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NASA NTRS1990

Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference

Approximations for the power levels at the output of an adaptive array that uses the diagonally loaded sample-matrix inversion (SMI) algorithm are derived. Diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion. This paper examines how the signal-to-interference-plus-noise ratio (SINR) and signal-to-interference ratio (SIR) at the array output vary with the number of samples taken when the input signals are CW. It is shown that positive loading produces more rapid convergence with a reduction in output SIR. Negative loading provides an improved SIR level, but positive loading produces more rapid convergence. Negative loading provides an improved SIR level, but the output power levels are erratic and slow to converge. Simulation results which verify the theoretical procedure are given.

Ganz, Matthew W.↗

NASA NTRS2000

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Barth, Timothy↗

NASA NTRS2002

Development of MLPG and LBIE Methods for Nonlinear Problems of Fracture

The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

Atluri, Satya N.↗

NASA NTRS1989

Adaptive Array for Weak Interfering Signals: Geostationary Satellite Experiments

The performance of an experimental adaptive array is evaluated using signals from an existing geostationary satellite interference environment. To do this, an earth station antenna was built to receive signals from various geostationary satellites. In these experiments the received signals have a frequency of approximately 4 GHz (C-band) and have a bandwidth of over 35 MHz. These signals are downconverted to a 69 MHz intermediate frequency in the experimental system. Using the downconverted signals, the performance of the experimental system for various signal scenarios is evaluated. In this situation, due to the inherent thermal noise, qualitative instead of quantitative test results are presented. It is shown that the experimental system can null up to two interfering signals well below the noise level. However, to avoid the cancellation of the desired signal, the use a steering vector is needed. Various methods to obtain an estimate of the steering vector are proposed.

Steadman, Karl↗

NASA NTRS1996

Three-Dimensional Multiscale MHD Model of Cometary Plasma Environments

First results of a three-dimensional multiscale MHD model of the interaction of an expanding cometary atmosphere with the magnetized solar wind are presented. The model starts with a supersonic and super-Alfvenic solar wind far upstream of the comet (25 Gm upstream of the nucleus) with arbitrary interplanetary magnetic field orientation. The solar wind is continuously mass loaded with cometary ions originating from a 10-km size nucleus. The effects of photoionization, electron impact ionization, recombination, and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our new multiscale upwind scalar conservation laws-type numerical technique (MUSCL). We have named this the multiscale adaptive upwind scheme for MHD (MAUS-MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. The main findings are the following: (1) Mass loading decelerates the solar wind flow upstream of the weak cometary shock wave (M approximately equals 2, M(sub A) approximately equals 2), which forms at a subsolar standoff distance of about 0.35 Gm. (2) A cometary plasma cavity is formed at around 3 x 10(exp 3) km from the nucleus. Inside this cavity the plasma expands outward due to the frictional interaction between ions and neutrals. On the nightside this plasma cavity considerably narrows and a relatively fast and dense cometary plasma beam is ejected into the tail. (3) Inside the plasma cavity a teardrop-shaped inner shock is formed, which is terminated by a Mach disk on the nightside. Only the region inside the inner shock is the 'true' diamagnetic cavity. (4) The model predicts four distinct current systems in the inner coma: the density peak current, the cavity boundary current, the inner shock current, and finally the cross-tail current. (5) The calculated plasma parameters (magnetic field, plasma density, speed, and temperature) are in very good agreement with published Giotto observations.

Gombosi, Tamas I.↗

NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗

NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

Vijayaraghavan, D.↗

NASA NTRS2001

Intrinsic near-24-h pacemaker period determines limits of circadian entrainment to a weak synchronizer in humans

Endogenous circadian clocks are robust regulators of physiology and behavior. Synchronization or entrainment of biological clocks to environmental time is adaptive and important for physiological homeostasis and for the proper timing of species-specific behaviors. We studied subjects in the laboratory for up to 55 days each to determine the ability to entrain the human clock to a weak circadian synchronizing stimulus [scheduled activity-rest cycle in very dim (approximately 1.5 lux in the angle of gaze) light-dark cycle] at three approximately 24-h periods: 23.5, 24.0, and 24.6 h. These studies allowed us to test two competing hypotheses as to whether the period of the human circadian pacemaker is near to or much longer than 24 h. We report here that imposition of a sleep-wake schedule with exposure to the equivalent of candle light during wakefulness and darkness during sleep is usually sufficient to maintain circadian entrainment to the 24-h day but not to a 23.5- or 24.6-h day. Our results demonstrate functionally that, in normally entrained sighted adults, the average intrinsic circadian period of the human biological clock is very close to 24 h. Either exposure to very dim light and/or the scheduled sleep-wake cycle itself can entrain this near-24-h intrinsic period of the human circadian pacemaker to the 24-h day.

NASA Discipline Regulatory Physiology↗

NASA NTRS1977

A numerical investigation of the finite element method in compressible primitive variable Navier-Stokes flow

The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.

Cook, C. H.↗

NASA NTRS2006

Modeling Gravitational Radiation Waveforms from Black Hole Mergers

Gravitational radiation from merging binary black hole systems is anticipated as a key source for gravitational wave observations. Ground-based instruments, such as the Laser Interferometer Gravitational-wave Observatory (LIGO) may observe mergers of stellar-scale black holes, while the space-based Laser Interferometer Space Antenna (LISA) observatory will be sensitive to mergers of massive galactic-center black holes over a broad range of mass scales. These cataclysmic events may emit an enormous amount of energy in a brief time. Gravitational waves from comparable mass mergers carry away a few percent of the system's mass-energy in just a few wave cycles, with peak gravitational wave luminosities on the order of 10^23 L_Sun. Optimal analysis and interpretation of merger observation data will depend on developing a detailed understanding, based on general relativistic modeling, of the radiation waveforms. We discuss recent progress in modeling radiation from equal mass mergers using numerical simulations of Einstein's gravitational field equations, known as numerical relativity. Our simulations utilize Adaptive Mesh Refinement (AMR) to allow high-resolution near the black holes while simultaneously keeping the outer boundary of the computational domain far from the black holes, and making it possible to read out gravitational radiation waveforms in the weak-field wave zone. We discuss the results from simulations beginning with the black holes orbiting near the system's innermost stable orbit, comparing the recent simulations with earlier "Lazarus" waveform estimates based on an approximate hybrid numerical/perturbative technique.

Baker, J. G.↗

NASA NTRS1997

Current Collection in a Magnetic Field

It is found that the upper-bound limit for current collection in the case of strong magnetic field from the current is close to that given by the Parker-Murphy formula. This conclusion is consistent with the results obtained in laboratory experiments. This limit weakly depends on the shape of the wire. The adiabatic limit in this case will be easily surpassed due to strong magnetic field gradients near the separatrix. The calculations can be done using the kinetic equation in the drift approximation. Analytical results are obtained for the region where the Earth's magnetic field is dominant. The current collection can be calculated (neglecting scattering) using a particle simulation code. Dr. Singh has agreed to collaborate, allowing the use of his particle code. The code can be adapted for the case when the current magnetic field is strong. The needed dm for these modifications is 3-4 months. The analytical description and essential part of the program is prepared for the calculation of the current in the region where the adiabatic description can be used. This was completed with the collaboration of Drs. Khazanov and Liemohn. A scheme of measuring the end body position is also proposed. The scheme was discussed in the laboratory (with Dr. Stone) and it was concluded that it can be proposed for engineering analysis.

Krivorutsky, E. N.↗

NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗

NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

This paper presents a new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system. In particular, our generalized approximate reasoning-based intelligent control (GARIC) architecture (1) learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward neural network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto et al. (1983) to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗

NASA NTRS2019

Spatially Resolved Outflows in a Seyfert Galaxy at z=2.39

We present the first spatially resolved analysis of rest-frame optical and UV (UltraViolet) imaging and spectroscopy for a lensed galaxy at z equals 2.39 hosting a Seyfert active galactic nucleus (AGN). Proximity to a natural guide star has enabled observations with high signal-to-noise ratio using Very Large Telescope SINFONI (Spectrograph for INtegral Field Observations in the Near Infrared) plus adaptive optics (AO) of rest-frame optical diagnostic emission lines, which exhibit an underlying broad component with full width at half maximum approximately 700 kilometers per second in both the Balmer and forbidden lines. Measured line ratios place the outflow robustly in the region of the ionization diagnostic diagrams associated with AGNs. This unique opportunity - combining gravitational lensing, AO guiding, redshift, and AGN activity - allows for a magnified view of two main tracers of the physical conditions and structure of the interstellar medium in a star-forming galaxy hosting a weak AGN at Cosmic Noon. By analyzing the spatial extent and morphology of the Lyman alpha spectral line and dust-corrected Hydrogen spectral line emission, disentangling the effects of star formation and AGN ionization on each tracer, and comparing the AGN-induced mass outflow rate to the host star formation rate, we find that the AGN does not significantly impact the star formation within its host galaxy.

Fischer, Travis C.↗

NASA NTRS1989

Analysis of Modified SMI Method for Adaptive Array Weight Control

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Dilsavor, Ronald Louis↗

NASA NTRS2001

Laboratory Experimentation Model of the 270 Degree Electron Tophat Analyzer

One of the most important space plasma measurements is that of a well-resolved low-energy (approximately 1 eV to 1 keV) electron spectrum. This range includes the regime where photoelectron and Auger processes are important as well as the very low energy range (down to 1 eV) where electron distributions of temperature 11,000 K are measurable. Knowledge of the structure (approx. eV scale) of the photoelectron spectrum can provide information on the composition of a planetary or cometary atmosphere. As evidence, scientists developing the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) Electron Spectrometer (ELS) flying on the European Space Agency (ESA) Mars Express Mission have adapted their electron instrument to increase energy resolution in the photoelectron energy region as a means of remotely sensing the Martian atmosphere; the idea being that the Martian magnetic field is so weak that electron interaction between the source and point of detection is nonexistent; the measured electrons are therefore reflective of the processes occurring in the Martian atmosphere.

Frahm, R. A.↗

NASA NTRS2005

Diagnostics Adapted for Heat-Treating Furnace Environment

Diagnostics developed for the in situ monitoring of rocket combustion environments were adapted for use in heat-treating furnaces. Simultaneous, in situ monitoring of the carbon monoxide, carbon dioxide, methane, water, and hydrogen concentrations in the endothermic gas of a heat-treating furnace were demonstrated under a Space Act Agreement between the NASA Lewis Research Center, the Heat Treating Network, and Akron Steel Treating Company. This endothermic gas, or "endogas," is produced in a catalytic process, where natural gas is "cracked" in the presence of air. Variations in the composition of the natural gas supplied lead to variations in the composition of the endothermic gas. These variations could lead to an unacceptable quality of steel products that are hardened through the carborization process that uses this gas. Conventional methods of monitoring the endogas include measuring the dew point of the gas and the oxygen concentration. From these data, the carbon monoxide content of the gas can be calculated. This carbon monoxide concentration creates the carbon potential needed for carburization. Several weak links are present in this approach. The oxygen monitor deteriorates over time, and the measurement might be inaccurate by 50 percent. Also, the chemistry equations, which are based on several assumptions, such as secondary species concentrations, provide only an approximate estimate of the carbon monoxide concentration. To address these weaknesses, we investigated a new method based on ordinary Raman spectroscopy, in which the carbon monoxide concentration is measured directly and in situ. This method measures the laser light scattered from the molecules. Each species interacts with the light and scatters the light at a different frequency. Spectral monitoring of the scattered light intensity at each molecular frequency of interest provides the species concentrations. One advantage over the conventional method is that several species can be monitored simultaneously. A second advantage is that the measurement is direct; there is no need to make assumptions, to filter the gas, or to calibrate the instrument. An instrument was designed consisting of a laser and a detection system within an enclosure, connected to an optical probe by fibers. For determining carbon monoxide concentration, the probe is mounted on the endothermic gas line, close to the generator. Optical fibers with a length of 150 ft have been used to transmit laser light from the instrument to the probe. There, the light is focused into the gas, and the scattered light is collected and transmitted back to the instrument where it is analyzed with a photomultiplier and lock-in amplifier. Laboratory tests have shown that with the current system the concentration of carbon monoxide, water, nitrogen, oxygen, and hydrogen in the air can be monitored with an accuracy of 1 percent. The concentration of carbon dioxide in the air can be monitored with an accuracy of 0.5 percent, and the concentration of methane with an accuracy of 0.2 percent. This instrument was taken to the Akron Steel Treating Plant, where field tests are in progress to verify the system capabilities. Planned developments are improving the accuracy, monitoring multiple locations, and reducing instrument size and cost.

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