Infrared and Raman spectroscopic studies of structural variations in minerals from Apollo 11, 12, 14 and 15 samples, volume 3

Infrared and Raman vibrational spectroscopic data, yielding direct information on molecular structure, were obtained for single grains ( 150 microns) of minerals, basalts, and glasses isolated from Apollo 11, 12, 14, and 15 rock and dust samples, and for grains in Apollo 14 polished butt samples. From the vibrational data, specification substitutions were determined for the predominant silicate minerals of plagioclase, pyroxene, and olivine. Unique spectral variations for grains of K-feldspar, orthopyroxene, pyroxenoid, and ilmenite were observed to exceed the ranges of terrestrial samples, and these variations may be correlatable with formation histories. Alpha-quartz was isolated as pure single grains, in granitic grains composited with sanidine, and in unique grains that were intimately mixed with varying amounts of glass. Accessory minerals of chromite and ulvospinel were isolated as pure grains and structurally characterized from their distinctive infrared spectra. Fundamental vibrations of the SiO4 tetrahedra in silicate minerals were used to classify bulk compositions in dust sieved fractions, basalt grains and glass particles, and to compare modal characteristics for maria, highland and rille samples. No hydrated minerals were found in any of the samples studied, indicating anhydrous formation conditions

Numerical approach to the Schrodinger equation in momentum space

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schrodinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound-states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio

Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

Emission-line Helium Abundances in Highly Obscured Nebulae

This paper outlines a way to determine the ICF using only infrared data. We identify four line pairs, [NeIII] 36\micron/[NeII] 12.8\micron, [NeIII]~15.6\micron /[NeII] 12.8\micron, [ArIII] 9\micron/[ArII] 6.9\micron, and [ArIII] 21\micron/[ArII] 6.9\micron, that are sensitive to the He ICF. This happens because the ions cover a wide range of ionization, the line pairs are not sensitive to electron temperature, they have similar critical densities, and are formed within the He$^+$/H$^+$ region of the nebula. We compute a very wide range of photoionization models appropriate for galactic HII regions. The models cover a wide range of densities, ionization parameters, stellar temperatures, and use continua from four very different stellar atmospheres. The results show that each line pair has a critical intensity ratio above which the He ICF is always small. Below these values the ICF depends very strongly on details of the models for three of the ratios, and so other information would be needed to determine the helium abundance. The [Ar III] 9\micron/[ArII] 6.9\micron ratio can indicate the ICF directly due to the near exact match in the critical densities of the two lines. Finally, continua predicted by the latest generation of stellar atmospheres are sufficiently hard that they routinely produce significantly negative ICFs.Comment: Accepted by PASP. Scheduled for the October 1999 issue. 11 pages, 5 figure

Task-Specific Ionic Liquids for Mars Exploration (Green Chemistry for a Red Planet)

Ionic Liquids (ILs) are organic salts with low melting points that are liquid at or near room temperature. The combinations of available ions and task-specific molecular designability make them suitable for a huge variety of tasks. Because of their low flammability, low vapor pressure, and stability in harsh environments (extreme temperatures, hard vacuum) they are generally much safer and "greener" than conventional chemicals and are thus suitable for a wide range of applications that support NASA exploration goals. This presentation describes several of the ongoing applications that are being developed at MSFC

Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems

Static Safety for an Actor Dedicated Process Calculus by Abstract Interpretation

The actor model eases the definition of concurrent programs with non uniform behaviors. Static analysis of such a model was previously done in a data-flow oriented way, with type systems. This approach was based on constraint set resolution and was not able to deal with precise properties for communications of behaviors. We present here a new approach, control-flow oriented, based on the abstract interpretation framework, able to deal with communication of behaviors. Within our new analyses, we are able to verify most of the previous properties we observed as well as new ones, principally based on occurrence counting