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At least 271 records · Page 15

Triangulation of multistation camera data to locate a curved line in space

A method is described for finding the location of a curved line in space from local azimuth as a function of elevation data obtained at several observation sites. A least-squares criterion is used to insure the best fit to the data. The method is applicable to the triangulation of an object having no identifiable structural features, provided its width is very small compared with its length so as to approximate a line in space. The method was implemented with a digital computer program and was successfully applied to data obtained from photographs of a barium ion cloud which traced out the earth's magnetic field line at very high altitudes.

Fricke, C. L.↗

Analysis of twisting stiffness for a multifiber composite layer

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

Bert, C. W.↗

Infinite-dimensional approach to system identification of Space Control Laboratory Experiment (SCOLE)

The identification of a unique set of system parameters in large space structures poses a significant new problem in control technology. Presented is an infinite-dimensional identification scheme to determine system parameters in large flexible structures in space. The method retains the distributed nature of the structure throughout the development of the algorithm and a finite-element approximation is used only to implement the algorithm. This approach eliminates many problems associated with model truncation used in other methods of identification. The identification is formulated in Hilbert space and an optimal control technique is used to minimize weighted least squares of error between the actual and the model data. A variational approach is used to solve the problem. A costate equation, gradients of parameter variations and conditions for optimal estimates are obtained. Computer simulation studies are conducted using a shuttle-attached antenna configuration, more popularly known as the Space Control Laboratory Experiment (SCOLE) as an example. Numerical results show a close match between the estimated and true values of the parameters.

Hossain, S. A.↗

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

Calibration of AIS Data Using Ground-based Spectral Reflectance Measurements

Present methods of correcting airborne imaging spectrometer (AIS) data for instrumental and atmospheric effects include the flat- or curved-field correction and a deviation-from-the-average adjustment performed on a line-by-line basis throughout the image. Both methods eliminate the atmospheric absorptions, but remove the possibility of studying the atmosphere for its own sake, or of using the atmospheric information present as a possible basis for theoretical modeling. The method discussed here relies on use of ground-based measurements of the surface spectral reflectance in comparison with scanner data to fix in a least-squares sense parameters in a simplified model of the atmosphere on a wavelength-by-wavelength basis. The model parameters (for optically thin conditions) are interpretable in terms of optical depth and scattering phase function, and thus, in principle, provide an approximate description of the atmosphere as a homogeneous body intervening between the sensor and the ground.

Conel, J. E.↗

Stormtime ring current and radiation belt ion transport: Simulations and interpretations

We use a dynamical guiding-center model to investigate the stormtime transport of ring current and radiation-belt ions. We trace the motion of representative ions' guiding centers in response to model substorm-associated impulses in the convection electric field for a range of ion energies. Our simple magnetospheric model allows us to compare our numerical results quantitatively with analytical descriptions of particle transport, (e.g., with the quasilinear theory of radial diffusion). We find that 10-145-keV ions gain access to L approximately 3, where they can form the stormtime ring current, mainly from outside the (trapping) region in which particles execute closed drift paths. Conversely, the transport of higher-energy ions (approximately greater than 145 keV at L approximately 3) turns out to resemble radial diffusion. The quasilinear diffusion coefficient calculated for our model storm does not vary smoothly with particle energy, since our impulses occur at specific (although randomly determined) times. Despite the spectral irregularity, quasilinear theory provides a surprisingly accurate description of the transport process for approximately greater than 145-keV ions, even for the case of an individual storm. For 4 different realizations of our model storm, the geometric mean discrepancies between diffusion coefficients D(sup sim, sub LL) obtained from the simulations and the quasilinear diffusion coefficient D(sup ql, sub LL) amount to factors of 2.3, 2.3, 1.5, and 3.0, respectively. We have found that these discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) can be reduced slightly by invoking drift-resonance broadening to smooth out the sharp minima and maxima in D(sup ql, sub LL). The mean of the remaining discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) for the 4 different storms then amount to factors of 1.9, 2.1, 1.5, and 2.7, respectively. We find even better agreement when we reduce the impulse amplitudes systematically in a given model storm (e.g., reduction of all the impulse amplitudes by half reduces the discrepancy factor by at least its square root) and also when we average our results over an ensemble of 20 model storms (agreement is within a factor of 1.2 without impulse-amplitude reduction). We use our simulation results also to map phase-space densities f in accordance with Liouville's theorem. We find that the stormtime transport of approximately greater than 145-keV ions produces little change in f-bar the drift-averaged phase-space density on any drift shell of interest. However, the stormtime transport produces a major enhancement from the pre-storm phase-space density at energies approximately 30-145 keV, which are representative of the stormtime ring current.

Lyons, Larry R.↗

A computer program for plotting stress-strain data from compression, tension, and torsion tests of materials

A computer program for plotting stress-strain curves obtained from compression and tension tests on rectangular (flat) specimens and circular-cross-section specimens (rods and tubes) and both stress-strain and torque-twist curves obtained from torsion tests on tubes is presented in detail. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 110000 octal locations of core storage. The program has the capability of plotting individual strain-gage outputs and/or the average output of several strain gages and the capability of computing the slope of a straight line which provides a least-squares fit to a specified section of the plotted curve. In addition, the program can compute the slope of the stress-strain curve at any point along the curve. The computer program input and output for three sample problems are presented.

Greenbaum, A.↗

Estimating slash pine biomass using radar backscatter

L-band HV multiple-incidence-angle aircraft synthetic aperture radar (SAR) data were analyzed in relation to average stand biomass, basal area, and tree height for 55 slash pine plantations located in northern Florida. This information was used to develop a system of equations to predict average stand biomass as a function of L-band (24.5-cm) radar backscatter. The system of equations developed in this study using three-stage least-squares and combinatorial screening accounted for 97 percent of the variability observed in average stand biomass per hectare. When applied to an independent data set, the biomass equations had an average bias of less than 1 percent with a standard error of approximately 3 percent. These results indicate that future Shuttle Imaging Radar Systems (e.g., SIR-C, which will have cross-polarized radar sensors) should be able to obtain better estimates of forest biomass than were obtained with previous satellite radar missions, which utilized only HH-polarized SAR data.

Hussin, Yousif Ali↗

Tracking performance and cycle slipping in the all-digital symbol synchronizer loop of the block 5 receiver

Computer simulated noise performance of the symbol synchronizer loop (SSL) in the Block 5 receiver is compared with the theoretical noise performance. Good agreement is seen at the higher loop SNR's (SNR(sub L)'s), with gradual degradation as the SNR(sub L) is decreased. For the different cases simulated, cycle slipping is observed (within the simulation time of 10(exp 4) seconds) at SNR(sub L)'s below different thresholds, ranging from 6 to 8.5 dB, comparable to that of a classical phase-locked loop. An important point, however, is that to achieve the desired loop SNR above the seemingly low threshold to avoid cycle slipping, a large data-to-loop-noise power ratio, P(sub D)/(N(sub 0)B(sub L)), is necessary (at least 13 dB larger than the desired SNR(sub L) in the optimum case and larger otherwise). This is due to the large squaring loss (greater than or equal to 13 dB) inherent in the SSL. For the special case of symbol rates approximately equaling the loop update rate, a more accurate equivalent model accounting for an extra loop update period delay (characteristic of the SSL phase detector design) is derived. This model results in a more accurate estimation of the noise-equivalent bandwidth of the loop.

Aung, M.↗

Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays

Abstract Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16 × 12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5% root mean square deviations from the ideal image require approximately 5 μ s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than 10 −3 , depending on the strength of the feedback.

Prasad, Nitin (ORCID:0000000180880164)↗

Space transportation vehicle design evaluation using saturated designs

An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.

Unal, Resit↗

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗

Velocity dispersions in galaxies. V - The nuclei of M31 and M32

Stigmatic spectra between 4160 and 4385 A of the central regions of M31 and M32 as well as the K0 III star 51 Ori are presented which were obtained using a SEC-vidicon integrating television tube and the coude spectrograph of the Hale telescope. Line-of-sight velocity dispersions of approximately 130 and 55 km/s are determined for the nuclei of M31 and M32, respectively, by directly comparing their spectra with Gaussian-broadened spectra of 51 Ori. The analytical techniques are outlined, and alternative methods for estimating velocity dispersions are evaluated, including least-squares fitting of intensities and division of Fourier transforms. It is noted that the broadened spectrum of 51 Ori fits the nucleus of M32 and the bulge of M31 much better than the nucleus of M31 in the region between 4180 and 4370 A.

Morton, D. C.↗

Synthesized map of a solar filament at 6 cm with approximately 15 arc sec resolution

Radio telescope observations have been used to provide the first synthesized map of a filament at 6 cm with angular resolution of about 15 arcsec. The 'dirty' map of the north limb of the sun is shown along with the dirty map of the residual after subtracting the three component least squares model. There is very good correspondence between the radio contours and the H alpha filament; the darkest feature of the filament has a radio temperature depression of 7500 plus or minus 1500 K, and the corresponding brightness temperature of the filament is 12500 plus or minus 1500 K. It is concluded that for this particular filament the radio size is not larger than the optical one.

Rao, A. P.↗

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗

Heat Transfer in High-Temperature Fibrous Insulation

The combined radiation/conduction heat transfer in high-porosity, high-temperature fibrous insulations was investigated experimentally and numerically. The effective thermal conductivity of fibrous insulation samples was measured over the temperature range of 300-1300 K and environmental pressure range of 1.33 x 10(exp -5)-101.32 kPa. The fibrous insulation samples tested had nominal densities of 24, 48, and 72 kilograms per cubic meter and thicknesses of 13.3, 26.6 and 39.9 millimeters. Seven samples were tested such that the applied heat flux vector was aligned with local gravity vector to eliminate natural convection as a mode of heat transfer. Two samples were tested with reverse orientation to investigate natural convection effects. It was determined that for the fibrous insulation densities and thicknesses investigated no heat transfer takes place through natural convection. A finite volume numerical model was developed to solve the governing combined radiation and conduction heat transfer equations. Various methods of modeling the gas/solid conduction interaction in fibrous insulations were investigated. The radiation heat transfer was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. A genetic-algorithm based parameter estimation technique was utilized with this model to determine the relevant radiative properties of the fibrous insulation over the temperature range of 300-1300 K. The parameter estimation was performed by least square minimization of the difference between measured and predicted values of effective thermal conductivity at a density of 24 kilograms per cubic meters and at nominal pressures of 1.33 x 10(exp -4) and 99.98 kPa. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements at other densities and pressures. The numerical model was also validated by comparison with a transient thermal test simulating reentry aerodynamic heating conditions.

Daryabeigi, Kamran↗

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

97 MATHEMATICS AND COMPUTING↗

Stability and Heat Transfer Characteristics of Condensing Films

The overall objective of this research is to investigate the fundamental physics of film condensation in reduced gravity. The condensation of vapor on a cool surface is important in many engineering problems,including spacecraft thermal control and also the behavior of condensate films that may form on the interior surfaces of spacecraft. To examine the effects of body force on condensing films, two different geometries have been tested in the laboratory: (1) a stabilizing gravitational body force (+1g, or condensing surface facing 'upwards') and (2) de-stabilizing gravitational body force (-1g, or 'downwards'). For each geometry, different fluid configurations are employed to help isolate the fluid mechanical and thermal mechanisms operative in condensing films. The fluid configurations are (a) a condensing film, and (b) a non-condensing film with film growth by mass addition by through the plate surface. Condensation experiments are conducted in a test cell containing a cooled copper or brass plate with an exposed diameter of 12.7 cm. The metal surface is polished to allow for double-pass shadowgraph imaging, and the test surface is instrumented with imbedded heat transfer gauges and thermocouples. Representative shadowgraph images of a condensing, unstable (-1g) n-pentane film are shown. The interfacial disturbances associated with the de-stabilizing body force leading to droplet formation and break-off can be clearly seen. The heat transfer coefficient associated with the condensing film is shown. The heat transfer coefficient is seen to initially decrease, consistent with the increased thermal resistance due to layer growth. For sufficiently long time, a steady value of heat transfer is observed, accompanied by continuous droplet formation and break-off. The non-condensing cell consists of a stack of thin stainless steel disks 10 cm in diameter mounted in a brass enclosure. The disks are perforated with a regular pattern of 361 holes each 0.25 mm in diameter. Non-condensing experiments in -1g have employed 50 cSt and 125 cSt silicone oil pumped through the perforated disks at a specified rate by a syringe micropump. The time to droplet break-off and the disturbance wavelengths appear to decrease with increasing pumping rate. The ability to reliably perform multi-point, ultrasonic measurements of the film thickness has been demonstrated. A linear array of eight transducers of 6 mm diameter (with a beam footprint of comparable size) are pulsed with a square-wave signal at a frequency of 5 MHz and a pulse duration of approximately 0.3 s. For thin films (60 m to 2-3 mm in thickness) the layer thickness is determined by frequency analysis, where the received ultrasound pulse is Fourier transformed and the spacing between the peaks in the frequency spectrum is analyzed. For thicker layers (up to at least 1 cm in thickness), time-domain analysis is performed of the received ultrasound pulses to generate directly the layer thickness. A time-trace of the film thickness at a point using a single transducer in the linear array is shown for the case of an unstable (-1g) n-pentane film. The oscillations in film thickness are evidently due to the passage and/or shedding of droplets from the cooled plate surface. The entire transducer array was used to measure the changes in film thickness resulting from the passage of gravity waves generated either by an oscillating wall or the impact of a single droplet on the free surface of a film. The enclosure in both cases was 14 cm square and the transducer spacing was 12 mm. Best results were obtained using as test fluid a mixture of 50% glycerol and 50% water with a fluid layer thickness of 3-5 mm. In both cases the measured wavelengths and wave propagation speeds using the ultrasound technique compared reasonably well with those observed by optical imaging. Additional information can be found in the original extended abstract.

Hermanson, J. C.↗