperature. The addition of 5 mol% Er2O3 to single-crystal ZrO2 improved its creep resistance at high temperatures by 2 to 3 orders of magnitude over state-of-the-art Y2O3-doped crystals. Detailed microstructural characterization of ZrO2-Er2O3 single crystals has identified new mechanisms for improving the creep resistance of this class of materials. Adding Er2O3 to ZrO2 results in microstructure of stable and metastable tetragonal precipitates that with thermal treatment evolve to a tweed structure of nanosize tetragonal lamellae. The superior high-temperature creep resistance of Er2O3-doped ZrO2 is attributed to nanoscale precipitation hardening. Doping with Er2O3 will significantly increase the upper-use temperature limit of ZrO2. Potential applications include using Er2O3-doped ZrO2 as a high-temperature fiber for structural applications and adding Er2O3 to reduce the sintering rates of ZrO2 thermal barrier coatings. This work was conducted at Dpto. de F sica de la Materia Condensada, Universidad de Sevilla, Spain, and at NASA Glenn.

Martinez-Fernandez, Julian↗

Hydrodynamics in a Degenerate, Strongly Attractive Fermi Gas

In summary, we use all-optical methods with evaporative cooling near a Feshbach resonance to produce a strongly interacting degenerate Fermi gas. We observe hydrodynamic behavior in the expansion dynamics. At low temperatures, collisions may not explain the expansion dynamics. We observe hydrodynamics in the trapped gas. Our observations include collisionally-damped excitation spectra at high temperature which were not discussed above. In addition, we observe weakly damped breathing modes at low temperature. The observed temperature dependence of the damping time and hydrodynamic frequency are not consistent with collisional dynamics nor with collisionless mean field interactions. These observations constitute the first evidence for superfluid hydrodynamics in a Fermi gas.

Thomas, John E.↗

Accurate Calculation of Oscillator Strengths for CI II Lines Using Non-orthogonal Wavefunctions

Non-orthogonal orbitals technique in the multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities for allowed and intercombination lines in Cl II. The relativistic corrections are included through the Breit-Pauli Hamiltonian. The Cl II wave functions show strong term dependence. The non-orthogonal orbitals are used to describe the term dependence of radial functions. Large sets of spectroscopic and correlation functions are chosen to describe adequately strong interactions in the 3s(sup 2)3p(sup 3)nl (sup 3)Po, (sup 1)Po and (sup 3)Do Rydberg series and to properly account for the important correlation and relaxation effects. The length and velocity forms of oscillator strength show good agreement for most transitions. The calculated radiative lifetime for the 3s3p(sup 5) (sup 3)Po state is in good agreement with experiment.

Tayal, S. S.↗

LES/RANS Simulation of a Supersonic Reacting Wall Jet

This work presents results from large-eddy / Reynolds-averaged Navier-Stokes (LES/RANS) simulations of the well-known Burrows-Kurkov supersonic reacting wall-jet experiment. Generally good agreement with experimental mole fraction, stagnation temperature, and Pitot pressure profiles is obtained for non-reactive mixing of the hydrogen jet with a non-vitiated air stream. A lifted flame, stabilized between 10 and 22 cm downstream of the hydrogen jet, is formed for hydrogen injected into a vitiated air stream. Flame stabilization occurs closer to the hydrogen injection location when a three-dimensional combustor geometry (with boundary layer development resolved on all walls) is considered. Volumetric expansion of the reactive shear layer is accompanied by the formation of large eddies which interact strongly with the reaction zone. Time averaged predictions of the reaction zone structure show an under-prediction of the peak water concentration and stagnation temperature, relative to experimental data and to results from a Reynolds-averaged Navier-Stokes calculation. If the experimental data can be considered as being accurate, this result indicates that the present LES/RANS method does not correctly capture the cascade of turbulence scales that should be resolvable on the present mesh. Instead, energy is concentrated in the very largest scales, which provide an over-mixing effect that excessively cools and strains the flame. Predictions improve with the use of a low-dissipation version of the baseline piecewise parabolic advection scheme, which captures the formation of smaller-scale structures superimposed on larger structures of the order of the shear-layer width.

Edwards, Jack R.↗

Reduction of Unsteady Forcing in a Vaned, Contra-Rotating Transonic Turbine Configuration

HPT blade unsteadiness in the presence of a downstream vane consistent with contra-rotation is characterized by strong interaction at the first harmonic of downstream vane passing. E An existing stage-and-one-half transonic turbine rig design was used as a baseline to investigate means of reducing such a blade-vane interaction. E Methods assessed included: Aerodynamic shaping of HPT blades 3D stacking of the downstream vane Steady pressure-side blowing E Of the methods assessed, a combination of vane bowing and steady pressure-side blowing produced the most favorable result. E Transonic turbine experiments are planned to assess predictive accuracy for the baseline turbine and any design improvements.

Clark, John↗

Gravitational-Wave Astronomy

Einstein's General Theory of Relativity is our best classical description of gravity, and informs modern astronomy and astrophysics at all scales: stellar, galactic, and cosmological. Among its surprising predictions is the existence of gravitational waves -- ripples in space-time that carry energy and momentum away from strongly interacting gravitating sources. In my talk, I will give an overview of the properties of this radiation, recent breakthroughs in computational physics allowing us to calculate the waveforms from galactic mergers, and the prospect of direct observation with interferometric detectors such as LIGO and LISA.

Kelly, Bernard J.↗

Fluids and their Effect on Measurements on Lunar Soil Particle size Distribution

From the late 1960s until now, lunar soil particle size distributions have typically been determined by sieving sometimes dry, and at other times with fluids such as water or Freon. Laser diffraction instruments allow rapid assessment of particle size distribution, and eventually may replace sieve measurements. However, when measuring lunar soils with laser diffraction instruments, care must be taken in choosing a carrier fluid that is compatible with lunar material. Distilled water is the fluid of choice for laser diffraction measurements of substances when there is no concern about adverse effects of water on the material being measured. When we began our analyses of lunar soils using laser diffraction, our first measurements were made with distilled water. Although the medians that we measured were comparable to earlier sieve data, the means tended to be significantly larger than expected. The effect of water vapor on lunar soil has been studied extensively. The particles interact strongly with water vapor, and subsequent adsorptions of nitrogen showed that the specific surface area increased as much as threefold after exposure to moisture. It was observed that significant porosity had been generated by this exposure to water vapor. The possibility of other physical changes in the surfaces of the grains was not studied.

Cooper, B. L.↗