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At least 937 records · Page 52

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DOE OSTI2019

The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

Physics↗

NASA NTRS1972

Respiratory protective device design using control system techniques

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

Burgess, W. A.↗

NASA NTRS1972

A review of some aspects of inferring the ozone profile by inversion of ultraviolet radiance measurements

The mathematical inversion of light-scattering observations to obtain the atmospheric ozone profile is discussed in terms of the filtering properties of the physical and mathematical processes for different spatial scales. Within this context, it is shown that the physical process of scattering acts as a low pass filter; which transfers large-scale profile information efficiently to radiance observations but very strongly attenuates small- or fine-scale profile information. To avoid domination of the mathematical inversion by the random error of radiance measurements, an equivalent spatial-scale filtering in the inversion procedure is essential. The available evidence suggests that mathematical inversion to obtain the low level ozone profile below 25 to 30 km is either inferior to or no better than the statistical estimation of the profile using total ozone as predictor. However, inversion profiles for high level ozone above 25 to 30 km appear to have moderately good accuracy.

Mateer, C. L.↗

NASA NTRS1978

Identification of the stability parameters of an aeroelastic airplane

Phase variable transformations are used to construct the mathematical model of an aeroelastic aircraft in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. The problem is one of parameter identification of large scale dynamic systems involving a system matrix characterized by about 200 elements. A mathematical model of the USAF Total In-Flight Simulator was computed using the FLEXSTAB program. As data became available during the progress of the flight test program, it was processed and substituted in the mathematical model for parameters obtained from the FLEXSTAB program. Results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.

Rynaski, E. G.↗

NASA NTRS1978

Identification of the stability parameters of an aeroelastic airplane

The problem of the parameter identification of large scale dynamic systems involving a system matrix characterized by approximately 200 elements is addressed. By using phase variable transformations, a mathematical model of an aeroelastic airplane is described in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. A mathematical model of the U.S. Air Force Total In-Flight Simulator was computed using the FLEXSTAB digital computer program. As data became available during the progress of the flight test program, this data was processed and substituted in the mathematical model for parameters analytically obtained from the FLEXSTAB program. The results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.

Rynaski, E. G.↗

NASA NTRS1987

Near Identifiability of Dynamical Systems

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Hadaegh, F. Y.↗

NASA NTRS1986

Formally verifying Ada programs which use real number types

Formal verification is applied to programs which use real number arithmetic operations (mathematical programs). Formal verification of a program P consists of creating a mathematical model of F, stating the desired properties of P in a formal logical language, and proving that the mathematical model has the desired properties using a formal proof calculus. The development and verification of the mathematical model are discussed.

Sutherland, David↗

NASA NTRS1989

Modeling and control of flexible space platforms with articulated payloads

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Graves, Philip C.↗

NASA NTRS1996

Test Outline for Flutter Analysis of Rectangular Panels in Rarefied Flow Conditions

Jet plume impingement forces acting on large flexible space structures may precipitate dynamically unstable behavior during space flights. Typical operating conditions in space involve rarefied gas flow regimes which are intrinsically distinct from continuum gas flow and are normally modeled using the kinetic theory of gas flow. Docking and undocking operations of the Space Shuttle with the Russian Mir space laboratory represent a scenario in which the stability boundaries of solar panels may be of interest. Extensive literature review of research work on the dynamic stability of rectangular panels in rarefied gas flow conditions indicated the lack of published reports dealing with this phenomenon. A recently completed preliminary study for NASA JSC dealing with the mathematical analysis of the stability of two-degree-of-freedom elastically supported rigid panels under the effect of rarefied gas flow was reviewed. A test plan outline is prepared for the purpose of conducting a series of experiments on four rectangular rigid test articles in a vacuum chamber under the effect of continuous and pulsating Nitrogen jet plumes. The purpose of the test plan is to gather enough data related to a number of key parameters to allow the validation of the two-degree-of-freedom mathematical model. The hardware required careful design to select a very lightweight material while satisfying rigidity and frequency requirements within the constraints of the test environment. The data to be obtained from the vacuum chamber tests can be compared with the predicted behavior of the theoretical two-degree-of-freedom model. Using the data obtained in this study, further research can identify the limitations of the mathematical model. In addition modifications to the mathematical model can be made, if warranted, to accurately predict the behavior of rigid panels under rarefied gas flow regimes.

Akl, Fred A.↗

NASA NTRS1996

Graphing Calculator Mini Course

The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

Karnawat, Sunil R.↗

NASA NTRS1995

Property-Based Software Engineering Measurement

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysis, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact, and rigorous, because it is based on precise mathematical concepts. This framework defines several important measurement concepts (size, length, complexity, cohesion, coupling). It is not intended to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalism and properties we introduce are convenient and intuitive. In addition, we have reviewed the literature on this subject and compared it with our work. This framework contributes constructively to a firmer theoretical ground of software measurement.

Briand, Lionel↗

NASA NTRS1997

Property-Based Software Engineering Measurement

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts, regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysts, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact and rigorous, because it is based on precise mathematical concepts. We use this framework to propose definitions of several important measurement concepts (size, length, complexity, cohesion, coupling). It does not intend to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalisms and properties we introduce are convenient and intuitive. This framework contributes constructively to a firmer theoretical ground of software measurement.

Briand, Lionel C.↗

NASA NTRS1999

Technology Development, Implementation and Assessment: K-16 Pre-Service, In-Service and Distance Learning Initiatives

The technologies associated with distance learning are evolving rapidly, giving to educators a potential tool for enhancing the educational experiences of large numbers of students simultaneously. This enhancement, in order to be effective, must take into account the various agendas of teachers, administrators, state systems, and of course students. It must also make use of the latest research on effective pedagogy. This combination, effective pedagogy and robust information technology, is a powerful vehicle for communicating, to a large audience of school children the excitement of mathematics and science--an excitement that for the most part is now well-hidden. This project,"Technology Development, Implementation and Assessment," proposed to bring to bear on the education of learners in grades 3 - 8 in science and mathematics both advances in information technology and in effective pedagogy. Specifically, the project developed components NASA CONNECT video series--problem-based learning modules that focus on the scientific method and that incorporate problem-based learning scenarios tied to national mathematics and science standards. These videos serve two purposes; they engage students in the excitement of hands-on learning and they model for the teachers of these students the problem-based learning practices that are proving to be excellent ways to teach science and mathematics to school students. Another component of NASA CONNECT is the accompanying web-site.

Williams, William B., Jr.↗

NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗

NASA NTRS2000

The University of Nebraska at Omaha Center for Space Data Use in Teaching and Learning

Within the context of innovative coursework and other educational activities, we are proposing the establishment of a University of Nebraska at Omaha (UNO) Center for the Use of Space Data in Teaching and Learning. This Center will provide an exciting and motivating process for educators at all levels to become involved in professional development and training which engages real life applications of mathematics, science, and technology. The Center will facilitate innovative courses (including online and distance education formats), systematic degree programs, classroom research initiatives, new instructional methods and tools, engaging curriculum materials, and various symposiums. It will involve the active participation of several Departments and Colleges on the UNO campus and be well integrated into the campus environment. It will have a direct impact on pre-service and in-service educators, the K12 (kindergarten through 12th grade) students that they teach, and other college students of various science, mathematics, and technology related disciplines, in which they share coursework. It is our belief that there are many exciting opportunities represented by space data and imagery, as a context for engaging mathematics, science, and technology education. The UNO Center for Space Data Use in Teaching and Learning being proposed in this document will encompass a comprehensive training and dissemination strategy that targets the improvement of K-12 education, through changes in the undergraduate and graduate preparation of teachers in science, mathematics and technology education.

Grandgenett, Neal↗

NASA NTRS2003

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗

NASA NTRS1990

The Design-To-Cost Manifold

Design-to-cost is a popular technique for controlling costs. Although qualitative techniques exist for implementing design to cost, quantitative methods are sparse. In the launch vehicle and spacecraft engineering process, the question whether to minimize mass is usually an issue. The lack of quantification in this issue leads to arguments on both sides. This paper presents a mathematical technique which both quantifies the design-to-cost process and the mass/complexity issue. Parametric cost analysis generates and applies mathematical formulas called cost estimating relationships. In their most common forms, they are continuous and differentiable. This property permits the application of the mathematics of differentiable manifolds. Although the terminology sounds formidable, the application of the techniques requires only a knowledge of linear algebra and ordinary differential equations, common subjects in undergraduate scientific and engineering curricula. When the cost c is expressed as a differentiable function of n system metrics, setting the cost c to be a constant generates an n-1 dimensional subspace of the space of system metrics such that any set of metric values in that space satisfies the constant design-to-cost criterion. This space is a differentiable manifold upon which all mathematical properties of a differentiable manifold may be applied. One important property is that an easily implemented system of ordinary differential equations exists which permits optimization of any function of the system metrics, mass for example, over the design-to-cost manifold. A dual set of equations defines the directions of maximum and minimum cost change. A simplified approximation of the PRICE H(TM) production-production cost is used to generate this set of differential equations over [mass, complexity] space. The equations are solved in closed form to obtain the one dimensional design-to-cost trade and design-for-cost spaces. Preliminary results indicate that cost is relatively insensitive to changes in mass and that the reduction of complexity, both in the manufacturing process and of the spacecraft, is dominant in reducing cost.

Dean, Edwin B.↗

NASA NTRS2005

Evaluating the Effectiveness of the 2003-2004 NASA CONNECT(trademark)Program

NASA CONNECT is an Emmy-award-winning series of instructional (distance learning) programs for grades 6-8. Produced by the NASA Center for Distance Learning, the nine programs in the 2003-2004 NASA CONNECT series are research-, inquiry-, standards-, teacher-, and technology-based and include a 30-minute program, an educator guide containing a hands-on activity, and a web-based component. The 1,500 randomly selected NASA CONNECT registered users were invited to complete an electronic (self-reported) survey that employed a 5-point Likert-type scale. Regarding NASA CONNECT, respondents reported that the programs (1) enhance the teaching of mathematics, science, and technology (4.53); (2) are aligned with the national mathematics, science, and technology standards (4.52); (3) raise student awareness of careers requiring mathematics, science, and technology (4.48); (4) demonstrate the application of mathematics, science, and technology (4.47); and (5) present women and minorities performing challenging engineering and science tasks (4.50).

Caton, Randall H.↗