Affine Matsuki correspondence for sheaves

We lift the affine Matsuki correspondence between real and symmetric loop group orbits in affine Grassmannians to an equivalence of derived categories of sheaves. In analogy with the finite-dimensional setting, our arguments depend upon the Morse theory of energy functions obtained from symmetrizations of coadjoint orbits. The additional fusion structures of the affine setting lead to further equivalences with Schubert constructible derived categories of sheaves on real affine Grassmannians

Mass and power modeling of communication satellites

Analytic estimating relationships for the mass and power requirements for major satellite subsystems are described. The model for each subsystem is keyed to the performance drivers and system requirements that influence their selection and use. Guidelines are also given for choosing among alternative technologies which accounts for other significant variables such as cost, risk, schedule, operations, heritage, and life requirements. These models are intended for application to first order systems analyses, where resources do not warrant detailed development of a communications system scenario. Given this ground rule, the models are simplified to 'smoothed' representation of reality. Therefore, the user is cautioned that cost, schedule, and risk may be significantly impacted where interpolations are sufficiently different from existing hardware as to warrant development of new devices

Physiological Response of Plants Grown on Porous Ceramic Tubes

This research involves the manipulation of the root-zone water potential for the purposes of discriminating the rate limiting step in the inorganic nutrient uptake mechanism utilized by higher plants. This reaction sequence includes the pathways controlled by the root-zone conditions such as water tension and gradient concentrations. Furthermore, plant based control mechanisms dictated by various protein productions are differentiated as well. For the nutrients limited by the environmental availability, the kinetics were modeled using convection and diffusion equations. Alternatively, for the nutrients dependent upon enzyme manipulations, the uptakes are modeled using Michaelis-Menten kinetics. In order to differentiate between these various mechanistic steps, an experimental apparatus known as the Porous Ceramic Tube - Nutrient Delivery System (PCT-NDS) was used. Manipulation of the applied suction pressure circulating a nutrient solution through this system imposes a change in the matric component of the water potential. This compensates for the different osmotic components of water potential dictated by nutrient concentration. By maintaining this control over the root-zone conditions, the rate limiting steps in the uptake of the essential nutrients into tomato plants (Lycopersicon esculentum cv. Cherry Elite) were differentiated. Results showed that the uptake of some nutrients were mass transfer limited while others were limited by the enzyme kinetics. Each of these were adequately modeled with calculations and discussions of the parameter estimations provided

Ice Shape Scaling for Aircraft in SLD Conditions

This paper has summarized recent NASA research into scaling of SLD conditions with data from both SLD and Appendix C tests. Scaling results obtained by applying existing scaling methods for size and test-condition scaling will be reviewed. Large feather growth issues, including scaling approaches, will be discussed briefly. The material included applies only to unprotected, unswept geometries. Within the limits of the conditions tested to date, the results show that the similarity parameters needed for Appendix C scaling also can be used for SLD scaling, and no additional parameters are required. These results were based on visual comparisons of reference and scale ice shapes. Nearly all of the experimental results presented have been obtained in sea-level tunnels. The currently recommended methods to scale model size, icing limit and test conditions are described

Further Assessment of MVD Effects in SLD Applications

The study reported here is part of an effort to develop scaling methods for super cooled large droplet (SLD) conditions. Previously reported results showed that SLD main ice shapes can be simulated quite successfully by appendix C conditions using scaling methods developed for appendix C. However, when the velocity was higher than 100 kt, the feather size and density for SLD tests at MVDs well above 100 m was not well represented by the scaled appendix C conditions. This paper reports additional results of a study of the feather region with the objective of identifying differences between SLD and appendix C feathers. Both the feather appearance and the angle at which feathers grow from the airfoil surface were recorded over a range of MVD from 20 to 190 m for airspeeds of 100 and 200 kt and stagnation freezing fractions of 0.3 to 1.0. Tests were performed in the NASA Glenn Icing Research Tunnel (IRT) using a 91-cm-chord NACA0012 airfoil model mounted at 0 degrees AOA. Photographs are presented to illustrate details of feather appearance. Appearance was noticeably affected by the stagnation freezing fraction of the test, but not by velocity or MVD. The angle of feather growth relative to the chord line decreased with increasing stagnation freezing fraction. For a velocity of 100 kt, no significant effect of MVD on feather angle was apparent, but at 200 kt, feather angle tended to increase with MVD for glaze conditions, but not rime. This finding is based on limited data, and its significance with respect to icing physics has not been determined

Evaluation and Validation of the Messinger Freezing Fraction

One of the most important non-dimensional parameters used in ice-accretion modeling and scaling studies is the freezing fraction defined by the heat-balance analysis of Messinger. For fifty years this parameter has been used to indicate how rapidly freezing takes place when super-cooled water strikes a solid body. The value ranges from 0 (no freezing) to 1 (water freezes immediately on impact), and the magnitude has been shown to play a major role in determining the physical appearance of the accreted ice. Because of its importance to ice shape, this parameter and the physics underlying the expressions used to calculate it have been questioned from time to time. Until now, there has been no strong evidence either validating or casting doubt on the current expressions. This paper presents experimental measurements of the leading-edge thickness of a number of ice shapes for a variety of test conditions with nominal freezing fractions from 0.3 to 1.0. From these thickness measurements, experimental freezing fractions were calculated and compared with values found from the Messinger analysis as applied by Ruff. Within the experimental uncertainty of measuring the leading-edge thickness, agreement of the experimental and analytical freezing fraction was very good. It is also shown that values of analytical freezing fraction were entirely consistent with observed ice shapes at and near rime conditions: At an analytical freezing fraction of unity, experimental ice shapes displayed the classic rime shape, while for conditions producing analytical freezing fractions slightly lower than unity, glaze features started to appear

Overview of Icing Physics Relevant to Scaling

An understanding of icing physics is required for the development of both scaling methods and ice-accretion prediction codes. This paper gives an overview of our present understanding of the important physical processes and the associated similarity parameters that determine the shape of Appendix C ice accretions. For many years it has been recognized that ice accretion processes depend on flow effects over the model, on droplet trajectories, on the rate of water collection and time of exposure, and, for glaze ice, on a heat balance. For scaling applications, equations describing these events have been based on analyses at the stagnation line of the model and have resulted in the identification of several non-dimensional similarity parameters. The parameters include the modified inertia parameter of the water drop, the accumulation parameter and the freezing fraction. Other parameters dealing with the leading edge heat balance have also been used for convenience. By equating scale expressions for these parameters to the values to be simulated a set of equations is produced which can be solved for the scale test conditions. Studies in the past few years have shown that at least one parameter in addition to those mentioned above is needed to describe surface-water effects, and some of the traditional parameters may not be as significant as once thought. Insight into the importance of each parameter, and the physical processes it represents, can be made by viewing whether ice shapes change, and the extent of the change, when each parameter is varied. Experimental evidence is presented to establish the importance of each of the traditionally used parameters and to identify the possible form of a new similarity parameter to be used for scaling

Additional Study of Water Droplet Median Volume Diameter (MVD) Effects on Ice Shapes

This paper reports the result of an experimental study in the NASA Glenn Icing Research Tunnel (IRT) to evaluate how well the MVD-independent effect identified previously might apply to SLD conditions in rime icing situations. Models were NACA 0012 wing sections with chords of 53.3 and 91.4 cm. Tests were conducted with a nominal airspeed of 77 m/s (150 kt) and a number of MVD's ranging from 15 to 100 m with LWC of 0.5 to 1 g/cu m. In the present study, ice shapes recorded from past studies and recent results at SLD and Appendix-C conditions are reviewed to show that droplet diameter is not important to rime ice shape for MVD of 30 microns or larger, but for less than 30 m drop sizes a rime ice shape transition from convex to wedge to spearhead type ice shape is observed

Propagation characteristics of guided waves in stratified metallic optical waveguides

An eigenvalue equation is derived for stratified metallic optical slab waveguides with any number of layers. The equation is solved using the numerical zoom analysis (NZA) method. The analysis is applied to various metallic optical slabs and the propagation characteristics of the guided waves are determined, which may be useful for optimizing the design parameters. It is found possible, with proper optimization, to design a polarizer having hundreds of decibels of extinction ratio at the cost of a fraction of a decibel of insertion loss. Examples of optimizations with respect to wavelength, relative refractive indices, core/clad geometries, etc. are demonstrated for slabs with single or double metal layers. Guidelines for determining the metal film thickness have been formulated and tabulated for many useful metals