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At least 37 records · Page 2

Uncertainty Estimates for Fitting Zernike Polynomials to Discrete Data

Zernike polynomials are a widely used metric in modern optical analysis. They conveniently represent surfaces as a series of weighted terms corresponding to various optical aberrations. Ideally, each term is independent of others in the series, but Zernike polynomials lose this property when working with sets of discrete data. This gives rise to uncertainty in each polynomial’s actual contribution and affects metrology and simulation estimates of their relative weights. Several factors influencing these estimates are the number and arrangement of sample locations, the method for calculating the weights, and the total number of Zernike terms used in the calculation. Discussed is the uncertainty associated with linear regression using random sampling. Other topics reviewed are complex Zernike polynomials and vector spaces of functions.

Zernike Polynomials↗

WISE J233237.05-505643.5: A Double-Peaked Broad-Lined AGN with Spiral-Shaped Radio Morphology

We present radio continuum mapping, optical imaging and spectroscopy of the newly discovered double-peaked broad-lined AGN WISE J233237.05-505643.5 at redshift z = 0.3447. This source exhibits an FR-I and FR-II hybrid-morphology, characterized by bright core, jet, and Doppler-boosted lobe structures in ATCA continuum maps at 1.5, 5.6, and 9 GHz. Unlike most FR-II objects, W2332-5056 is hosted by a disk-like galaxy. The core has a projected 5" linear radio feature that is perpendicular to the curved primary jet, hinting at unusual and complex activity within the inner 25 kpc. The multi-epoch optical-near-IR photometric measurements indicate significant variability over a 3-20 year baseline from the AGN component. Gemini-South optical data shows an unusual double-peaked emission-line features: the centroids of the broad-lined components of H-alpha and H-beta are blueshifted with respect to the narrow lines and host galaxy by approximately 3800 km/s. We examine possible cases which involve single or double supermassive black holes in the system, and discuss required future investigations to disentangle the mystery nature of this system.

galaxies: individual↗

Waves in Turbulent Stably Stratified Shear Flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It was found, however, that a continuous distribution of the phase angle is present in weakly and strongly stratified flow. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. It was found that a solution of the fully nonlinear viscous Navier-Stokes equations can be represented by the linearized inviscid solution. The projection yields a decomposition into vertical wave modes and horizontal vortical modes.

Jacobitz, F. G.↗

Waves in Turbulent Stably-Stratified Shear Flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It is found, however, that a continuous distribution of the phase angle is present in weakly and strongly stratified flow. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. It is found that a solution of the fully nonlinear viscous Navier-Stokes equations can be represented by the linearized inviscid solution. The projection yields a decomposition into vertical wave modes and horizontal vortical modes.

Jacobitz, F. G.↗

Projection of Stabilized Aerial Imagery Onto Digital Elevation Maps for Geo-Rectified and Jitter-Free Viewing

As imagery is collected from an airborne platform, an individual viewing the images wants to know from where on the Earth the images were collected. To do this, some information about the camera needs to be known, such as its position and orientation relative to the Earth. This can be provided by common inertial navigation systems (INS). Once the location of the camera is known, it is useful to project an image onto some representation of the Earth. Due to the non-smooth terrain of the Earth (mountains, valleys, etc.), this projection is highly non-linear. Thus, to ensure accurate projection, one needs to project onto a digital elevation map (DEM). This allows one to view the images overlaid onto a representation of the Earth. A code has been developed that takes an image, a model of the camera used to acquire that image, the pose of the camera during acquisition (as provided by an INS), and a DEM, and outputs an image that has been geo-rectified. The world coordinate of the bounds of the image are provided for viewing purposes. The code finds a mapping from points on the ground (DEM) to pixels in the image. By performing this process for all points on the ground, one can "paint" the ground with the image, effectively performing a projection of the image onto the ground. In order to make this process efficient, a method was developed for finding a region of interest (ROI) on the ground to where the image will project. This code is useful in any scenario involving an aerial imaging platform that moves and rotates over time. Many other applications are possible in processing aerial and satellite imagery.

Ansar, Adnan I.↗

Mixed Integer Linear Programming in Planning

This project, Activity Planning with Resources for the Exploration of Space (APRES), uses a mixed-integer linear program (MILP) to solve planning problems. This work enables APRES to interpret a model file and output a solution with improved human readability. A plan model is optimized using a MILP solver and the best solution is taken. Once a plan is generated, it is parsed allowing it to retain only desired information and modified for swift human readability.

Christina Erwin↗

Finite rotation and nonlinear beam kinematics

Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.

Hodges, Dewey H.↗

Experimental Demonstration and System Analysis for Plasmonic Force Propulsion

This project developed a higher-fidelity model of a recently envisioned small spacecraft propulsion system for precision pointing and proximity control. Plasmonic force propulsion harnesses solar light focused onto plasmon reactive subwavelength nanostructures to accelerate and expel nanoparticle propellant via strong optical forces. The goal of the project was to show that plasmonic space propulsion can provide the level of proximity and attitude control envisioned for future NASA nano/picosatellite missions, a level that is better than state-of-the-art approaches. We achieved this goal by showing that plasmonic force thrusters are feasible for a range of advanced mission concepts requiring swarm formations in a deep space environment. We performed three case studies that evaluated the performance of the plasmonic force propulsion thruster in a deep space, microsatellite swarm formation. These case studies assumed the propulsion system could generate thrust at the level predicted from our Phase 1 study (1.6 μN). Through these cases we were able to analyze the concept within a mission specific context through detailed orbital dynamics calculations. Results indicate that, with the Phase 1 estimated thrust level, the approach is promising for providing attitude control to swarm formation spacecraft. Further, we achieved goals related to technology development. Specifically, we experimentally demonstrated nanoparticle acceleration due to plasmonic forces with asymmetric nanostructures excited by focused laser light. Additionally, we investigated the thrust sensitivity and nanoparticle propellant injection dependencies upon thermal effects. As a result of our study, plasmonic force propulsion is at an early TRL 3. Active research and design has been conducted analytically and in the laboratory. Furthermore, practical applications such as the three case studies have been identified for the scientific basic principles that were observed. Future efforts related to fundamental understanding of these techniques should focus on 1) developing a standalone array of asymmetric nanostructures that can effectively interact with a stream or reservoir of particles or 2) experimentally evaluate a dielectrophoretic injector for nanoparticle propellant. The main limitation discovered about plasmonic propulsion regards performance estimates significantly below the Phase 1 estimations. Specifically, original assumptions in the Phase 1 project (notably, a linear array of asymmetric nanostructures) is not a viable approach to achieving significant acceleration, high exhaust velocity, of nanoparticles. More specifically, we assumed in Phase 1 that nanoparticles would be accelerated in series by a long linear array of asymmetric nanostructures. That is, the acceleration of the nanoparticle would build and increase with the kick received by each subsequent nanostructure. This is fundamentally flawed. The potential profile of a single nanostructure is such that it prohibits this phenomenon. The potential energy associated with the plasmon-generated dielectrophoretic force is a potential well, which is good for trapping nanoparticles, but cannot provide significant acceleration of particles to expel them out and away from the nanostructure. Further, a nanoparticle expelled from the first nanostructure would need to overcome the potential barrier for entry into the next nanostructure accelerating stage. Fundamentally, this effect means that a linear array of nanostructures is not a viable accelerating structure. Correspondingly then, acceleration can, or should, only be provided by one nanostructure, and the net acceleration and thrust force of a single nanostructure is small (~cm/s exhaust velocities, sub-nN level thrust vs. the 100’s m/s, μN originally envisioned). While our experiments demonstrated acceleration and manipulation of a nanoparticle using laser light in aqueous environment, the achievable energy and momentum addition to the nanoparticle from a single nanostructure stage is too low for useful propulsion. In terms of thrust prediction, the estimated thrust of 1.6 μN in Phase 1 is reduced to a few nN of thrust with this new insight and understanding of the concept. This thrust level is too small to achieve attitude control of swarms as originally envisioned.

Plasmonic Force↗

Structural and lithologic study of northern coast ranges and Sacramento Valley, California

The author has identified the following significant results. The pattern of linear systems within the project area has been extended into the western foothill belt of the Sierra Nevada. The chief pattern of linear features in the western Sierran foothill belt trends about N. 10 - 15 deg W., but in the vicinity of the Feather River the trend of the features abruptly changes to about N. 50-60 deg W and appears to be contiguous across the Sacramento Valley with a similar system of linear features in the Coast Ranges. The linear features in the Modoc Plateau and Klamath Mt. areas appear unrelated to the systems detected in the Coast Ranges of Sierran foothill belt. Although the change in trend of the Sierran structural features has been previously suggested and the interrelationship of the Klamath Mt. region with the northern Sierra Nevadas has been postulated, the data obtained from the ERTS-1 imagery strengthens these notions and provides for the first time evidence of a direct connection of the structural trends within the alluviated part of the Sacramento Valley. In addition rocks of Pleistocene and Holocene age are offset by some of the linear features seen on ERTS-1 imagery and hence may record the latest episode of geologic deformation in north-central California.

Rich, E. I.↗

Another Geometric Interpretation of Cramer’s Rule

We develop a geometric interpretation of Cramer’s rule as a generalization of projection onto orthogonal basis vectors using the rows of the adjugate. This interpretation makes connections between elementary linear algebra concepts like the solution to linear equations, inner products, and projections. Such connections are useful for introducing broader concepts related to Hilbert spaces and geometric algebras like Grassman algebra. Such connections were essential for the author’s mathematical education as an engineer.

linear algebra↗

Ground-based microwave probing

Theoretical and experimental activities in remote sensing were conducted. The projects are: (1) the linear statistical inversion method, (2) vertical temperature profile determination from microwave emission measurements near 60 GHz, (3) radio path length correction determination from emission measurements at 20.6 GHz, and (4) liquid water content determination of thunderstorm cells by emission measurements at 10.7 GHz.

Westwater, E. R.↗

Radio structure of 3C147 determined by multi-element very long baseline interferometry

The radio structure of the quasar 3C147 has been determined from multi-baseline VLBI data at 609 MHz using both a conventional method and a technique which uses the 'closure' phase information to produce a good approximation to a synthesis map of the source. The structure is similar to the central part of M87, with a bright core and a linear 'jet' of a projected length of about 1.5 kpc which is concentrated in bright 'knots'.

Wilkinson, P. N.↗

Coded-aperture imaging in nuclear medicine

Coded-aperture imaging is a technique for imaging sources that emit high-energy radiation. This type of imaging involves shadow casting and not reflection or refraction. High-energy sources exist in x ray and gamma-ray astronomy, nuclear reactor fuel-rod imaging, and nuclear medicine. Of these three areas nuclear medicine is perhaps the most challenging because of the limited amount of radiation available and because a three-dimensional source distribution is to be determined. In nuclear medicine a radioactive pharmaceutical is administered to a patient. The pharmaceutical is designed to be taken up by a particular organ of interest, and its distribution provides clinical information about the function of the organ, or the presence of lesions within the organ. This distribution is determined from spatial measurements of the radiation emitted by the radiopharmaceutical. The principles of imaging radiopharmaceutical distributions with coded apertures are reviewed. Included is a discussion of linear shift-variant projection operators and the associated inverse problem. A system developed at the University of Arizona in Tucson consisting of small modular gamma-ray cameras fitted with coded apertures is described.

Smith, Warren E.↗

Project resource reallocation algorithm

A methodology for adjusting baseline cost estimates according to project schedule changes is described. An algorithm which performs a linear expansion or contraction of the baseline project resource distribution in proportion to the project schedule expansion or contraction is presented. Input to the algorithm consists of the deck of cards (PACE input data) prepared for the baseline project schedule as well as a specification of the nature of the baseline schedule change. Output of the algorithm is a new deck of cards with all work breakdown structure block and element of cost estimates redistributed for the new project schedule. This new deck can be processed through PACE to produce a detailed cost estimate for the new schedule.

Myers, J. E.↗

A study of the use of linear programming techniques to improve the performance in design optimization problems

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

Young, Katherine C.↗

A homotopy algorithm for digital optimal projection control GASD-HADOC

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

Collins, Emmanuel G., Jr.↗