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NASA NTRS2002

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one- dimensional convection-diffusion-reaction (CDR) equations. Accuracy, stability, conservation, and dense-output are first considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, (N = 2), additive Runge-Kutta (ARK(sub 2)) methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms of the partitioned method are of equal order to those of the elemental methods. Derived ARK(sub 2) methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z['] yields -infinity, and retain high stability efficiency in the absence of stiffness, z['] yield 0. Extrapolation-type stage- value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK(sub 2) error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK(sub 2) methods.

Kennedy, Christopher A.↗
NASA NTRS2018

Vertical Profile of Cloud Optical Parameters Derived from Airborne Measurements Above, Inside and Below Clouds

Past strategies for retrieving cloud optical properties from remote sensing assumed significant limits for desired parameters such as semi-infinite optical thickness, single scattering albedo equaling unity (non-absorbing scattering), absence of spectral dependence of the optical thickness, etc., and only one optical parameter could be retrieved (either optical thickness or single scattering albedo). Here, we demonstrate a new method based on asymptotic theory for thick atmospheres, and the presence of a diffusion domain within the clouds that does not put restrictions and makes it possible to get two or even three optical parameters (optical thickness, single scattering albedo and phase function asymmetry parameter) for every wavelength independently. We applied this method to measurements of angular distribution of solar radiation above, inside and below clouds, obtained with NASA's Cloud Absorption Radiometer (CAR) over two cases of marine stratocumulus clouds; first case, offshore of Namibia and the second case, offshore of California. The observational and retrieval errors are accounted for by regularization, which allows stable and smooth solutions. Results show good potential for parameterization of the shortwave radiative properties (reflection, transmission, radiative divergence and heating rate) of water clouds.

airborne observations↗
NASA NTRS1996

Application of the pressure sensitive paint technique to steady and unsteady flow

Pressure sensitive paint is a newly-developed optical measurement technique with which one can get a continuous pressure distribution in much shorter time and lower cost than a conventional pressure tap measurement. However, most of the current pressure sensitive paint applications are restricted to steady pressure measurement at high speeds because of the small signal-to-noise ratio at low speed and a slow response to pressure changes. In the present study, three phases of work have been completed to extend the application of the pressure sensitive paint technique to low-speed testing and to investigate the applicability of the paint technique to unsteady flow. First the measurement system using a commercially available PtOEP/GP-197 pressure sensitive paint was established and applied to impinging jet measurements. An in-situ calibration using only five pressure tap data points was applied and the results showed good repeatability and good agreement with conventional pressure tap measurements on the whole painted area. The overall measurement accuracy in these experiments was found to be within 0.1 psi. The pressure sensitive paint technique was then applied to low-speed wind tunnel tests using a 60 deg delta wing model with leading edge blowing slots. The technical problems encountered in low-speed testing were resolved by using a high grade CCD camera and applying corrections to improve the measurement accuracy. Even at 35 m/s, the paint data not only agreed well with conventional pressure tap measurements but also clearly showed the suction region generated by the leading edge vortices. The vortex breakdown was also detected at alpha=30 deg. It was found that a pressure difference of 0.2 psi was required for a quantitative pressure measurement in this experiment and that temperature control or a parallel temperature measurement is necessary if thermal uniformity does not hold on the model. Finally, the pressure sensitive paint was applied to a periodically changing pressure field with a 12.8s time period. A simple first-order pole model was applied to deal with the phase lag of the paint. The unsteady pressure estimated from the time-changing pressure sensitive paint data agreed well with the pressure transducer data in regions of higher pressure and showed the possibility of extending the technique to unsteady pressure measurements. However, the model still needs further refinement based on the physics of the oxygen diffusion into the paint layer and the oxygen quenching on the paint luminescence.

Shimbo, Y.↗
NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗
NASA NTRS1994

Measurements of striae in CR+ doped YAG laser crystals

Striations in Czochralski (CZ) grown crystals have been observed in materials such as GaAs, silicon, photorefractive crystals used for data storage, potassium titanyl phosphate crystals and LiNbO3. Several techniques have been used for investigating these defects including electron microscopy, laser scanning tomography, selective photoetching, X-ray diffuse scattering, interference orthoscopy, laser interferometry and micro-Fourier transform infrared spectroscopy mapping. A 2mm thick sample of the material to be investigated is illuminated with light that is absorbed and non-absorbed by the ion concentration to be observed. The back surface of the sample is focused onto a solid-state image detector and images of the input beam and absorbed (and diffracted) beams are captured at two wavelengths. The variation of the coefficient of absorption asa function of distance on the sample can be derived from these measurements. A Big Sky Software Beamcode system is used to capture and display images. Software has been written to convert the Beamcode data files to a format that can be imported into a spreadsheet program such as Quatro Pro. The spreadsheet is then used to manipulate and display data. A model of the intensity map of the striae collected by the imaging system has been proposed and a data analysis procedure derived. From this, the variability of the attenuation coefficient alpha can be generated. Preliminary results show that alpha may vary by a factor of four or five over distances of 100 mu m. Potential errors and problems have been discovered and additional experiments and improvements to the experimental setup are in progress and we must now show that the measurement techniques and data analysis procedures provide 'real' information. Striae are clearly visible at all wavelengths including white light. Their basic spatial frequency does not change radically, at least when changing from blue to green to white light. Further experimental and theoretical work can be done to improve the data collection techniques and to verify the data analysis procedures.

Cady, Fredrick M.↗
NASA NTRS2007

Science Archives in the 21st Century: A NASA LAMBDA Report

Lambda is a thematic data center that focuses on serving the cosmic microwave background (CMB) research community. LAMBDA is an active archive for NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) mission data sets. In addition, LAMBDA provides analysis software, on-line tools, relevant ancillary data and important web links. LAMBDA also tries to preserve the most important ground-based and suborbital CMB data sets. CMB data is unlike other astrophysical data, consisting of intrinsically diffuse surface brightness photometry with a signal contrast of the order 1 part in 100,000 relative to the uniform background. Because of the extremely faint signal levels, the signal-to-noise ratio is relatively low and detailed instrument-specific knowledge of the data is essential. While the number of data sets being produced is not especially large, those data sets are becoming large and complex. That tendency will increase when the many polarization experiments currently being deployed begin producing data. The LAMBDA experience supports many aspects of the NASA data archive model developed informally over the last ten years-that small focused data centers are often more effective than larger more ambitious collections, for example; that data centers are usually best run by active scientists; that it can be particularly advantageous if those scientists are leaders in the use of the archived data sets; etc. LAMBDA has done some things so well that they might provide lessons for other archives. A lot of effort has been devoted to developing a simple and consistent interface to data sets, for example; and serving all the documentation required via simple 'more' pages and longer explanatory supplements. Many of the problems faced by LAMBDA will also not surprise anyone trying to manage other space science data. These range from persuading mission scientists to provide their data as quickly as possible, to dealing with a high volume of nuisance (spam) messages. Because so many data center problems and solutions are common across individual data centers and disciplines it would be very valuable to establish some new systems of communication - such as informal email lists for administrators and developers. But resources are very limited, so new timeconsuming and inefficient mechanisms - like too-frequent and too-structured meetingsshould be avoided. Although there are great advantages to being small, agile and independent, there are also some areas where science data centers within and without NASA could be better coordinated - for the assignment of persistent identifiers; to encourage the early adoption of useful standards and technologies; etc. Some super-structure to facilitate such coordination might be beneficial as long as it doesn't begin to control the other work of the archives, and become a "methodology police". In this respect the CCSDS "Reference Model for an Open Archive Information System" is a little worrying. It may be that the closer a data center gets to following such a detailed prescription, the less effective it will become. It is much better to have an informal coordination process than a bureaucratic straight-jacket.

Butterworth, P.↗
NASA NTRS2011

Non-Contact Thermal Properties Measurement with Low-Power Laser and IR Camera System

As shown by the Phoenix Mars Lander's Thermal and Electrical Conductivity Probe (TECP), contact measurements of thermal conductivity and diffusivity (using a modified flux-plate or line-source heat-pulse method) are constrained by a number of factors. Robotic resources must be used to place the probe, making them unavailable for other operations for the duration of the measurement. The range of placement is also limited by mobility, particularly in the case of a lander. Placement is also subject to irregularities in contact quality, resulting in non-repeatable heat transfer to the material under test. Most important from a scientific perspective, the varieties of materials which can be measured are limited to unconsolidated or weakly-cohesive regolith materials, rocks, and ices being too hard for nominal insertion strengths. Accurately measuring thermal properties in the laboratory requires significant experimental finesse, involving sample preparation, controlled and repeatable procedures, and, practically, instrumentation much more voluminous than the sample being tested (heater plates, insulation, temperature sensors). Remote measurements (infrared images from orbiting spacecraft) can reveal composite properties like thermal inertia, but suffer both from a large footprint (low spatial resolution) and convolution of the thermal properties of a potentially layered medium. In situ measurement techniques (the Phoenix TECP is the only robotic measurement of thermal properties to date) suffer from problems of placement range, placement quality, occupation of robotic resources, and the ability to only measure materials of low mechanical strength. A spacecraft needs the ability to perform a non-contact thermal properties measurement in situ. Essential components include low power consumption, leveraging of existing or highly-developed flight technologies, and mechanical simplicity. This new in situ method, by virtue of its being non-contact, bypasses all of these problems. The use of photons to both excite and measure the thermal response of any surface material to a high resolution (estimated footprint = 10 square centimeters) is a generational leap in physical properties measurements. The proposed method consists of spot-heating the surface of a material with a low (less than 1 W) power laser. This produces a moderate (5-10 K) temperature increase in the material.

Hudson, Troy L.↗
NASA NTRS2002

Computational Nanomechanics of Carbon Nanotubes and Composites

Nanomechanics of individual carbon and boron-nitride nanotubes and their application as reinforcing fibers in polymer composites has been reviewed with interplay of theoretical modeling, computer simulations and experimental observations. The emphasis in this work is on elucidating the multi-length scales of the problems involved, and of different simulation techniques that are needed to address specific characteristics of individual nanotubes and nanotube polymer-matrix interfaces. Classical molecular dynamics simulations are shown to be sufficient to describe the generic behavior such as strength and stiffness modulus but are inadequate to describe elastic limit and nature of plastic buckling at large strength. Quantum molecular dynamics simulations are shown to bring out explicit atomic nature dependent behavior of these nanoscale materials objects that are not accessible either via continuum mechanics based descriptions or through classical molecular dynamics based simulations. As examples, we discus local plastic collapse of carbon nanotubes under axial compression and anisotropic plastic buckling of boron-nitride nanotubes. Dependence of the yield strain on the strain rate is addressed through temperature dependent simulations, a transition-state-theory based model of the strain as a function of strain rate and simulation temperature is presented, and in all cases extensive comparisons are made with experimental observations. Mechanical properties of nanotube-polymer composite materials are simulated with diverse nanotube-polymer interface structures (with van der Waals interaction). The atomistic mechanisms of the interface toughening for optimal load transfer through recycling, high-thermal expansion and diffusion coefficient composite formation above glass transition temperature, and enhancement of Young's modulus on addition of nanotubes to polymer are discussed and compared with experimental observations.

Srivastava, Deepak↗
NASA NTRS1990

Welding arc plasma physics

The problems of weld quality control and weld process dependability continue to be relevant issues in modern metal welding technology. These become especially important for NASA missions which may require the assembly or repair of larger orbiting platforms using automatic welding techniques. To extend present welding technologies for such applications, NASA/MSFC's Materials and Processes Lab is developing physical models of the arc welding process with the goal of providing both a basis for improved design of weld control systems, and a better understanding of how arc welding variables influence final weld properties. The physics of the plasma arc discharge is reasonably well established in terms of transport processes occurring in the arc column itself, although recourse to sophisticated numerical treatments is normally required to obtain quantitative results. Unfortunately the rigor of these numerical computations often obscures the physics of the underlying model due to its inherent complexity. In contrast, this work has focused on a relatively simple physical model of the arc discharge to describe the gross features observed in welding arcs. Emphasis was placed of deriving analytic expressions for the voltage along the arc axis as a function of known or measurable arc parameters. The model retains the essential physics for a straight polarity, diffusion dominated free burning arc in argon, with major simplifications of collisionless sheaths and simple energy balances at the electrodes.

Cain, Bruce L.↗
NASA NTRS2001

Effect of Marangoni Convection Generated by Voids on Segregation During Low-G and 1-G Solidification

Solidification experiments, especially microgravity solidification experiments, are often compromised by the evolution of unwanted voids or bubbles in the melt. Although these voids and/or bubbles are highly undesirable, there is currently no effective means of preventing their formation or of eliminating their adverse effects, particularly during microgravity experiments. Marangoni convection caused by these voids can drastically change the transport processes in the melt. Recent microgravity experiments by Matthiesen (1) Andrews (2) and Fripp (3) are perfect examples of how voids and bubbles can affect the outcome of costly space experiments and significantly increase the level of difficulty in interpreting their results. Formation of bubbles have caused problems in microgravity experiments for a long time. Even in the early Skylab mission an unexpectedly large number of bubbles were detected in the four materials processing experiments reported by Papazian and Wilcox (4). They demonstrated that while during ground-based tests bubbles were seen to detach from the interface easily and float to the top of the melt, in low-gravity tests no detachment from the interface occurred and large voids were grown in the crystal. More recently, the lead-tin-telluride crystal growth experiment of Fripp et al.(3) flown aboard the USMP-3 mission has provided very interesting results. The purpose of the study was to investigate the effect of natural convection on the solidification process by growing the samples at different orientations with respect to the gravitational field. Large pores and voids were found in the three solid crystal samples processed in space. Post-growth characterization of the compositional profiles of the cells indicated considerable levels of mixing even in the sample grown in the hot-on-top stable configuration. The mixing was attributed to thermocapillary convection caused by the voids and bubbles which evolved during growth. Since the thermocapillary convection is orientation-independent, diffusion-controlled growth was not possible in any of the samples, even the top-heated one. These results are consistent with recent studies of thermocapillary convection generated by a bubble on a heated surface undertaken by Kassemi and Rashidnia (5-7) where it is numerically and experimentally shown that the thermocapillary flow generated by a bubble in a model fluid (silicone oil) can drastically modify the temperature field through vigorous mixing of the fluid around it, especially under microgravity conditions.

Kassemi, M.↗
NASA NTRS2001

Flow Range of Centrifugal Compressor Being Extended

General Aviation will benefit from turbine engines that are both fuel-efficient and reliable. Current engines fall short of their potential to achieve these attributes. The reason is compressor surge, which is a flow stability problem that develops when the compressor is subjected to conditions that are outside of its operating range. Compressor surge can occur when fuel flow to the engine is increased, temporarily back pressuring the compressor and pushing it past its stability limit, or when the compressor is subjected to inlet flow-field distortions that may occur during takeoff and landing. Compressor surge can result in the loss of an aircraft. As a result, engine designers include a margin of safety between the operating line of the engine and the stability limit line of the compressor. Unfortunately, the most efficient operating line for the compressor is usually closer to its stability limit line than it is to the line that provides an adequate margin of safety. A wider stable flow range will permit operation along the most efficient operating line of the compressor, improving the specific fuel consumption of the engine and reducing emissions. The NASA Glenn Research Center is working to extend the stable flow range of the compressor. Significant extension has been achieved in axial compressors by injecting air upstream of the compressor blade rows. Recently, the technique was successfully applied to a 4:1 pressure ratio centrifugal compressor by injecting streams of air into the diffuser. Both steady and controlled unsteady injection were used to inject air through the diffuser shroud surface and extend the range. Future work will evaluate the effect of air injection through the diffuser hub surface and diffuser vanes with the goal of maximizing the range extension while minimizing the amount of injected air that is required.

Skoch, Gary J.↗
NASA NTRS2002

Molnets: An Artificial Chemistry Based on Neural Networks

The fundamental problem in the evolution of matter is to understand how structure-function relationships are formed and increase in complexity from the molecular level all the way to a genetic system. We have created a system where structure-function relationships arise naturally and without the need of ad hoc function assignments to given structures. The idea was inspired by neural networks, where the structure of the net embodies specific computational properties. In this system networks interact with other networks to create connections between the inputs of one net and the outputs of another. The newly created net then recomputes its own synaptic weights, based on anti-hebbian rules. As a result some connections may be cut, and multiple nets can emerge as products of a 'reaction'. The idea is to study emergent reaction behaviors, based on simple rules that constitute a pseudophysics of the system. These simple rules are parameterized to produce behaviors that emulate chemical reactions. We find that these simple rules show a gradual increase in the size and complexity of molecules. We have been building a virtual artificial chemistry laboratory for discovering interesting reactions and for testing further ideas on the evolution of primitive molecules. Some of these ideas include the potential effect of membranes and selective diffusion according to molecular size.

Colombano, Silvano↗
NASA NTRS1991

The energy decay in self-preserving isotropic turbulence revisited

The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup - alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state towards which a complete self-preseving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.

Speziale, Charles G.↗
NASA NTRS1992

The energy decay in self-preserving isotropic turbulence revisited

The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup -alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.

Speziale, Charles G.↗
NASA NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required a fine initial mesh. Results indicate that our parallel load balancing strategy will remain viable on large numbers of processors.

Oliker, Leonid↗
NASA NTRS2002

Development of a New Membrane Casting Apparatus for Studying Macrovoid Defects in Low-G

A new membrane-casting apparatus is developed for studying macrovoid defects in polymeric membranes made by the wet- and dry-casting process in low-gravity. Macrovoids are large (10-50 micron), open cavities interspersed among the smaller pores in the substructure under the gelled skin surface layer of the cast membrane. Although their occurrence is considered endemic to the wet- and dry-casting process since they can lead to compaction or skin rupture in the membrane process, recent studies suggest several useful applications such as transdermal and osmotic drug delivery systems, miniature bioreactors, etc. However, lack of knowledge about the macrovoid formation mechanism is an obstacle to further development of applications using them. An on-going debate is the role of the surface-tension-driven solutocapillary convection during macrovoid formation. The rapid growth of macrovoids within 1-5 seconds and the high polymer concentration in and near macrovoids make it difficult to explain the mechanism of macrovoid growth by diffusion alone, which is the widely accepted hypothesis proposed by Reuvers et al. The hypothesis advanced by our research group can explain this rapid growth via a mechanism that involves diffusion from the casting solution in the meta-stable region to the macrovoid enhanced by solutocapillary convection induced by the steep nonsolvent concentration gradient in the vicinity of the macrovoid. Since macrovoid growth is hypothesized to be the interplay of a solutocapillary-induced driving force counteracted by viscous drag and buoyancy, eliminate the latter provides a means for testing this hypothesis. Moreover, free convection mass transfer in the nonsolvent immersion bath used to cause phase-separation in membrane casting complicates developing a model for both the wet-casting process and macrovoid growth. The low-g environment minimizes gravitationally induced free convection thereby permitting a tractable solution to the ternary diffusion equations that characterize membrane formation. NASA's Parabolic Flight Research Aircraft provides a small window of low-g (approximately 25 s) that can be used to study macrovoid development in both wet- and dry-cast membranes if an appropriate casting apparatus is used. This casting apparatus should be able to cast the membrane in both low- and high-g in a manner so that essential one-dimensional mass transfer conditions are achieved to insure lateral uniformity in the membrane. The apparatus used in previous research on membrane casting in low-gravity was operated with the plunger driven mechanism. The spring-loaded plunger pushes the bottom block containing the polymer casting solution well directly under the absorbent chamber located in the upper stationary block. However, membranes made via this casting apparatus often displayed lateral nonuniformities that precluded obtaining quantitative information on the macrovoid growth process. Thus, it was necessary to determine the reason for these structural irregularities observed in the low-g casting apparatus. Both experimental as well as computer simulation studies of the low-g casting apparatus established that the impulsive action of the plunger caused the undesired structural nonuniformities. The simulation results showed that the width-to-depth aspect ratio of the shallow well that contains the casting solution in this apparatus was not an important factor in minimizing this problem. Even for a 40:1 (width : depth) aspect ratio, any convection induced by the horizontal motion of the interface of the casting solution will be damped out within 6.25x10(exp 4) seconds. However, the experimental studies revealed that the impulsive motion of the plunger caused a 'sloshing' of the casting solution that had to be eliminated. Therefore, the plungerdriven mechanism was changed to a cam-driven mechanism that did not cause any impulsive motion of the casting solution. Other refinements to this new membrane-casting apparatus include provision for removing the membranes from the casting wells in a less destructive manner. This was accomplished by using a slit geometry for the casting well that permitted disassembly for removal of the cast membrane. The materials used in the construction of this casting apparatus were chosen to insure wetting at the side walls and to maintain precise control of the thickness of the polymer solution in the casting well. An additional provision in this new casting apparatus is the ability to carry out both wet- as well as dry-casting. As such, this apparatus permitted the first studies of the wet-casting of polymeric membranes in low-g. Both wet- and dry-casting experiments on NASA's KC-135 research aircraft employing this new membrane-casting apparatus are scheduled in July 2002. The morphology of the resulting membranes will be characterized using an environmental scanning electron microscope (ESEM). The results of these low-g studies will be reported later.

Lee, Hanyong↗
NASA NTRS2011

Observation of Hydrological Processes Using Remote Sensing: Volume 2: The Science of Hydrology - Chapter 2.14

Improving water management can make a significant contribution to achieving most of the Millennium Development Goals established by the UN General Assembly in 2000, especially those related to poverty, hunger, and major diseases. The World Summit on Sustainable Development (WSSD) in 2002 recognized this need. Water and sanitation in particular received great attention from the Summit. The Johannesburg Plan of Implementation recommended to improve water resources management and scientific understanding of the water cycle through joint cooperation and research. For this purpose, it is recommended to promote knowledge sharing, provide capacity building, and facilitate the transfer of technology including remote-sensing (RS) and satellite technologies, especially to developing countries and countries with economies in transition, and to support these countries in their efforts to monitor and assess the quantity and quality of water resources, for example, by establishing and/or further developing national monitoring networks and water resources databases and by developing relevant national indicators. The Johannesburg Plan also adopted integrated water resources management as the overarching concept in addressing and solving water-related issues. As a result of the commitments made in the Johannesburg Plan of Implementation, several global and regional initiatives have emerged. Current international initiatives such as the Global Monitoring for Environment and Security (GMES) program of the European Commission and the European Space Agency (ESA), and the Global Earth Observation System of Systems (GEOSS) 10-Year Implementation Plan, have all identified Earth observation (EO) of the water cycle as the key in helping to solve the world s water problems. The availability of spatial information on water quantity and quality will also enable closure of the water budget at river basin and continental scales to the point where effective water management is essential (e.g., as requested by the European Union s Water Framework Directive (WFD), as well as national policies). Geo-information science and EO are vital in achieving a better understanding of the water cycle and better monitoring, analysis, prediction, and management of the world s water resources. The major components of the water cycle of the Earth system and their possible observations are presented. Such observations are essential to understand the global water cycle and its variability, both spatially and temporally, and can only be achieved consistently by means of EOs. Additionally, such observations are essential to advance our understanding of coupling between the terrestrial, atmospheric, and oceanic branches of the water cycle, and how this coupling may influence climate variability and predictability. Water resources management directly interferes with the natural water cycle in the forms of building dams, reservoirs, water transfer systems, and irrigation systems that divert and redistribute part of the water storages and fluxes on land. The water cycle is mainly driven and coupled to the energy cycle in terms of phase changes of water (changes among liquid, water vapor, and solid phases) and transport of water by winds in addition to gravity and diffusion processes. The water-cycle components can be observed with in situ sensors as well as airborne and satellite sensors in terms of radiative quantities. Processing and conversion of these radiative signals are necessary to retrieve the water-cycle components.

Wilder, Peter↗
NASA NTRS1994

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Webb, G. M.↗