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NASA NTRS1974

Optimizing acoustical treatment

A mathematical linear programming model is presented for optimizing acoustical treatment and interior decoration of concert and other public halls. This method provides the designer with a range of acoustically correct solutions at increased economical efficiency. The mathematical model uses geometrical data about the room, recommended reverberation time values, the architect's choice of given sound absorbing structures and finishing materials. The model permits inclusion of aesthetical considerations about conditioning, proportioning, or, on the contrary, reciprocal exclusion of any classes of material and/or sound absorbing structure.

Beuran, N.↗

NASA NTRS1975

Elastic modulus of the human intact left ventricle - Determination and physiological interpretation

The left ventricle (l.v.) is represented as a shell of muscle whose performance is characterized in terms of the chamber pressure and stress/strain in the ventricular wall; the effective elastic modulus of the l.v. relates these performance variables, and hence represents the transfer function of the left ventricular physiological system. A method is presented for indirectly determining the effective modulus E for the left ventricle. The method employs a thick-walled mathematical model of the l.v. having a homogeneous isotropic medium. Instantaneous values of E are determined for subjects with heart diseases of varied etiologies, in order to assess the responses of the l.v. to chronic overloads of pressure and volume. Resulting values for E are used diagnostically to characterize the physiological state of the l.v. Normal values of E, at systole, indicate that the strength of contraction exercised by the l.v. is normal, and hence is an indication of the l.v. having adjusted to the heart disease.

Ghista, D. N.↗

NASA NTRS1985

Munsell color analysis of Landsat color-ratio-composite images of limonitic areas in southwest New Mexico

The causes of color variations in the green areas on Landsat 4/5-4/6-6/7 (red-blue-green) color-ratio-composite (CRC) images, defined as limonitic areas, were investigated by analyzing the CRC images of the Lordsburg, New Mexico area. The red-blue-green additive color system was mathematically transformed into the cylindrical Munsell color coordinates (hue, saturation, and value), and selected areas were digitally analyzed for color variation. The obtained precise color characteristics were then correlated with properties of surface material. The amount of limonite (L) visible to the sensor was found to be the primary cause of the observed color differences. The visible L is, is turn, affected by the amount of L on the material's surface and by within-pixel mixing of limonitic and nonlimonitic materials. The secondary cause of variation was vegetation density, which shifted CRC hues towards yellow-green, decreased saturation, and increased value.

Kruse, F. A.↗

NASA NTRS1987

Forced cocurrent smoldering combustion

An analytical model of cocurrent smoldering combustion through a very porous solid fuel is developed. Smoldering is initiated at the top of a long radially insulated uniform fuel cylinder, so that the smolder wave propagates downward, opposing an upward-forced flow of oxidizer, with the solid fuel and the gaseous oxidizer entering the reaction zone from the same direction (hence, cocurrent). Radiative heat transfer was incorporated using a diffusion approximation, and smoldering was modeled using a one-step reaction mechanism. The results indicate that, for a given fuel, the final temperature depends only on the initial oxygen mass flux, increasing logarithmically with the mass flux. The smolder velocity is linearly dependent on the initial oxygen mass flux, and, at a fixed value of the flux, increases with initial oxygen mass fraction. The mathematical relationship determining the conditions for steady smolder propagation is presented.

Dosanjh, Sudip S.↗

NASA NTRS1990

Noncontact measurement of high temperature using optical fiber sensors

The primary goal of this research program was the investigation and application of noncontact temperature measurement techniques using optical techniques and optical fiber methods. In particular, a pyrometer utilizing an infrared optical light pipe and a multiwavelength filtering approach was designed, revised, and tested. This work was motivated by the need to measure the temperatures of small metallic pellets (approximately 3 mm diameter) in free fall at the Microgravity Materials Processing Drop Tube at NASA Marshall Space Flight Center. In addition, research under this program investigated the adaptation of holography technology to optical fiber sensors, and also examined the use of rare-earth dopants in optical fibers for use in measuring temperature. The pyrometer development effort involved both theoretical analysis and experimental tests. For the analysis, a mathematical model based on radiative transfer principles was derived. Key parameter values representative of the drop tube system, such as particle size, tube diameter and length, and particle temperature, were used to determine an estimate of the radiant flux that will be incident on the face of an optical fiber or light pipe used to collect radiation from the incandescent falling particle. An extension of this work examined the advantage of inclining or tilting the collecting fiber to increase the time that the falling particle remains in the fiber field-of-view. Those results indicate that increases in total power collected of about 15 percent may be realized by tilting the fiber. In order to determine the suitability of alternative light pipes and optical fibers, and experimental set-up for measuring the transmittance and insertion loss of infrared fibers considered for use in the pyrometer was assembled. A zirconium fluoride optical fiber and several bundles of hollow core fiber of varying diameters were tested. A prototype two-color pyrometer was assembled and tested at Virginia Tech, and then tested on the Drop Tube at Marshall Space Flight Center. Radiation from 5 mm diameter niobium drops falling in the Drop Tube was successfully detected, and recorded for later analysis. Subsequent analysis indicated that the imaging of light output from the light pipe onto the detector active areas was not identical for both detectors.

Claus, R. O.↗

NASA NTRS2001

Modeling of two-phase flow in membranes and porous media in microgravity as applied to plant irrigation in space

In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems.

Plant Roots/growth & development↗

NASA NTRS1995

Scientific Visualization and Computational Science: Natural Partners

Scientific visualization is developing rapidly, stimulated by computational science, which is gaining acceptance as a third alternative to theory and experiment. Computational science is based on numerical simulations of mathematical models derived from theory. But each individual simulation is like a hypothetical experiment; initial conditions are specified, and the result is a record of the observed conditions. Experiments can be simulated for situations that can not really be created or controlled. Results impossible to measure can be computed.. Even for observable values, computed samples are typically much denser. Numerical simulations also extend scientific exploration where the mathematics is analytically intractable. Numerical simulations are used to study phenomena from subatomic to intergalactic scales and from abstract mathematical structures to pragmatic engineering of everyday objects. But computational science methods would be almost useless without visualization. The obvious reason is that the huge amounts of data produced require the high bandwidth of the human visual system, and interactivity adds to the power. Visualization systems also provide a single context for all the activities involved from debugging the simulations, to exploring the data, to communicating the results. Most of the presentations today have their roots in image processing, where the fundamental task is: Given an image, extract information about the scene. Visualization has developed from computer graphics, and the inverse task: Given a scene description, make an image. Visualization extends the graphics paradigm by expanding the possible input. The goal is still to produce images; the difficulty is that the input is not a scene description displayable by standard graphics methods. Visualization techniques must either transform the data into a scene description or extend graphics techniques to display this odd input. Computational science is a fertile field for visualization research because the results vary so widely and include things that have no known appearance. The amount of data creates additional challenges for both hardware and software systems. Evaluations of visualization should ultimately reflect the insight gained into the scientific phenomena. So making good visualizations requires consideration of characteristics of the user and the purpose of the visualization. Knowledge about human perception and graphic design is also relevant. It is this breadth of knowledge that stimulates proposals for multidisciplinary visualization teams and intelligent visualization assistant software. Visualization is an immature field, but computational science is stimulating research on a broad front.

Uselton, Samuel P.↗

NASA NTRS1995

Integrated Logistics Support Analysis of the International Space Station Alpha, Background and Summary of Mathematical Modeling and Failure Density Distributions Pertaining to Maintenance Time Dependent Parameters

The process of predicting the values of maintenance time dependent variable parameters such as mean time between failures (MTBF) over time must be one that will not in turn introduce uncontrolled deviation in the results of the ILS analysis such as life cycle costs, spares calculation, etc. A minor deviation in the values of the maintenance time dependent variable parameters such as MTBF over time will have a significant impact on the logistics resources demands, International Space Station availability and maintenance support costs. There are two types of parameters in the logistics and maintenance world: a. Fixed; b. Variable Fixed parameters, such as cost per man hour, are relatively easy to predict and forecast. These parameters normally follow a linear path and they do not change randomly. However, the variable parameters subject to the study in this report such as MTBF do not follow a linear path and they normally fall within the distribution curves which are discussed in this publication. The very challenging task then becomes the utilization of statistical techniques to accurately forecast the future non-linear time dependent variable arisings and events with a high confidence level. This, in turn, shall translate in tremendous cost savings and improved availability all around.

Sepehry-Fard, F.↗

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 NTRS1986

Effects of noise on modal parameters identified by the Eigensystem Realization Algorithm

The basic concept of the Eigensystem Realization Algorithm for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators, such as the singular values of the data matrix and modal amplitude coherence, is provided, based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo Simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1986

Effects of noise on ERA-identified modal parameters

The basic concept of the Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators such as the singular values of the data matrix and modal amplitude coherence is provided based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1989

Nonlinear Curve-Fitting Program

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Everhart, Joel L.↗

NASA NTRS1991

Forward flight trim calculation and frequency response validation of a high-order helicopter simulation model

This paper describes a new trim procedure, that includes the calculation of the steady-state response of the rotor blades, and that is applicable to straight flight and steady coordinated turns. This paper also describes the results of a validation study for a high order linearized model of helicopter flight dynamics, that includes rotor, inflow, and actuator dynamics. The model is obtained by numerical perturbations of a nonlinear, blade element type mathematical model. Predicted responses are compared with flight test data for two values of flight speed. The comparison is carried out in the frequency domain. Numerical simulations show that the trim algorithm is very accurate, and preserves the periodicity of the aircraft states. The results also indicate that the predictions of the linearized model are in good agreement with flight test data, especially at medium and high frequencies.

Kim, Frederick D.↗

NASA NTRS1993

Two color holographic interferometry for microgravity application

Holographic interferometry is a primary candidate for the measurement of temperature and concentration in various crystal growth experiments destined for space. The method measures refractive index changes in the experiment test cell. A refractive index change can be caused by concentration changes, temperature changes, or a combination of temperature and concentration changes. If the refractive index changes are caused by temperature and concentration changes occurring simultaneously in the experiment test cell, the contributions by the two effects cannot be separated by conventional measurement methods. By using two wavelengths, two independent interferograms can be produced from the reconstruction of the hologram. The two interferograms will be different due to dispersion properties of fluid materials. These differences provide the additional information that allows the separation of simultaneously occurring temperature and concentration gradients. There is no other technique available that can provide this type of information. The primary objectives of this effort are to experimentally verify the mathematical theory of two color holographic interferometry and to determine the practical value of this technique for space application. To achieve these objectives, the accuracy and sensitivity of the technique must be determined for geometry's and materials that are relevant to the Materials Processing in the Space program of NASA. This will be achieved through the use of a specially designed two-color holographic interferometry breadboard optical system. In addition to experiments to achieve the primary goals, the breadboard will also provide inputs to the design of an optimum space flight system.

Trolinger, James D.↗

NASA NTRS1994

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Ristorcelli, J. R.↗

NASA NTRS1997

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

Balling, R. J.↗

NASA NTRS1949

Lame's Wave Functions of the Ellipsoid of Revolution

It has recently Miss Gertrude Blanch that errors exist in been brought to the attention of the NACA by of the Bureau of Standards, Department of Commerce the tabulated values appearing in tables 11 to 17 of TM 1224. Miss Blanch notes that C. J. Bouwkamp~ from whom Meixner obtained the values presented, subsequently corrected them in tables. appearing in the Journal of Mathematics and Physics, vol. XXVI, no. 2, JULY 1947, pp. 88-91. In spite of the difference in symbols and notation in the two papers, reprints of tables I to IX included in the July 1947 issue of the Journal of Mathematics and Physics are attached for the use of those interested in receiving them. The NACA wishes to express its appreciation to the Journal of Mathematics and Physics for permitting these tables to be reproduced for this purpose.

Meixner, J.↗

NASA NTRS2007

Noncoherent DTTLs for Symbol Synchronization

Noncoherent data-transition tracking loops (DTTLs) have been proposed for use as symbol synchronizers in digital communication receivers. [Communication- receiver subsystems that can perform their assigned functions in the absence of synchronization with the phases of their carrier signals ( carrier synchronization ) are denoted by the term noncoherent, while receiver subsystems that cannot function without carrier synchronization are said to be coherent. ] The proposal applies, more specifically, to receivers of binary phase-shift-keying (BPSK) signals generated by directly phase-modulating binary non-return-to-zero (NRZ) data streams onto carrier signals having known frequencies but unknown phases. The proposed noncoherent DTTLs would be modified versions of traditional DTTLs, which are coherent. The symbol-synchronization problem is essentially the problem of recovering symbol timing from a received signal. In the traditional, coherent approach to symbol synchronization, it is necessary to establish carrier synchronization in order to recover symbol timing. A traditional DTTL effects an iterative process in which it first generates an estimate of the carrier phase in the absence of symbol-synchronization information, then uses the carrier-phase estimate to obtain an estimate of the symbol-synchronization information, then feeds the symbol-synchronization estimate back to the carrier-phase-estimation subprocess. In a noncoherent symbol-synchronization process, there is no need for carrier synchronization and, hence, no need for iteration between carrier-synchronization and symbol- synchronization subprocesses. The proposed noncoherent symbolsynchronization process is justified theoretically by a mathematical derivation that starts from a maximum a posteriori (MAP) method of estimation of symbol timing utilized in traditional, coherent DTTLs. In that MAP method, one chooses the value of a variable of interest (in this case, the offset in the estimated symbol timing) that causes a likelihood function of symbol estimates over some number of symbol periods to assume a maximum value. In terms that are necessarily oversimplified to fit within the space available for this article, it can be said that the mathematical derivation involves a modified interpretation of the likelihood function that lends itself to noncoherent DTTLs. The proposal encompasses both linear and nonlinear noncoherent DTTLs. The performances of both have been computationally simulated; for comparison, the performances of linear and nonlinear coherent DTTLs have also been computationally simulated. The results of these simulations show that, among other things, the expected mean-square timing errors of coherent and noncoherent DTTLs are relatively insensitive to window width. The results also show that at high signal-to-noise ratios (SNRs), the performances of the noncoherent DTTLs approach those of their coherent counterparts at, while at low SNRs, the noncoherent DTTLs incur penalties of the order of 1.5 to 2 dB.

Simon, Marvin↗