Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized functions”

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 955 records · Page 53

Experimental philosophy leading to a small scale digital data base of the conterminous United States for designing experiments with remotely sensed data

Research using satellite remotely sensed data, even within any single scientific discipline, often lacked a unifying principle or strategy with which to plan or integrate studies conducted over an area so large that exhaustive examination is infeasible, e.g., the U.S.A. However, such a series of studies would seem to be at the heart of what makes satellite remote sensing unique, that is the ability to select for study from among remotely sensed data sets distributed widely over the U.S., over time, where the resources do not exist to examine all of them. Using this philosophical underpinning and the concept of a unifying principle, an operational procedure for developing a sampling strategy and formal testable hypotheses was constructed. The procedure is applicable across disciplines, when the investigator restates the research question in symbolic form, i.e., quantifies it. The procedure is set within the statistical framework of general linear models. The dependent variable is any arbitrary function of remotely sensed data and the independent variables are values or levels of factors which represent regional climatic conditions and/or properties of the Earth's surface. These factors are operationally defined as maps from the U.S. National Atlas (U.S.G.S., 1970). Eighty-five maps from the National Atlas, representing climatic and surface attributes, were automated by point counting at an effective resolution of one observation every 17.6 km (11 miles) yielding 22,505 observations per map. The maps were registered to one another in a two step procedure producing a coarse, then fine scale registration. After registration, the maps were iteratively checked for errors using manual and automated procedures. The error free maps were annotated with identification and legend information and then stored as card images, one map to a file. A sampling design will be accomplished through a regionalization analysis of the National Atlas data base (presently being conducted). From this analysis a map of homogeneous regions of the U.S.A. will be created and samples (LANDSAT scenes) assigned by region.

Labovitz, M. L.↗

A remark about pointed bubbles

The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.

Garabedian, P. R.↗

Transient engine performance with water ingestion

The immediate effects on the transient performance of a generic, high bypass ratio jet engine on account of water ingestion are discussed. The air compression subsystem has been analyzed with respect to four aerothermodynamic and mechanical processes associated with two-phase fluid flow and the engine simulation has been carried out under three limiting cases of interest in practice, one pertaining to draining of water at the end of compression and the other two, to partial evaporation at two different locations in the burner. General observations are made on engine operability as a function of engine and control design under various engine and (control input) sensor operating conditions, with various mass fractions of water in the air-water mixture entering the engine, during various pilot-initiated power demand changes.

Haykin, T.↗

A recursive solution for a fading memory filter derived from Kalman filter theory

A simple recursive solution for a class of fading memory tracking filters is presented. A fading memory filter provides estimates of filter states based on past measurements, similar to a traditional Kalman filter. Unlike a Kalman filter, an exponentially decaying weight is applied to older measurements, discounting their effect on present state estimates. It is shown that Kalman filters and fading memory filters are closely related solutions to a general least squares estimator problem. Closed form filter transfer functions are derived for a time invariant, steady state, fading memory filter. These can be applied in loop filter implementation of the Deep Space Network (DSN) Advanced Receiver carrier phase locked loop (PLL).

Statman, J. I.↗

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Osher, Stanley↗

The effect of sulfur and zirconium Co-doping on the oxidation of NiCrAl

The adhesion behavior of Al2O3 scales formed on NiCrAl+Zr alloys was examined as a function of both sulfur and zirconium doping levels. In general, very high levels of zirconium were required to counteract the detrimental effects of sulfur. A sulfur-zirconium adherence map was constructed, as determined from the oxidation and spalling behavior in 1100 C cyclic tests. For low sulfur alloys, the amount of zirconium required for adherence at any given sulfur level can be described by Zr greater than 600 S sup 0.2 (in ppma). These results underscore the importance of sulfur to adhesion mechanisms and suggests that sulfur gettering is a first order effect of reactive element additions to MCrAl alloys.

Smialek, James L.↗

Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semiinfinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l1-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations.

Dahleh, Munther A.↗

A new way to interpret the DIRAC equation in a non-Riemannian manifold

The idea of internal mass terms introduced in ref. (1), is shown not to be an appropriate hypothesis when it is placed in connection with the components of the generalized (matrix) vierbeins being proportional to the Riemannian (gravitational) vierbeins. It would result in an undesirable canceling of the Electromagnetic and the Yang-Mills components in the generalized metric. Another hypothesis is introduced where the wave function psi is Taylor expanded in a small parameter p.

Marques-Bonham, Sirley↗

The effect of sulfur and zirconium co-doping on the oxidation of NiCrAl

The adhesion behavior of Al2O3 scales formed on NiCrAl+Zr alloys was examined as a function of both sulfur and zirconium doping levels. In general, very high levels of zirconium were required to counteract the detrimental effects of sulfur. A sulfur-zirconium adherence map was constructed, as determined from the oxidation and spalling behavior in 1100 C cyclic tests. For low sulfur alloys (less than 500 ppma), the amount of zirconium required for adherence at any given sulfur level can be described by Zr greater than 600 S(0.2) (in ppma). These results underscore the importance of sulfur to adhesion mechanisms and suggest that sulfur gettering is a first order effect of reactive element additions to MCrAl alloys.

Smialek, James L.↗

Experimental investigation of a new device to control the asymmetric flowfield on forebodies at large angles of attack

An exploratory experimental investigation of a new device to control the asymmetric flowfield on forebodies at large angles of attack has been conducted. The device is a rotatable forebody tip, which varies in cross section from circular at its base to elliptic at its tip. The device itself extends over a small portion of the aircraft or missile forebody. The device provides two important improvements. First, it replaced the normally random behavior of the nose side force as a function of nose tip orientation with a predictable and generally sinusoidal distribution and, second, the device showed promise for use as part of a vehicle control system, to be deflected in a prescribed manner to provide additional directional control for the vehicle. The device was tested on a cone/cylinder model having a 10 deg semiapex angle and on a 3.0 caliber tangent ogive model, each with a base diameter of 3.5 in, for angles of attack from 30 to 60 deg. Data were taken from 3 circumferential rows of pressure taps on each model at a Reynolds number of 84,000 based on cylinder diameter and by a helium-bubble flow visualization technique at a Reynolds number of 24,000.

Moskovitz, Cary A.↗

Advanced applications of BEM to inelastic analysis of solids

Newly evolved boundary element solution algorithms are utilized for solving a range of elastoplastic and thermoplastic problems. The first algorithm is the typical iterative procedure in which the unknown boundary solution and the initial stress (or strain) rates are found together in an incremental iterative fashion. The second one is a variable stiffness type approach in which the incremental boundary solution is obtained in a direct (noniterative) manner. The third procedure differs from the two prior algorithms in that volume integration is not needed to incorporate the nonlinear effects in the analysis. Instead, initial stress rates are introduced in the boundary element system by way of particular integrals. The methodology is used in a general purpose, multiregion system that employs quadratic isoparametric shape functions to model the geometry and field variables of the body and can admit up to 15 substructured areas of different material properties.

Banerjee, P. K.↗

Improved Nystrom Integrators

New formulation for Nystrom integrators offers increased precision and speed of computation. Formulation takes advantage of capabilities of modern electronic computers. Independent and dependent variables and various partial and total derivatives expressed via compact tensor notation. In this approach, typical set of constraint equations derived in about 1 day. Solution of constraint equations speeded by SEARCH computer program. Is general-purpose optimization program, which maximizes or minimizes cost function defined by user. Used successfully, to make least-squares fit of about 4,000 equations in 12 unknowns.

Lear, William M.↗

Calculation of optimum airfoils using direct solutions of the Navier-Stokes equations

A method has been developed which calculates the optimum airfoil shape at a specified operating condition. The Reynolds-averaged Navier-Stokes equations with a turbulence model are used as the governing equations for the fluid flow, and are explicitly introduced into the optimization analysis as constraint equations. The locations of all grid points which define the surface of the airfoil are design variables, eliminating the need for shape functions to describe changes in the airfoil geometry. A generalized reduced-gradient method is used to find the optimum airfoil shape. The use of a direct solution technique (Newton's method) to solve the Navier-Stokes equations allows for the efficient solution of the problem. This paper describes the optimization method and presents sample results.

Felker, Fort F.↗

Portable Habitat for Antarctic Scientific Research (PHASR)

The Portable Habitat for Antarctic Scientific Research, PHASR, is designed as a versatile, general purpose habitat system that addresses the problem of functional space and environmental soundness in a partially fabric-covered shelter. PHASR is used for remote field site applications that can be quickly deployed. PHASR will also provide four scientists with a comfortable and efficient use of interior space. PHASR is a NASA/USRA Advanced Design Program project conducted at the University of Houston College of Architecture, Sasadawa International Center for Space Architecture (SICSA). This report is prepared for NASA/USRA.

Griswold, Samantha S.↗

A genetic technique for planning a control sequence to navigate the state space with a quasi-minimum-cost output trajectory for a non-linear multi-dimnensional system

There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.

Hein, C.↗

Numerical solution of differential equations by artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J., Jr.↗

Radiant Heat Transfer Between Nongray Parallel Plates of Tungsten

Net radiant heat flow between two infinite, parallel, tungsten plates was computed by summing the monochromatic energy exchange; the results are graphically presented as a function of the temperatures of the two surfaces. In general these fluxes range from approximately a to 25 percent greater than the results of gray-body computations based on the same emissivity data. The selection of spectral emissivity data and the computational procedure are discussed. The present analytical procedure is so arranged that, as spectral emissivity data for a material become available, these data can be readily introduced into the NASA data-reduction equipment, which has been programmed to compute the net heat flux for the particular geometry and basic assumptions cited in the text. Nongray-body computational techniques for determining radiant heat flux appear practical provided the combination of select spectral emissivity data and the proper mechanized data-reduction equipment are brought to bear on the problem.

Branstetter, J. Robert↗

Heat Transfer Through Turbulent Friction Layers

The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.

Reichardt, H.↗