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NASA NTRS2003

Long-Range Solar Activity Predictions: A Reprieve from Cycle #24's Activity

We discuss the field of long-range solar activity predictions and provide an outlook into future solar activity. Orbital predictions for satellites in Low Earth Orbit (LEO) depend strongly on exospheric densities. Solar activity forecasting is important in this regard, as the solar ultra-violet (UV) and extreme ultraviolet (EUV) radiations inflate the upper atmospheric layers of the Earth, forming the exosphere in which satellites orbit. Rather than concentrate on statistical, or numerical methods, we utilize a class of techniques (precursor methods) which is founded in physical theory. The geomagnetic precursor method was originally developed by the Russian geophysicist, Ohl, using geomagnetic observations to predict future solar activity. It was later extended to solar observations, and placed within the context of physical theory, namely the workings of the Sun s Babcock dynamo. We later expanded the prediction methods with a SOlar Dynamo Amplitude (SODA) index. The SODA index is a measure of the buried solar magnetic flux, using toroidal and poloidal field components. It allows one to predict future solar activity during any phase of the solar cycle, whereas previously, one was restricted to making predictions only at solar minimum. We are encouraged that solar cycle #23's behavior fell closely along our predicted curve, peaking near 192, comparable to the Schatten, Myers and Sofia (1996) forecast of 182+/-30. Cycle #23 extends from 1996 through approximately 2006 or 2007, with cycle #24 starting thereafter. We discuss the current forecast of solar cycle #24, (2006-2016), with a predicted smoothed F10.7 radio flux of 142+/-28 (1-sigma errors). This, we believe, represents a reprieve, in terms of reduced fuel costs, etc., for new satellites to be launched or old satellites (requiring reboosting) which have been placed in LEO. By monitoring the Sun s most deeply rooted magnetic fields; long-range solar activity can be predicted. Although a degree of uncertainty in the long-range predictions remains, requiring future monitoring, we do not expect the next cycle's + 2-sigma value will rise significantly above solar cycle #23's activity level.

Richon, K.↗

NASA NTRS1994

Orthostatic hypotension in patients, bed rest subjects, and astronauts

Orthostatic hypotension after even short space flights has affected a significant number of astronauts. Given the need for astronauts to function at a high level of efficiency during and after their return from space, the application of pharmacologic and other treatments is strongly indicated. This report addresses the clinical problem of orthostatic hypotension and its treatments to ascertain whether pharmacologic or physiologic treatment may be useful in the prevention of orthostatic hypotension associated with space flight. Treatment of orthostatic hypotension in patients now includes increasing intravascular volume with high sodium intake and mineralocorticoids, or increasing vascular resistance through the use of drugs to stimulate alpha or block beta vascular receptors. Earlier treatment used oral sympathomimetic ephedrine hydrochloride alone or with "head-up" bed rest. Then long-acting adrenocortical steroid desoxycorticosterone preparations with high-salt diets were used to expand volume. Fludrocortisone was shown to prevent the orthostatic drop in blood pressure. The combination of the sympathomimetic amine hydroxyamphetamine and a monoamine oxidase inhibitor tranylcypromine has been used, as has indomethacin alone. Davies et al. used mineralocorticoids at low doses concomitantly with alpha-agonists to increase vasoconstrictor action. Schirger et al used tranylcypromine and methylphenidate with or without a Jobst elastic leotard garment or the alpha-adrenergic agonist midodrine (which stimulates both arterial and venous systems without direct central nervous system or cardiac effects). Vernikos et al established that the combination of fludrocortisone, dextroamphetamine, and atropine exhibited a beneficial effect on orthostatic hypotension induced by 7-day 6 degrees head-down bed rest (a model used to simulate the weightlessness of space flight). Thus, there are numerous drugs that, in combination with mechanical techniques, including lower body negative pressure to elevate transmural pressure, could be studied to treat orthostatic hypotension after space flight.

Review↗

NASA NTRS2008

Efficient Modal Basis Selection Criteria for Reduced-Order Nonlinear Simulation

A modal basis selection technique for a reduced-order nonlinear numerical simulation with application to two-dimensional structures is presented as a two-step procedure. A system identification analysis is first performed using proper orthogonal decomposition. Using these results, a set of load-invariant bases consisting of the normal modes is next selected. Two criteria for making the basis selection are offered; one using the modal assurance criterion and the other using the modal expansion theorem. The quality of the subsequent reduced-order analyses are examined through comparison with computationally intensive finite element nonlinear simulations in physical degrees-of-freedom. A clamped flat isotropic plate under a random acoustic loading is considered to demonstrate the procedure. It is found that the subject procedure enables formation of an accurate and computationally efficient reduced-order system applicable to a broad range of loading conditions.

Przekop, Adam↗

NASA NTRS2020

Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens

For free-space optical communication systems, numerical wave optics simulations provide a useful technique for modeling turbulence-induced beam degradation when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such applications we use a split-step method modeling the turbulence as a series of random phase screens using the Hufnagel-Valley turbulence profile. We employ a space-to-ground case study to examine the irradiance and phase statistics for uniformly and non-uniformly located screens and find better agreement with theory using a non-uniform discretization minimizing the contribution of each screen to the total scintillation. In this poster, we summarize the method and the results of the case study including a comparison to layered models used in astronomical imaging applications.

Chahine, Yousef K.↗

NASA NTRS2024

Accelerating Continuous Variable Coherent Ising Machines Via Momentum

The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary differential equations that have been proven to be useful for the optimization of continuous variables nonconvex quadratic optimization problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage optimization via optical pulses whose amplitudes are determined by the negative gradient of the objective; however, standard gradient descent is known to be trapped by local minima and hampered by poor problem conditioning. In this work, we propose to modify the CV-CIM dynamics using more sophisticated pulse injections based on tried-and-true optimization techniques such as momentum and Adam. Through numerical experiments, we show that the momentum and Adam updates can significantly speed up the CV-CIM’s convergence and improve sample diversity over the original CV-CIM dynamics. We also find that the Adam-CV-CIM’s performance is more stable as a function of feedback strength, especially on poorly conditioned instances, resulting in an algorithm that is more robust, reliable, and easily tunable. More broadly, we identify the CIM dynamical framework as a fertile opportunity for exploring the intersection of classical optimization and modern analog computing.

Ising Model↗

NASA NTRS1987

Parallel pivoting combined with parallel reduction

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Alaghband, Gita↗

DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

A generalized vortex lattice method for subsonic and supersonic flow applications

If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.

Miranda, L. R.↗

NASA NTRS1993

High-order cyclo-difference techniques: An alternative to finite differences

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

Carpenter, Mark H.↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

NASA NTRS2002

High Resolution X-ray Imaging

Cash, Webster↗

NASA NTRS2002

High Resolution X-ray Imaging

NAG5-5020 covered a period of 7.5 years during which a great deal of progress was made in x-ray optical techniques under this grant. We survived peer review numerous times during the effort to keep the grant going. In 1994, when the grant started we were actively pursuing the application of spherical mirrors to improving x-ray telescopes. We had found that x-ray detectors were becoming rapidly more sophisticated and affordable, but that x-ray telescopes were only being improved through the intense application of money within the AXAF program. Clearly new techniques for the future were needed. We were successful in developing and testing at the HELSTF facility in New Mexico a four reflection coma-corrected telescope made from spheres. We were able to demonstrate 0.3 arcsecond resolution, almost to the diffraction limit of the system. The community as a whole was, at that time, not particularly interested in looking past AXAF (Chandra) and the effort needed to evolve. Since we had reached the diffraction limit using non-Wolter optics we then decided to see if we could build an x-ray interferometer in the laboratory. In the lab the potential for improved resolution was substantial. If synthetic aperture telescopes could be built in space, then orders of magnitude improvement would become feasible. In 1998 NASA, under the direction of Dr Nick White of Goddard, started a study to assess the potential and feasibility of x-ray interferometry in space. My work became of central interest to the committee because it indicated that such was possible. In early 1999 we had the breakthrough that allowed us build a practical interferometer. By using flats and hooking up with the Marshall Space Flight Center facilities we were able to demonstrate fringes at 1.25keV on a one millimeter baseline. This actual laboratory demonstration provided the solid proof of concept that NASA needed. As the year progressed the future of x-ray astronomy jelled around the Maxim program. Maxim is a set of two major x-ray astronomy missions based on the concepts I developed and demonstrated under this SR&T grant. The first Maxim is to image the sky at 100 micro-arcsecond resolution. That is one thousand times higher resolution than Hubble. The full Maxim has the ultimate goal of imaging the event horizon of a black hole in an active galactic nucleus (ALAN). This will require 0.1 micro-arcsecond resolution - one million times higher than Hubble! Nonetheless, using the techniques developed under this grant, it has become possible. Maxim Pathfinder is now in the NASA planning for a new start in approximately 20 10. The full Maxim is carried as a vision mission for the post 2015 timeframe. Finally, this grant is the evolved version of the SR&T grant we carried during the 1980s and up to 1994. At that point in time this grant was also working on x-ray optics, but concentrating on x-ray spectroscopy. The techniques developed by 1990 were not chosen for use on Chandra or XMM-Newton because they were too new. During the last year, however, the Constellation-X mission recognized the need for better spectroscopy techniques and tapped our expertise. We were able to support the initial work on Con-X through this program. It now appears that the off-plane mount will be used in Con-X, increasing performance and decreasing cost and risk.

Cash, Webster↗

NASA NTRS2005

Machine Vision for High Precision Volume Measurement Applied to Levitated Containerless Materials Processing

By combining the best practices in optical dilatometry with new numerical methods, a high-speed and high precision technique has been developed to measure volume of levitated, containerlessly processed samples with sub- pixel resolution. Containerless processing provides the ability to study highly reactive materials without the possibility of contamination affecting thermo-physical properties. Levitation is a common technique used to isolate a sample as it is being processed. Noncontact optical measurement of thermo-ophysical properties is very important as traditional measuring methods cannot be used. Modern, digitally recorded images require advanced numerical routines to recover the sub-pixel locations of sample edges and, in turn produce high precision measurements.

Bradshaw, R. C.↗

NASA NTRS1992

Assimilation of ERBE data with a nonlinear programming technique to improve cloud-cover diagnosis

A method is developed to assimilate satellite data for the purpose of improving the diagnosis of fractional cloud cover within a numerical weather prediction model. The method makes use of a nonlinear programming technique to find a set of parameters for the cloud diagnosis that minimizes the difference between the observed and model-produced outgoing longwave radiation (OLR). The algorithm and theoretical basis of the method are presented. The method has been applied in two forecast experiments using a numerical weather prediction model. The results from a winter case demonstrate that the root-mean-square (rms) difference between the observed and forecasted OLR can be reduced by 50 percent when the optimized cloud diagnosis is used, with the remaining rms difference within the background noise.

Wu, Xiangqian↗

NASA NTRS1991

Effects of measurement errors on microwave antenna holography

The effects of measurement errors appearing during the implementation of the microwave holographic technique are investigated in detail, and many representative results are presented based on computer simulations. The numerical results are tailored for cases applicable to the utilization of the holographic technique for the NASA's Deep Space Network antennas, although the methodology of analysis is applicable to any antenna. Many system measurement topics are presented and summarized.

Rochblatt, David J.↗

NASA NTRS1986

High efficiency crystalline silicon solar cells

A review of the entire research program since its inception ten years ago is given. The initial effort focused on the effects of impurities on the efficiency of silicon solar cells to provide figures of maximum allowable impurity density for efficiencies up to about 16 to 17%. Highly accurate experimental techniques were extended to characterize the recombination properties of the residual imputities in the silicon solar cell. A numerical simulator of the solar cell was also developed, using the Circuit Technique for Semiconductor Analysis. Recent effort focused on the delineation of the material and device parameters which limited the silicon efficiency to below 20% and on an investigation of cell designs to break the 20% barrier. Designs of the cell device structure and geometry can further reduce recombination losses as well as the sensitivity and criticalness of the fabrication technology required to exceed 20%. Further research is needed on the fundamental characterization of the carrier recombination properties at the chemical impurity and physical defect centers. It is shown that only single crystalline silicon cell technology can be successful in attaining efficiencies greater than 20%.

Sah, C. Tang↗

NASA NTRS1993

Next generation initiation techniques

Four-dimensional data assimilation strategies can generally be classified as either current or next generation, depending upon whether they are used operationally or not. Current-generation data-assimilation techniques are those that are presently used routinely in operational-forecasting or research applications. They can be classified into the following categories: intermittent assimilation, Newtonian relaxation, and physical initialization. It should be noted that these techniques are the subject of continued research, and their improvement will parallel the development of next generation techniques described by the other speakers. Next generation assimilation techniques are those that are under development but are not yet used operationally. Most of these procedures are derived from control theory or variational methods and primarily represent continuous assimilation approaches, in which the data and model dynamics are 'fitted' to each other in an optimal way. Another 'next generation' category is the initialization of convective-scale models. Intermittent assimilation systems use an objective analysis to combine all observations within a time window that is centered on the analysis time. Continuous first-generation assimilation systems are usually based on the Newtonian-relaxation or 'nudging' techniques. Physical initialization procedures generally involve the use of standard or nonstandard data to force some physical process in the model during an assimilation period. Under the topic of next-generation assimilation techniques, variational approaches are currently being actively developed. Variational approaches seek to minimize a cost or penalty function which measures a model's fit to observations, background fields and other imposed constraints. Alternatively, the Kalman filter technique, which is also under investigation as a data assimilation procedure for numerical weather prediction, can yield acceptable initial conditions for mesoscale models. The third kind of next-generation technique involves strategies to initialize convective scale (non-hydrostatic) models.

Warner, Tom↗

NASA NTRS2000

Effect of Elevated Pressure on the Heat Transfer and Power Requirements During Bridgman Growth of PMN-PT Crystals

Performance of the furnace during Bridgman growth of the lead magnesium niobate-lead titanate crystal (PMN-PT) is analyzed. PMN-PT is electrostrictive ceramic that has near ideal strain-voltage function. Furthermore piezoelectric (2000 to 2300 pC/N) and coupling (92 to 95%) constants are exceptionally good. Due to these properties PMN-PT has wide range of applications - from sonars to transducers in a high precision optical systems. In this research first attempt to crystallize PMN-PT in a Mellen type vertical Bridgman furnace was not successful, as melting temperature of precursor materials was not achieved. At this point choice was between building a new more powerful facility or finding ways to enhance performance of the existing furnace. Besides adjusting power supply to the individual heating elements, redesigning ampoule holding cartridge and improving furnace insulation one more radical improvement was proposed. The entire furnace was placed into the high pressure chamber. Further experiments confirmed that temperature inside the furnace was increased sufficiently to melt precursor materials to obtain PMN-PT. Numerical modeling is undertaken to find limitations of this technique and to predict temperature distribution inside the ampoule. It is of interest also to account for main factors contributing to a higher temperatures achieved in the furnace under the higher pressure (up to 10 atm.). Numerical model of the furnace is based on general purpose finite - element code FIDAP and on previous efforts to model Bridgman type furnace with multiply heaters. In order to account for all heat transfer mechanism involved - conduction, convection and radiation - different parts of the furnace are modeled in accordance with expected dominant mode of heat transfer - conduction in the solid parts, conduction and radiation in the ampoule, gas convection and conduction in the furnace openings complemented with wall-to-wall radiation. Because of these complicating factors, dimensional rather than non-dimensional modeling is performed using steady-state 2-D and 3-D models. Particular attention is paid to the modeling of radiation in a semitransparent material of ampoule 7 sapphire. The radiation model is validated by solving realistic test problem - conduction and radiation heat transfer in the fused quartz. Results are in agreement with both experimental and analytical data.

Bune, Andris↗