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Mathematical model for removing integrals over scattering angle and particle size in analyzing observations of zodiacal light
Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.
The accurate modeling and analysis of two-phase fluid networks found in environmental control and life support systems is presently undertaken by computer-aided engineering (CAE) techniques whose generalized fluid dynamics package can solve arbitrary flow networks. The CAE system for integrated test bed modeling and analysis will also furnish interfaces and subsystem/test-article mathematical models. Three-dimensional diagrams of the test bed are generated by the system after performing the requisite simulation and analysis.
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
The mathematical development for the expanded capabilities of the G400 rotor aeroelastic analysis was examined. The G400PA expanded analysis simulates the dynamics of all conventional rotors, blade pendulum vibration absorbers, and the higher harmonic excitations resulting from prescribed vibratory hub motions and higher harmonic blade pitch control. The methodology for modeling the unsteady stalled airloads of two dimensional airfoils is discussed. Formulations for calculating the rotor impedance matrix appropriate to the higher harmonic blade excitations are outlined. This impedance matrix, and the associated vibratory hub loads, are the rotor dynamic characteristic elements for use in the simplified coupled rotor/fuselage vibration analysis (SIMVIB). Updates to the development of the original G400 theory, program documentation, user instructions and information are presented.
A more automated process to produce wind tunnel models using existing facilities is discussed. A process was sought to more rapidly determine the aerodynamic characteristics of advanced aircraft configurations. Such aerodynamic characteristics are determined from theoretical analyses and wind tunnel tests of the configurations. Computers are used to perform the theoretical analyses, and a computer aided manufacturing system is used to fabricate the wind tunnel models. In the past a separate set of input data describing the aircraft geometry had to be generated for each process. This process establishes a common data base by enabling the computer aided manufacturing system to use, via a software interface, the geometric input data generated for the theoretical analysis. Thus, only one set of geometric data needs to be generated. Tests reveal that the process can reduce by several weeks the time needed to produce a wind tunnel model component. In addition, this process increases the similarity of the wind tunnel model to the mathematical model used by the theoretical aerodynamic analysis programs. Specifically, the wind tunnel model can be machined to within 0.008 in. of the original mathematical model. However, the software interface is highly complex and cumbersome to operate, making it unsuitable for routine use. The procurement of an independent computer aided design/computer aided manufacturing system with the capability to support both the theoretical analysis and the manufacturing tasks was recommended.
The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.
The purpose of the research project was to continue the development of new methods for efficient aeroservoelastic analysis and optimization. The main targets were as follows: to complete the development of analytical tools for the investigation of flutter with large stiffness changes; to continue the work on efficient continuous gust response and sensitivity derivatives; and to advance the techniques of calculating dynamic loads with control and unsteady aerodynamic effects. An efficient and highly accurate mathematical model for time-domain analysis of flutter during which large structural changes occur was developed in cooperation with Carol D. Wieseman of NASA LaRC. The model was based on the second-year work 'Modal Coordinates for Aeroelastic Analysis with Large Local Structural Variations'. The work on continuous gust response was completed. An abstract of the paper 'Continuous Gust Response and Sensitivity Derivatives Using State-Space Models' was submitted for presentation in the 33rd Israel Annual Conference on Aviation and Astronautics, Feb. 1993. The abstract is given in Appendix A. The work extends the optimization model to deal with continuous gust objectives in a way that facilitates their inclusion in the efficient multi-disciplinary optimization scheme. Currently under development is a work designed to extend the analysis and optimization capabilities to loads and stress considerations. The work is on aircraft dynamic loads in response to impulsive and non-impulsive excitation. The work extends the formulations of the mode-displacement and summation-of-forces methods to include modes with significant local distortions, and load modes. An abstract of the paper,'Structural Dynamic Loads in Response to Impulsive Excitation' is given in appendix B. Another work performed this year under the Grant was 'Size-Reduction Techniques for the Determination of Efficient Aeroservoelastic Models' given in Appendix C.
Computer program for the analysis of a single propellant tank pressurization system includes many pertinent physical phenomena previously ignored in other mathematical models. This program can be used for analysis, simulation, and design of propellant pressurization systems.
Writing software is difficult. However, writing complex, well tested and designed, and functionally correct software is incredibly difficult. An entire field of study is devoted to the validation and verification of software to address this problem, and in this paper we analyze the landscape of currently available third party software. We have divided our analyses into three separate subsections with regards to software validation: formal methods, static analysis, and test generation. Formal verification is the most complex method in which to validate software correctness, but also the most thorough as it truly validates the mathematical validity of the source code. Static analysis generally is relegated to abstract syntax tree traversal techniques to find errors related to faulty software such as memory leaks or stack overflow issues. Automatic test generation is similar in implementation to static analysis, but pushes a bit further in verifying the boundedness of function inputs and outputs with regards to annotated or parsed criteria. The crux of this report is to analyze and describe the software tools that implement these techniques to validate and verify software. Pros and cons related to installation, utilization, and capabilities of the frameworks are described, and reproducible examples are provided with a focus on usability. The initial survey concluded that the most interesting tools of note are Z3, Isabelle/HOL, and TLA+ with regards to formal verification; and Infer, Frama-C, and SonarQube with regards to static analysis. With these tools in mind, a final conjecture is provided that describes future avenues of utilizing these tools for developing a verification framework to assist in validating existing software at Sandia National Laboratories.
Mathematical modeling and digital computer root locus technique for analysis and synthesis of DLA networks
An analytical study was made of an automatic reaction-control system for the upper stages of a missile to determine limit cycle characteristics, corresponding duty cycles, and the effects of the various system parameters on these quantities. A nonlinear servo analysis (describing function) technique was used to obtain a mathematical representation of the nonlinear components of the system. The results obtained by this analysis are compared with the results obtained from an analog simulation including the jet reaction-control hardware. The good agreement between the results of the two studies tends to indicate the feasibility of using such an analysis technique in the early design phase of a reaction-control system, since by so doing, the parameters for good system performance can be determined quite readily.
Traditional human reliability analysis (HRA) methods have difficulty dealing with the dynamic nature of factors such as time and rely on static and expert-judgment-based assessments of performance-shaping factors (PSFs) across limited levels. In this study, we introduce a mathematical approach for dynamically evaluating the experience and training PSF. Our proposed method integrates the psychological concept of the “forgetting curve” to evaluate how PSFs are impacted by the number of trainings and the time elapsed since training. To confirm the validity of the model, we provide experimental data fitted by identifying the quantitative relationship between training and human performance. This research enables dynamic and objective assessments, thus reducing reliance on subjective expert judgment and improving the accuracy of HRA.
This report documents a design agency (DA) method to evaluate coordinate measuring machine (CMM) data by constructing an algorithm that is equivalent to the production agency (PA) algorithm for processing the raw CMM data. Several refinements of the CMM analyses were implemented at both the PA and the DA to process inherent limitations of the raw data, such as the absence of measurements at the exact ends of the connector-adapter assembly (CAA) and the recovery from these limitations through (worst-case) adjustments to the the positional errors. Also, inherent errors of the CMM measurements were accommodated by introducing a guard band, which effectively lowered the tolerance so that the CMM code could not pass bad parts. The DA and the PA showed remarkable agreement in all areas of analysis. The ultimate comparison is shown in Figures 13a and 13b, where the effect of using a guard band and end adjustments to the CMM measurements were clearly shown.
The National Renewable Energy Laboratory's flagship Regional Energy Deployment System (ReEDS) electric grid planning model is informing the answers to some of the biggest questions surrounding electricity sector research. Powered By ReEDS is the third webinar in the Powered By series. Each webinar highlights an innovative NREL grid planning and analysis tool and its real-world applications. The series is an exciting opportunity to learn directly from NREL's grid experts, so make sure to bring your questions.
This paper concerns the accuracy of three related mathematical models (developed by Hedgepeth, Eringen and Sendeckyj and Jones) used in the stress analysis and in fracture studies of continuous-fiber composites. These models have particular application in the investigation of fiber and matrix stresses in unidirectional composites in the region near a crack tip. The interest in such models is motivated by the desire to be able to simplify the equations of elasticity to the point that they can be solved in a relatively easy manner.
This paper concerns the accuracy of three related mathematical models (developed by Hedgepeth, Eringen and Sendeckyj and Jones) used in the stress analysis and in fracture studies of continuous-fiber composites. These models have particular application in the investigation of fiber and matrix stresses in unidirectional composites in the region near a crack tip. The interest in such models is motivated by the desire to be able to simplify the equations of elasticity to the point that they can be solved in a relatively easy manner.
The basic objectives are to further the professional knowledge of qualified engineering and science faculty members; to stimulate an exchange of ideas between participants and NASA: to enrich and refresh the research and teaching activities of the participants' institutions; and to contribute to the research objectives of the NASA centers. Topics addressed include: cryogenics; thunderstorm simulation; computer techniques; computer assisted instruction; system analysis weather forecasting; rocket engine design; crystal growth; control systems design; turbine pumps for the Space Shuttle Main engine; electron mobility; heat transfer predictions; rotor dynamics; mathematical models; computational fluid dynamics; and structural analysis.