Extreme copositive quadratic forms.
Extreme points of copositive quadratic forms constituting closed convex cone in Euclidean space
MATHEMATICS↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The production of drops by the bursting of a bubble at an air liquid interface
The fundamental mechanism arising during the bursting of a bubble at an air-liquid interface is described. A single bubble was followed from an arbitrary depth in the liquid, up to the creation and motion of the film and jet drops. Several phenomena were involved and their relative order of magnitude was compared in order to point out the dimensionless parameters which govern each step of the motion. High-speed cinematography is employed. The characteristic bubble radius which separates the creation of jet drops from cap bursting without jet drops is expressed mathematically. The corresponding numerical value for water is 3 mm and agrees with experimental observations.
Darrozes, J. S.↗
Non-contacting gas lubricated face seals for high p x v-values
The authors discuss recently developed mathematical fundamentals concerning the calculation of noncontacting gas lubricated face seals. They carried out extensive experiments using three different designs at pressures up to 10 MPa and sliding velocities up to 110 m/s. A comparison between the experimental results and the calculations indicates that a stable operation without wear can be ensured in all cases, provided that the materials and geometrical parameters of the seal have been properly chosen.
Glienicke, J.↗
Boolean difference equations. I - Formulation and dynamic behavior
In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. It is suggested that delay-difference equations for Boolean-valued variables are an appropriate mathematical framework for such situations: the feedback thresholds result in the discrete, on-off character of the variables, and the interaction time scales of the feedbacks are expressed as delays. The initial-value problem for Boolean delay equations (B-Delta-Es) is formulated, and shown to have unique solutions for all times. Examples of periodic and aperiodic solutions are given. Aperiodic solutions have increasing complexity which depends on time t roughly as t to the l-1 power, l being the number of delays. Stability of solutions is defined, and some examples of stability analysis are given; additional stability questions are raised. The present formulation of (B-Delta-Es) is compared with related work and generalizations are suggested.
Dee, D.↗
QCUncertainty/sigma
Sigma is a header-only C++ library for uncertainty propagation throughout mathematical operations on floating point values.
Waldrop, Jonathan M.↗
Lubricant pressure rippling in dynamic Hertzian contacts induced by surface roughness
A numerical analysis of the pressure distribution of a lubricant in contact with a rough surface was conducted. The magnitude of the pressures was determined by their root mean square value for the contact of two dimensional cylinders. The pressure was found to vary in the following manner: (1) the location in the contact, (2) the spectrum or frequency content of the surface roughness, (3) the mean plateau film thickness, and (4) the root mean square value of the surface roughness. Mathematical models are developed to show the relationships of the parameters.
Tallian, T. E.↗
Tests of Low-Concentration-Ratio Photovoltaic Elements
Report describes performance measurements on elements of low-concentrationratio solar arrays (LCRSA's) employing silicon and gallium arsenide photovoltaic cells. Measurements intended to verify predictions of performance based on mathematical models. Measured and predicted values found to agree closely for both normal and off-normal pointing of array toward Sun.
Mills, M. W.↗
Nonlinear problems in flight dynamics involving aerodynamic bifurcations
Aerodynamic bifurcation is defined as the replacement of an unstable equilibrium flow by a new stable equilibrium flow at a critical value of a parameter. A mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations. Important bifurcations such as, the onset of large-scale vortex-shedding are defined. The amended mathematical model is capable of incorporating various forms of aerodynamic responses, including those associated with dynamic stall of airfoils.
Tobak, M.↗
Nonlinear problems in flight dynamics involving aerodynamic bifurcations
Aerodynamic bifurcation is defined as the replacement of an unstable equilibrium flow by a new stable equilibrium flow at a critical value of a parameter. A mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations. Important bifurcations such as, the onset of large-scale vortex shedding are defined. The amended mathematical model is capable of incorporating various forms of aerodynamic responses, including those associated with dynamic stall of airfoils.
Murray Tobak↗
Global Reference Atmosphere Model-1988
Four-D Global Reference Atmosphere computer program (GRAM) developed from empirical mathematical model of atmosphere generating values for pressure, density, temperature, and winds from surface level to orbital altitudes. Generates altitude profiles of parameters of atmosphere along any simulated trajectory through atmosphere. Developed from design applications in Space Shuttle program. Other potential applications include studies of global circulation and diffusion and generation of profiles for comparison with results of other atmospheric-measurement techniques such as satellite-measured temperature profiles and wind profiles from infrasonic measurements. Written in STANDARD FORTRAN 77.
Johnson, D. L.↗
Microgravity nucleation and particle coagulation experiments support
Modifications to the nucleation apparatus suggested by our first microgravity flight campaign are complete. These included a complete 'repackaging' of the equipment into three racks along with an improved vapor spout shutter mechanism and additional thermocouples for gas temperature measurements. The 'repackaged' apparatus was used in two KC-135 campaigns: one during the week of June 3, 1991 consisting of two flights with Mg and two with Zn, and another series consisting of three flights with Zn during the week of September 23, 1991. Our effort then was focused on the analysis of these data, including further development of the mathematical models to generate the values of temperature and supersaturation at the observed points of nucleation. The efforts to apply Hale's Scaled Nucleation Theory to our experimental data have met with only limited success, most likely due to still inadequate temperature field determination. Work on the development of a preliminary particle collector system designed to capture particles from the region of nucleation and condensation, as well as from other parts of the chamber, are discussed.
Lilleleht, L. U.↗
GRCop-84 Developed for Rocket Engines
GRCop-84 (Cu-8 at.% Cr-4 at.% Nb) was developed at the NASA Glenn Research Center for use in regeneratively cooled rocket engines. This alloy possesses an excellent combination of conductivity, thermal expansion, strength, creep resistance, ductility, and low-cycle fatigue (LCF) life. In comparison to the currently used alloy, NARloy-Z (Cu-3 wt % Ag-0.5 wt % Zr), GRCop-84's significantly better properties give it the potential for significant gains in engine performance and reliability. For GRCop-84 to be safely used in a rocket engine, it is critical to develop a detailed data base of the important thermophysical and mechanical properties. Work has focused on five major properties: thermal conductivity, thermal expansion, tensile strength, creep resistance, and LCF life. The analysis went beyond simply measuring the data and reporting averages. A detailed statistical analysis was conducted that allowed regression of the data over the entire temperature range tested and establishment of design minimums. The design values were expressed as simple mathematical formulas that are highly amenable to use in computer codes such as in finite element analysis and related computer modeling work.
Ellis, David L.↗
Active State Model for Autonomous Systems
The concept of the active state model (ASM) is an architecture for the development of advanced integrated fault-detection-and-isolation (FDI) systems for robotic land vehicles, pilotless aircraft, exploratory spacecraft, or other complex engineering systems that will be capable of autonomous operation. An FDI system based on the ASM concept would not only provide traditional diagnostic capabilities, but also integrate the FDI system under a unified framework and provide mechanism for sharing of information between FDI subsystems to fully assess the overall health of the system. The ASM concept begins with definitions borrowed from psychology, wherein a system is regarded as active when it possesses self-image, self-awareness, and an ability to make decisions itself, such that it is able to perform purposeful motions and other transitions with some degree of autonomy from the environment. For an engineering system, self-image would manifest itself as the ability to determine nominal values of sensor data by use of a mathematical model of itself, and selfawareness would manifest itself as the ability to relate sensor data to their nominal values. The ASM for such a system may start with the closed-loop control dynamics that describe the evolution of state variables. As soon as this model was supplemented with nominal values of sensor data, it would possess self-image. The ability to process the current sensor data and compare them with the nominal values would represent self-awareness. On the basis of self-image and self-awareness, the ASM provides the capability for self-identification, detection of abnormalities, and self-diagnosis.
Park, Han↗
A Polar Scaling Technique for the Regularization of Strongly Singular and Strongly Near-Singular Helmholtz Surface Integrals Evaluated Over 2-D Domains
The numerical integration of expressions containing strong singularities or strong near-singularities has long been a challenging problem in the electromagnetics community. Much attention has been paid to this problem, as strong $1/R^{{2}}$ singularities routinely appear when implementing electromagnetic simulation techniques like the method of moments (MoM). To date, several techniques, from singularity extraction to singularity cancellation (SC), have been employed to deal with problems that require the evaluation of 2-D strongly singular integrals. However, no single technique has been proposed that can deal with both strong singularities and strong near-singularities in a fully numerical manner for arbitrary 2-D domains. Moreover, it has been claimed that the Helmholtz-type strongly singular integral found in the MoM is convergent in a principal value sense, but this convergence value has yet to be proven mathematically. In this work, we will conduct the convergence proof and introduce a “polar scaling” change of variables method that may be used to evaluate Helmholtz integrals with both strong and weak singularities/near-singularities. The technique is fully numerical and can in principle be applied to any planar or curved polygon and any nonsingular basis function. We will also provide numerical results showing useful convergence behavior for integrals involving both exact and near-singularities.
47 OTHER INSTRUMENTATION↗
Dynamic visual acuity using "far" and "near" targets
CONCLUSIONS: DVA may be useful for assessing the functional consequences of an impaired gaze stabilization mechanism or for testing the effectiveness of a rehabilitation paradigm. Because target distance influences the relative contributions of canal and otolith inputs, the ability to measure DVA at near and far viewing distances may also lead to tests that will independently assess canal and otolith function. OBJECTIVE: To present and test a methodology that uses dynamic visual acuity (DVA) to assess the efficacy of compensatory gaze mechanisms during a functionally relevant activity that differentially measures canal and otolith function. MATERIAL AND METHODS: The effect of treadmill walking at a velocity of 1.79 m/s on subjects' visual acuity was assessed at each of two viewing distances. A custom-written threshold determination program was used to display Landolt C optotypes on a laptop computer screen during a "far" (4 m) target condition and on a micro-display for a "near" (50 cm) target condition. The walking acuity scores for each target distance were normalized by subtracting a corresponding acuity measure obtained while standing still on the treadmill belt. RESULTS: As predicted by subjective reports of relative target motion, the decrease in visual acuity was significantly greater (p < 0.00001) for the near compared to the far condition.
Pattern Recognition, Visual/physiology↗
A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands
Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.
Lei, Ning↗
Development and Applications of a Stage Stacking Procedure
The preliminary design of multistage axial compressors in gas turbine engines is typically accomplished with mean-line methods. These methods, which rely on empirical correlations, estimate compressor performance well near the design point, but may become less reliable off-design. For land-based applications of gas turbine engines, off-design performance estimates are becoming increasingly important, as turbine plant operators desire peaking or load-following capabilities and hot-day operability. The current work develops a one-dimensional stage stacking procedure, including a newly defined blockage term, which is used to estimate the off-design performance and operability range of a 13-stage axial compressor used in a power generating gas turbine engine. The new blockage term is defined to give mathematical closure on static pressure, and values of blockage are shown to collapse to curves as a function of stage inlet flow coefficient and corrected shaft speed. In addition to these blockage curves, the stage stacking procedure utilizes stage characteristics of ideal work coefficient and adiabatic efficiency. These curves are constructed using flow information extracted from computational fluid dynamics (CFD) simulations of groups of stages within the compressor. Performance estimates resulting from the stage stacking procedure are shown to match the results of CFD simulations of the entire compressor to within 1.6% in overall total pressure ratio and within 0.3 points in overall adiabatic efficiency. Utility of the stage stacking procedure is demonstrated by estimation of the minimum corrected speed which allows stable operation of the compressor. Further utility of the stage stacking procedure is demonstrated with a bleed sensitivity study, which estimates a bleed schedule to expand the compressors operating range.
Kulkarni, Sameer↗
Assessing and Promoting Functional Resilience in Flight Crews During Exploration Missions
NASA plans to send humans to Mars in about 20 years. The NASA Human Research Program supports research to mitigate the major risks to human health and performance on extended missions. However, there will undoubtedly be unforeseen events on any mission of this nature - thus mitigation of known risks alone is not sufficient to ensure optimal crew health and performance. Research should be directed not only to mitigating known risks, but also to providing crews with the tools to assess and enhance resilience, as a group and individually. We can draw on ideas from complexity theory and network theory to assess crew and individual resilience. The entire crew or the individual crewmember can be viewed as a complex system that is composed of subsystems (individual crewmembers or physiological subsystems), and the interactions between subsystems are of crucial importance for overall health and performance. An understanding of the structure of the interactions can provide important information even in the absence of complete information on the component subsystems. This is critical in human spaceflight, since insufficient flight opportunities exist to elucidate the details of each subsystem. Enabled by recent advances in noninvasive measurement of physiological and behavioral parameters, subsystem monitoring can be implemented within a mission and also during preflight training to establish baseline values and ranges. Coupled with appropriate mathematical modeling, this can provide real-time assessment of health and function, and detect early indications of imminent breakdown. Since the interconnected web of physiological systems (and crewmembers) can be interpreted as a network in mathematical terms, we can draw on recent work that relates the structure of such networks to their resilience (ability to self-organize in the face of perturbation). There are many parameters and interactions to choose from. Normal variability is an established characteristic of a healthy physiological response. Healthy coupling has been investigated less extensively, but there are cases in which too tight or too loose coupling can be problematic. This might be in inter-individual behaviors, such as sleep cycles, coordination of work and meal times, and coupled motions during communication. Less apparent are couplings of physiological systems, nevertheless examples abound of coupled systems which might be monitored: cardio-respiratory rhythms; circadian rhythms, body temperature, and sleep; stress markers and cognition, sleep, and performance; profiles of biochemical markers related to immune function and nutritional status; sensorimotor aspects such as motion sickness, ataxia, reaction time, and manual control. Tools for resilience are then the means to measure and analyze these parameters, incorporate them into appropriate models of normal variability and interconnectedness, and recognize when parameters or their couplings are outside of normal limits. What to do when a problem is identified depends on its nature. Changes can be made to crew procedures, work pacing, interpersonal interactions, sleep cycles, meal timing and content, as guided by the model. Use and continued development of these methods could not only provide tools for resilience, but also meaningful autonomous work for the crew on an extended flight.
Shelhamer, Mark↗