Search NASA⌕ Search

SEARCH · Search NASA

Results for “COMPLEX VARIABLE”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Effects of head-down bed rest on complex heart rate variability: Response to LBNP testing

Head-down bed rest is used to model physiological changes during spaceflight. We postulated that bed rest would decrease the degree of complex physiological heart rate variability. We analyzed continuous heart rate data from digitized Holter recordings in eight healthy female volunteers (age 28-34 yr) who underwent a 13-day 6 deg head-down bed rest study with serial lower body negative pressure (LBNP) trials. Heart rate variability was measured on a 4-min data sets using conventional time and frequency domain measures as well as with a new measure of signal 'complexity' (approximate entropy). Data were obtained pre-bed rest (control), during bed rest (day 4 and day 9 or 11), and 2 days post-bed rest (recovery). Tolerance to LBNP was significantly reduced on both bed rest days vs. pre-bed rest. Heart rate variability was assessed at peak LBNP. Heart rate approximate entropy was significantly decreased at day 4 and day 9 or 11, returning toward normal during recovery. Heart rate standard deviation and the ratio of high- to low-power frequency did not change significantly. We conclude that short-term bed rest is associated with a decrease in the complex variability of heart rate during LBNP testing in healthy young adult women. Measurement of heart rate complexity, using a method derived from nonlinear dynamics ('chaos theory'), may provide a sensitive marker of this loss of physiological variability, complementing conventional time and frequency domain statistical measures.

Goldberger, Ary L.↗
NASA NTRS2014

Preliminary Results from a Coordinated Hisaki/Chandra/XMM-Newton Study of the Jovian Aurora and Io Plasma Torus

We present preliminary results from a coordinated Hisaki/Chandra/XMM-Newton observational campaign of the Jovian aurora and Io plasma torus. The data were taken over a three week period in April, 2014. Jupiter was observed continuously with Hisaki, six times with the Chandra/HRC instrument for roughly 12 hours per observation, and twice by XMM-Newton. The goal of this observational campaign was to understand how energy and matter are exchanged between the Jovian aurora, the IPT, and the Solar wind. X-ray observations provide key diagnostics on highly stripped ions and keV electrons in the Jovian magnetosphere. We use the temporal, spatial, and spectral capabilities of the three instruments to search for correlated variability between the Solar wind, the EUV-emitting plasma of the IPT and UV aurora, and the ions responsible for the X-ray aurora. Preliminary analysis suggests a strong 45 min periodicity in the EUV emission from the electron aurora. There is some evidence for complex variability of the X-ray auroras on scales of tens of minutes. There is also clear morphological changes in the X-ray aurora that do not appear to be correlated with either variations in the IPT or Solar wind.

Kraft, Ralph↗
NASA NTRS1995

New approaches to optimization in aerospace conceptual design

Aerospace design can be viewed as an optimization process, but conceptual studies are rarely performed using formal search algorithms. Three issues that restrict the success of automatic search are identified in this work. New approaches are introduced to address the integration of analyses and optimizers, to avoid the need for accurate gradient information and a smooth search space (required for calculus-based optimization), and to remove the restrictions imposed by fixed complexity problem formulations. (1) Optimization should be performed in a flexible environment. A quasi-procedural architecture is used to conveniently link analysis modules and automatically coordinate their execution. It efficiently controls a large-scale design tasks. (2) Genetic algorithms provide a search method for discontinuous or noisy domains. The utility of genetic optimization is demonstrated here, but parameter encodings and constraint-handling schemes must be carefully chosen to avoid premature convergence to suboptimal designs. The relationship between genetic and calculus-based methods is explored. (3) A variable-complexity genetic algorithm is created to permit flexible parameterization, so that the level of description can change during optimization. This new optimizer automatically discovers novel designs in structural and aerodynamic tasks.

Gage, Peter J.↗
NASA NTRS1983

Elasticity solutions for a class of composite laminate problems with stress singularities

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Wang, S. S.↗
DOE OSTI2024

Development and Implementation of a Bag Degradation Predictive Tool at Los Alamos National Laboratory

Nuclear material packaging involves many complex variables derived from the stored material's properties, the storage environment, and the synergistic interaction of said material and its environment on the containment boundary. In the Plutonium Facility (PF-4) at Los Alamos National Laboratory (LANL) the typical containment boundary found, starting from the stored material itself to the outermost containment layer, consists of the material contained within a stainless steel (typically 304) slip-lid (or other equivalent stainless steel packaging layer) wrapped in an sPVC bag-out bag contained within a facility approved outer container stored within the boundaries of an approved facility (i.e., a building designed and approved to store nuclear material). This packaging configuration, though occasionally deviated from in the past, represents the current procedurally enforced, expected containment structure for all interim nuclear material containment outside of an engineered control barrier (e.g., a glovebox). Over the life of containerization research at LANL, packaging engineers have become increasingly concerned with the degradation of the sPVC bag-out bag, which can cause corrosion to the outermost packaging layer as well as possible exposure to alpha contamination if the bag-out bag layer is degraded to the point of containment failure. A bag-out bag degradation predictive tool (BDT) is therefore needed to assess the current and future nuclear material inventory for possible bag degradation in order to continue to ensure safe operations for the facility and its workers to deliver on the vital national security mission of 30 PPY.

42 ENGINEERING↗
DOE OSTI2026

Deep Learning and Photogrammetric Reconstruction for Automated Crack Detection and Dimensional Measurement in Mining Operations

Surface crack detection and dimensional measurement at active mining sites present significant safety and operational challenges. Manual inspection methods are labor-intensive, spatially incomplete, and expose personnel to hazardous environments, while existing automated approaches have been developed primarily for concrete civil infrastructure and have not been validated on the complex, variable surfaces characteristic of mining environments. This dissertation presents an automated pipeline that integrates deep learning semantic segmentation with Structure-from-Motion photogrammetry to detect surface cracks and measure their aperture, length, and vertical displacement from standard RGB imagery acquired during routine Uncrewed Aerial Vehicle (UAV) survey operations, without requiring additional sensor hardware or manual measurement. The pipeline combines a U-Net architecture with an EfficientNet-B0 encoder, pretrained on the SDNET2018 concrete crack dataset and fine-tuned on a mining-specific dataset spanning laboratory concrete specimens, coal refuse impoundment embankments, and post-blast limestone quarry benches. Photogrammetric reconstruction is performed using COLMAP Structure-from-Motion and Multi-View Stereo, with crack segmentation masks projected into the reconstructed point cloud to enable three-dimensional vertical displacement measurement through local plane fitting and bimodal surface detection. The pipeline was validated across 36 controlled laboratory specimens at three imaging distances and four vertical displacement levels, achieving aperture measurement RMSE of 0.047 cm and R² of 0.954, and vertical displacement RMSE of 0.140 cm and R² of 0.966, against independent caliper measurements. Field application at a coal refuse impoundment in southwestern Pennsylvania detected 71 crack components across the embankment crest, with a dominant longitudinal crack exhibiting aperture values reaching 28 cm and a 95th percentile vertical displacement of 35.53 cm, consistent in magnitude and spatial distribution with simultaneously acquired LiDAR-derived estimates. Application across four post-blast limestone quarry bench datasets in California successfully characterized blast-induced fracture networks at ground sampling distances ranging from 0.59 to 1.23 cm/pixel, with detected crack geometries physically consistent with observable surface conditions at each site. The results demonstrate that deep learning-based crack detection and photogrammetric measurement can be integrated into routine UAV inspection workflows at mining sites, providing repeatable, scalable, and quantitative crack characterization across surface types, crack scales, and displacement magnitudes not previously addressed in the literature. The pipeline requires no dedicated surveying equipment beyond the UAV platforms already deployed at mine sites for survey and monitoring purposes, supporting practical adoption within existing operational workflows.

Crack detection, Dimensional Measurement↗
NASA NTRS1968

Digital filter synthesis computer program

Digital filter synthesis computer program expresses any continuous function of a complex variable in approximate form as a computational algorithm or difference equation. Once the difference equation has been developed, digital filtering can be performed by the program on any input data list.

Moyer, R. A.↗
NASA NTRS1971

Borehole probes: Summary of previous work

Previous research explored the applicability of some devices to lunar borehold testing and, in particular, examined the use of such instruments to assess the strength of soils and rocks. Special attention was given to borehole jacks, which essentially conduct a plate bearing test across opposing wall areas. Analytical work employed finite element analysis, the theory of plasticity, and the theory of elasticity using the complex variable method. A number of solutions were reached for tractable subproblems in the set of problems posed when a jack is used to expand sectors of a borehole. In addition, an investigation with physical models was made to explore the modes of behavior for varying boundary conditions and materials, including both elastic and plastic media.

Goodman, R. E.↗
NASA NTRS1973

Algebraic criteria for positive realness relative to the unit circle.

A definition is presented of the circle positive realness of real rational functions relative to the unit circle in the complex variable plane. The problem of testing this kind of positive reality is reduced to the algebraic problem of determining the distribution of zeros of a real polynomial with respect to and on the unit circle. Such reformulation of the problem avoids the search for explicit information about imaginary poles of rational functions. The stated algebraic problem is solved by applying the polynomial criteria of Marden (1966) and Jury (1964), and a completely recursive algorithm for circle positive realness is obtained.

Siljak, D. D.↗
NASA NTRS1975

Magnetic field of the magnetosheath

The magnetic field of the magnetosheath is most naturally discussed in terms of its steady state and its fluctuating components. Theory of the steady state field is quite well developed and its essential features have been confirmed by observations. The interplanetary field is convected through the bow shock where its magnitude is increased and its direction changed by the minimal amount necessary to preserve the normal component across the shock. Convection within the magnetosheath usually increases the magnitude still further near the subsolar point and further distortes the direction until the field is aligned approximately tangent to the magnetopause. Fluctuations of the magnetosheath field are very complex, variable and not well understood. Spectral peaks are common features which occur at different frequencies at various times. Perturbation vectors of hydromagnetic waves tend to be aligned with the shock and magnetopause surfaces. Magnetosheath waves may be generated upstream, within the magnetosheath, at the bow shock, or at the magnetopause, but the relative importance of these sources is not known.

Fairfield, D. H.↗
NASA NTRS1976

Magnetic fields of the magnetosheath

The magnetic field of the magnetosheath is most naturally discussed in terms of its steady state and its fluctuating components. The theory of the steady-state field is quite well developed, and its essential features have been confirmed by observations. The interplanetary field is convected through the bow shock, where its magnitude is increased and its direction changed by the minimal amount necessary to preserve the normal component across the shock. Convection within the magnetosheath usually increases the magnitude still further near the subsolar point and further distorts the direction until the field is aligned approximately tangent to the magnetopause. Fluctuations of the magnetosheath field are very complex, variable, and not well understood. Transverse waves are often dominant at frequencies below 0.002 Hz, and compressional waves are often dominant at somewhat higher frequencies. Perturbation vectors of hydromagnetic waves tend to be aligned with the shock and magnetopause surfaces. Magnetosheath waves may be generated upstream, within the magnetosheath, at the bow shock, or at the magnetopause.

Fairfield, D. H.↗
NASA NTRS1976

Interaction between an elastic circular inclusion and two symmetrically placed collinear cracks

The paper investigates the fracture toughness of a flat large elastic cracked plate containing an elastic circular inclusion, using the plane stress crack-tip stress intensity factor as a criterion for fracture. In this plane stress geometry, each of the two collinear finite cracks is located on either side of the elastic circular inclusion and the geometry is subjected to uniform stresses at infinity. The analysis is based on the two-dimensional theory of elasticity by using the Muskhelishvili complex variable approach. Numerical calculations are reported for the case of simple tension normal to the crack direction and show the variation of the stress intensity factor with the configuration and elastic properties of the plate and the inclusion.

Hsu, Y. C.↗
NASA NTRS1976

Waves in the vicinity of the magnetopause

IMP 6 magnetic-field measurements demonstrate that the magnetopause is a complex variable boundary with few specific characteristics that persist from orbit to orbit. The appearance of the local magnetopause is determined largely by the boundary conditions imposed by the interplanetary field and the geomagnetic dipole. Magnitude changes across the magnetopause are frequently absent, and if concurrently the magnetosheath and magnetosphere fields also happen to be aligned, then the Chapman-Ferraro current sheet is absent. Ion-cyclotron waves are identified in the magnetosheath near the magnetopause. Similar waves near the proton gyrofrequency are frequently seen in the current sheet associated with a large-angle change at the boundary. Such waves may be important in the transfer of particles and momentum into the magnetosphere. Tailward propagating waves on the magnetopause boundary are found to be responsible for multiple crossings of the tail boundary at 32 earth radii. Monochromatic waves are occasionally seen in the magnetosphere at frequencies slightly below the proton gyrofrequency.

Fairfield, D. H.↗
NASA NTRS1978

A well posed boundary value problem in transonic gas dynamics

A boundary value problem for the Tricomi equation was studied in connection with transonic gas dynamics. The transformed equation delta u plus 1/3Y u sub Y equals 0 in canonical coordinates was considered in the complex domain of two independent complex variables. A boundary value problem was then set by prescribing the real part of the solution on the boundary of the real unit circle. The Dirichlet problem in the upper unit semicircle with vanishing values of the solution at Y = 0 was solved explicitly in terms of the hypergeometric function for the more general Euler-Poisson-Darboux equation. An explicit representation of the solution was also given for a mixed Dirichlet and Neumann problem for the same equation and domain.

Sanz, J. M.↗
NASA NTRS1979

Crack propagation in aluminum sheets reinforced with boron-epoxy

An analysis was developed to predict both the crack growth and debond growth in a reinforced system. The analysis was based on the use of complex variable Green's functions for cracked, isotropic sheets and uncracked, orthotropic sheets to calculate inplane and interlaminar stresses, stress intensities, and strain-energy-release rates. An iterative solution was developed that used the stress intensities and strain-energy-release rates to predict crack and debond growths, respectively, on a cycle-by-cycle basis. A parametric study was made of the effects of boron-epoxy composite reinforcement on crack propagation in aluminum sheets. Results show that the size of the debond area has a significant effect on the crack propagation in the aluminum. For small debond areas, the crack propagation rate is reduced significantly, but these small debonds have a strong tendency to enlarge. Debond growth is most likely to occur in reinforced systems that have a cracked metal sheet reinforced with a relatively thin composite sheet.

Roderick, G. L.↗
NASA NTRS1978

Investigation of ODE integrators using interactive graphics

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Brown, R. L.↗