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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.

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NASA NTRS1984

Research in applied mathematics, numerical analysis, and computer science

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Source record↗
NASA NTRS1985

Mathematical physics approaches to lightning discharge problems

Mathematical physics arguments useful for lightning discharge and generation problems are pursued. A soliton Ansatz for the lightning stroke is treated including a charge generation term which is the ultimate source for the phenomena. Equations are established for a partially ionized plasma inding the effects of pressure, magnetic field, electric field, gravitation, viscosity, and temperature. From these equations is then derived the non-stationary generalized Ohm's Law essential for describing field/current density relationships in the horizon channel of the lightning stroke. The discharge initiation problem is discussed. It is argued that the ionization rate drives both the convective current and electric displacement current to increase exponentially. The statistical distributions of charge in the thundercloud preceding a lightning dischage are considered. The stability of the pre-lightning charge distributions and the use of Boltzmann relaxational equations to determine them are discussed along with a covered impedance path provided by the aircraft.

Kyrala, A.↗
NASA NTRS1985

A mathematical formulation of the Scole control problem, part 1

A mathematical formulation of the SCOLE control problem in terms of a continuous model described by partial differential equations with delta functions on the boundary is presented along with three techniques of solution. The abstract wave equation approach leads immediately to a linear feedback law that can ensure (strong) stability. The boundary control approach yields an explicit solution, albeit in a simple case.

Balakrishnan, A. V.↗
NASA NTRS1984

A system-level mathematical model for evaluation of power train performance of load-leveled electric-vehicles

The power train performance of load leveled electric vehicles can be compared with that of nonload leveled systems by use of a simple mathematical model. This method of measurement involves a number of parameters including the degree of load leveling and regeneration, the flywheel mechanical to electrical energy fraction, and efficiencies of the motor, generator, flywheel, and transmission. Basic efficiency terms are defined and representative comparisons of a variety of systems are presented. Results of the study indicate that mechanical transfer of energy into and out of the flywheel is more advantageous than electrical transfer. An optimum degree of load leveling may be achieved in terms of the driving cycle, battery characteristics, mode of mechanization, and the efficiency of the components. For state of the art mechanically coupled flyheel systems, load leveling losses can be held to a reasonable 10%; electrically coupled systems can have losses that are up to six times larger. Propulsion system efficiencies for mechanically coupled flywheel systems are predicted to be approximately the 60% achieved on conventional nonload leveled systems.

Purohit, G. P.↗
NASA NTRS1985

Predictions of cardiovascular responses during STS reentry using mathematical models

The physiological adaptation to weightless exposure includes cardiovascular deconditioning arising in part from a loss of total circulating blood volume and resulting in a reduction of orthostatic tolerance. The crew of the Shuttle orbiter are less tolerant to acceleration forces in the head-to-foot direction during the reentry phase of the flight at a time they must function at a high level of performance. The factors that contribute to orthostatic intolerance during and following reentry and to predict the likelihood of impaired crew performance are evaluated. A computer simulation approach employing a mathematical model of the cardiovascular system is employed. It is shown that depending on the severity of blood volume loss, the reentry acceleration stress may be detrimental to physiologic function and may place the physiologic status of the crew near the borderline of some type of impairment. They are in agreement with conclusions from early ground-based experiments and from observations of early Shuttle flights.

Leonard, J. I.↗
NASA NTRS1984

Mathematical modeling of fluid-electrolyte alterations during weightlessness

Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.

Leonard, J. I.↗
NASA NTRS1985

Space-flight simulations of calcium metabolism using a mathematical model of calcium regulation

The results of a series of simulation studies of calcium matabolic changes which have been recorded during human exposure to bed rest and space flight are presented. Space flight and bed rest data demonstrate losses of total body calcium during exposure to hypogravic environments. These losses are evidenced by higher than normal rates of urine calcium excretion and by negative calcium balances. In addition, intestinal absorption rates and bone mineral content are assumed to decrease. The bed rest and space flight simulations were executed on a mathematical model of the calcium metabolic system. The purpose of the simulations is to theoretically test hypotheses and predict system responses which are occurring during given experimental stresses. In this case, hypogravity occurs through the comparison of simulation and experimental data and through the analysis of model structure and system responses. The model reliably simulates the responses of selected bed rest and space flight parameters. When experimental data are available, the simulated skeletal responses and regulatory factors involved in the responses agree with space flight data collected on rodents. In addition, areas within the model that need improvement are identified.

Brand, S. N.↗
NASA NTRS1985

A systems analysis of the erythropoietic responses to weightlessness. Volume 1: Mathematical model simulations of the erythropoietic responses to weightlessness

Theoretical responses to weightlessness are summarized. The studies include development and validation of a model of erythropoiesis regulation, analysis of the behavior of erythropoiesis under a variety of conditions, simulations of bed rest and space flight, and an evaluation of ground-based animal studies which were conducted as analogs of zero-g. A review of all relevant space flight findings and a set of testable hypotheses which attempt to explain how red cell mass decreases in space flight are presented. An additional document describes details of the mathematical model used in these studies.

Leonard, J. I.↗
NASA NTRS1985

New formalism for two-photon quantum optics. I - Quadrature phases and squeezed states. II - Mathematical foundation and compact notation

A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).

Caves, C. M.↗
NASA NTRS1985

Mathematical Models of Continuous Flow Electrophoresis

Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.

Saville, D. A.↗
NASA NTRS1985

Expanding your horizons in science and mathematics

Through the presentation of its Expanding Your Horizons in Science and Mathematics career education conferences for secondary school young women, the Math/Science Network continues its efforts to remove the educational, psychological, and cultural barriers which prevent women from entering math-and science-based careers. The Expanding Your Horizons conferences were presented on 77 college, university and high school campuses across the United States. This year, these unique one day conferences reached 15,500 students, 3,000 parents and educators, and involved 3,000 career women who volunteered their services as conference planners, workshop leaders, speakers, and role models.

Source record↗
NASA NTRS1986

Mathematical correlation of modal parameter identification methods via system realization theory

A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.

Juang, J. N.↗
NASA NTRS1986

A lumped parameter mathematical model for simulation of subsonic wind tunnels

Equations for a lumped parameter mathematical model of a subsonic wind tunnel circuit are presented. The equation state variables are internal energy, density, and mass flow rate. The circuit model is structured to allow for integration and analysis of tunnel subsystem models which provide functions such as control of altitude pressure and temperature. Thus the model provides a useful tool for investigating the transient behavior of the tunnel and control requirements. The model was applied to the proposed NASA Lewis Altitude Wind Tunnel (AWT) circuit and included transfer function representations of the tunnel supply/exhaust air and refrigeration subsystems. Both steady state and frequency response data are presented for the circuit model indicating the type of results and accuracy that can be expected from the model. Transient data for closed loop control of the tunnel and its subsystems are also presented, demonstrating the model's use as a control analysis tool.

Krosel, S. M.↗
NASA NTRS1986

A mathematical approach for evaluating nickel-hydrogen cells

A mathematical equation is presented which gives a quantitative relationship between time-voltage discharge curves, when a cell's ampere-hour capacity is determined at a constant discharge current. In particular the equation quantifies the initial exponential voltage decay; the rate of voltage decay; the overall voltage shift of the curve and the total capacity of the cell at the given discharge current. The results of 12 nickel-hydrogen boiler plate cells cycled to 80 percent depth-of-discharge (DOD) are discussed in association with these equations.

Leibecki, H. F.↗
NASA NTRS1986

A mathematical model for the doubly-fed wound rotor generator. II

A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components.

Brady, F. J.↗
NASA NTRS1987

Structural Error and Identifiability in Mathematical Models

Errors and previously implicit assumptions treated explicitly. Paper discusses errors in mathematical models of physical systems and problem of identifying model from system input and output. Problem approached by explicitly taking account of erroneous choices of model structure. Paper concerned specifically with linear or weakly nonlinear models.

Hadaegh, F. Y.↗