Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - CALCUS, OPERATIONAL”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

A Markovian model for assessment of personnel hiring plans

As a result of the current economic environment, many organizations are having to operate with fewer resources. In the manpower area, these constraints have forced organizations to operate within well-defined hiring plans. Exceeding personnel ceilings is in most cases an intolerable situation. A mathematical model, based on the theory of Markov processes, is presented which can be used to assess the chances of success of personnel hiring plans. The model considers a plan to be successful if the final population size, at the end of the planning period, lies within a range specified by management. Although this model was developed to assess personnel hiring plans at the Goddard Space Flight Center, it is directly applicable wherever personnel hiring plans are used.

Katz, L. G.↗
NASA NTRS1979

Problems in processing multizonal video information at specialized complexes

Architectural requirements of a minicomputer-based specialized complex for automated digital analysis of multizonal video data are examined. The logic structure of multizonal video data and the complex mathematical provision required for the analysis of such data are described. The composition of the specialized complex, its operating system, and the required set of peripheral devices are discussed. It is noted that although much of the analysis can be automated, the operator-computer dialog mode is essential for certain stages of the analysis.

Shamis, V. A.↗
NASA NTRS1984

Intersection of parametric surfaces using lookup tables

When primitive structures in the form of parametric surfaces are combined and modified interactively to form complex intersecting surfaces, it becomes important to find the curves of intersection. One must distinguish between finding the shape of the intersection curve, which may only be useful for display purposes, and finding an accurate mathematical representation of the curve, which is important for any meaningful geometric modeling, analysis, design, or manufacturing involving the intersection. The intersection curve between two or more parametric surfaces is important in a variety of computer-aided design and manufacture areas. A few examples are shape design, analysis of groins, design of fillets, and computation of numerically controlled tooling paths. The algorithm presented here provides a mathematical representation of the intersection curve to a specified accuracy. It also provides the database that can simplify operations such as hidden-surface removal, surface rendering, profile identification, and interference or clearance computations.

Hanna, S. L.↗
NASA NTRS1984

Economic impact of fuel properties on turbine powered business aircraft

The principal objective was to estimate the economic impact on the turbine-powered business aviation fleet of potential changes in the composition and properties of aviation fuel. Secondary objectives include estimation of the sensitivity of costs to specific fuel properties, and an assessment of the directions in which further research should be directed. The study was based on the published characteristics of typical and specific modern aircraft in three classes; heavy jet, light jet, and turboprop. Missions of these aircraft were simulated by computer methods for each aircraft for several range and payload combinations, and assumed atmospheric temperatures ranging from nominal to extremely cold. Five fuels were selected for comparison with the reference fuel, nominal Jet A. An overview of the data, the mathematic models, the data reduction and analysis procedure, and the results of the study are given. The direct operating costs of the study fuels are compared with that of the reference fuel in the 1990 time-frame, and the anticipated fleet costs and fuel break-even costs are estimated.

Powell, F. D.↗
NASA NTRS1989

The art of spacecraft design: A multidisciplinary challenge

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Abdi, F.↗
NASA NTRS1990

Verification of floating-point software

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Hoover, Doug N.↗
NASA NTRS2011

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics: Basic Concepts and Operations - Part 1

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Farassat, Fereidoun↗
NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗
NASA NTRS2012

Advancing Data Assimilation in Operational Hydrologic Forecasting: Progresses, Challenges, and Emerging Opportunities

Data assimilation (DA) holds considerable potential for improving hydrologic predictions as demonstrated in numerous research studies. However, advances in hydrologic DA research have not been adequately or timely implemented in operational forecast systems to improve the skill of forecasts for better informed real-world decision making. This is due in part to a lack of mechanisms to properly quantify the uncertainty in observations and forecast models in real-time forecasting situations and to conduct the merging of data and models in a way that is adequately efficient and transparent to operational forecasters. The need for effective DA of useful hydrologic data into the forecast process has become increasingly recognized in recent years. This motivated a hydrologic DA workshop in Delft, the Netherlands in November 2010, which focused on advancing DA in operational hydrologic forecasting and water resources management. As an outcome of the workshop, this paper reviews, in relevant detail, the current status of DA applications in both hydrologic research and operational practices, and discusses the existing or potential hurdles and challenges in transitioning hydrologic DA research into cost-effective operational forecasting tools, as well as the potential pathways and newly emerging opportunities for overcoming these challenges. Several related aspects are discussed, including (1) theoretical or mathematical aspects in DA algorithms, (2) the estimation of different types of uncertainty, (3) new observations and their objective use in hydrologic DA, (4) the use of DA for real-time control of water resources systems, and (5) the development of community-based, generic DA tools for hydrologic applications. It is recommended that cost-effective transition of hydrologic DA from research to operations should be helped by developing community-based, generic modeling and DA tools or frameworks, and through fostering collaborative efforts among hydrologic modellers, DA developers, and operational forecasters.

forecasting↗
NASA NTRS1991

Mathematical modeling of control subsystems for CELSS: Application to diet

The dynamic control of a Closed Ecological Life Support System (CELSS) in a closed space habitat is of critical importance. The development of a practical method of control is also a necessary step for the selection and design of realistic subsystems and processors for a CELSS. Diet is one of the dynamic factors that strongly influences, and is influenced, by the operational states of all major CELSS subsystems. The problems of design and maintenance of a stable diet must be obtained from well characterized expert subsystems. The general description of a mathematical model that forms the basis of an expert control program for a CELSS is described. The formulation is expressed in terms of a complete set of time dependent canonical variables. System representation is dynamic and includes time dependent storage buffers. The details of the algorithm are described. The steady state results of the application of the method for representative diets made from wheat, potato, and soybean are presented.

Waleh, Ahmad↗
NASA NTRS1990

Detecting perceptual groupings in textures by continuity considerations

A generalization is presented for the second derivative of a Gaussian D(sup 2)G operator to apply to problems of perceptual organization involving textures. Extensions to other problems of perceptual organization are evident and a new research direction can be established. The technique presented is theoretically pleasing since it has the potential of unifying the entire area of image segmentation under the mathematical notion of continuity and presents a single algorithm to form perceptual groupings where many algorithms existed previously. The eventual impact on both the approach and technique of image processing segmentation operations could be significant.

Greene, Richard J.↗
NASA NTRS1972

Investigation of the performance characteristics of Doppler radar technique for aircraft collision hazard warning, phase 3

System studies, equipment simulation, hardware development and flight tests which were conducted during the development of aircraft collision hazard warning system are discussed. The system uses a cooperative, continuous wave Doppler radar principle with pseudo-random frequency modulation. The report presents a description of the system operation and deals at length with the use of pseudo-random coding techniques. In addition, the use of mathematical modeling and computer simulation to determine the alarm statistics and system saturation characteristics in terminal area traffic of variable density is discussed.

Source record↗
NASA NTRS1972

Remote manipulator dynamic simulation

A simulator to generate the real time visual scenes required to perform man in the loop investigations of remote manipulator application and design concepts for the space shuttle is described. The simulated remote manipulator consists of a computed display system that uses a digital computer, the electronic scene generator, an operator's station, and associated interface hardware. A description of the capabilities of the implemented simulation is presented. The mathematical models and programs developed for the simulation are included.

Wild, E. C.↗
NASA NTRS1972

Applications of aerospace technology in the environmental sciences

Detailed information is reported on the operations and accomplishments of the RTI Technology Application Team for the period October 11, 1971 to March 10, 1972. Mathematical models for prediction of pollutant formation during combustion are discussed along with generic areas of air pollution problems, which NASA technology offers a high potential for solving. Recommendations for future work are included.

Source record↗
NASA NTRS1971

Optimization of life support systems and their systems reliability

The identification, analysis, and optimization of life support systems and subsystems have been investigated. For each system or subsystem that has been considered, the procedure involves the establishment of a set of system equations (or mathematical model) based on theory and experimental evidences; the analysis and simulation of the model; the optimization of the operation, control, and reliability; analysis of sensitivity of the system based on the model; and, if possible, experimental verification of the theoretical and computational results. Research activities include: (1) modeling of air flow in a confined space; (2) review of several different gas-liquid contactors utilizing centrifugal force: (3) review of carbon dioxide reduction contactors in space vehicles and other enclosed structures: (4) application of modern optimal control theory to environmental control of confined spaces; (5) optimal control of class of nonlinear diffusional distributed parameter systems: (6) optimization of system reliability of life support systems and sub-systems: (7) modeling, simulation and optimal control of the human thermal system: and (8) analysis and optimization of the water-vapor eletrolysis cell.

Fan, L. T.↗
NASA NTRS1973

Automated sizing of large structures by mixed optimization methods

A procedure for automating the sizing of wing-fuselage airframes was developed and implemented in the form of an operational program. The program combines fully stressed design to determine an overall material distribution with mass-strength and mathematical programming methods to design structural details accounting for realistic design constraints. The practicality and efficiency of the procedure is demonstrated for transport aircraft configurations. The methodology is sufficiently general to be applicable to other large and complex structures.

Sobieszczanski, J.↗
NASA NTRS1975

Determination of the center of brightness of the lunar crescent

The operational characteristics of the lunar sensor which was used to point the sounding rocket are discussed briefly. The associated mathematical model of the system is developed and the computer programs which were written to implement the model are described. Data pertinent to the two launches is presented.

Rose, C.↗
NASA NTRS1985

Study of one- and two-dimensional filtering and deconvolution algorithms for a streaming array computer

The development of vector processing computers of the streaming array architectures has made possible a dramatic decrease in the time required for the solution of problems, i.e., for those algorithms which readily lend themselves to sequential operations on long vectors. There has concurrently been rapid growth in the applications of the techniques generally known as mathematical digital filtering, also called signal analysis, digital signal processing, time series analysis, and digital image processing. The best known applications of these techniques is to seismic data and two-dimensional images, data types consisting of very large collections of numbers. A major limitation for these cases is the size and speed of the computer available. Therefore, a move to the streaming array architecture can result in marked improvement in the data analysis techniques which may be employed.

Ioup, G. E.↗