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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Theory of resonant tunneling in a variably spaced multiquantum well structure - An Airy function approach

A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented herein is easily extended to many layer structures where it is more accurate than other existing transfer matrix or Wentzel-Kramers-Brillouin (WKB) models. The transmission resonances are compared to the bound-state energies calculated for a finite square well under bias using either an asymmetric square-well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound-state energies. The calculations were then applied to a new superlattice structure, the variably spaced superlattice energy filter, which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.

Brennan, K. F.↗
NASA NTRS1980

A solution of one dimensional Fredholm integral equations of the second kind

Fredholm integral equations of the second kind of the one dimension are numerically solved. It is proven that the numerical solution converges to the exact solution of the integral equation. This is shown for periodic kernels and then extended to nonperiodic kernels. This development helps delineate a basic theory which has the potential of solving very complex problems.

Gabrielsen, R. E.↗
NASA NTRS1984

Performance of the h, p and h-p versions

There are three basic versions of the finite element method, called the h, p and h-p versions. They are characterized by the way in which the finite element meshes and polynomial degree of elements are chosen. They differ in computer implementation (program architecture) and mathematical analysis. The manner in which the meshes and polynomial degree of the elements affect the accuracy of finite element solutions is examined. The approach is to fix certain parameters and increase the number of degrees of freedom so that the finie element solutions converge to the exact solution. Such a systematic increase of the number of degrees of freedom is called extension because it can be interpreted as a systematic extension of finite element spaces.

Babuska, I.↗
NASA NTRS1986

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗
NASA NTRS1987

Vibration suppression using a constrained rate-feedback Threshold control strategy

Quasi-closed form solutions are derived for the finite time, minimum force rate-feedback threshold controller to bring a system with or without known external disturbances back into an 'allowable' state manifold in finite time. The disturbances are assumed to be expandable in terms of Fourier series. The quasi-closed form solutions replace the solution of the two-point boundary value problem and definite integral constraints with the solution of algebraic equations and the calculation of matrix exponentials. Examples demonstrate the threshold control technique and compare the quasi-closed form solutions with MACSYMA generated exact solutions (for small system order) and with the numerical solution of the two-point boundary value problem.

Zimmerman, D. C.↗
NASA NTRS1967

Integrating Matrix Method for Determining the Natural Vibrations of a Rotating, Unsymmetrical Beam with Application to Twisted Propeller Blades

A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.

Hunter, William F.↗
NASA NTRS2002

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Bartels, Robert E.↗
NASA NTRS1976

Solution of linear systems by a singular perturbation technique

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Ardema, M. D.↗
NASA NTRS1981

Solution of complex nonlinear problems by a generalized application of the method of base and comparison solutions with applications to aerodynamics problems

A theory for obtaining approximate solutions to nonlinear problems whose exact solutions require the use of large computational procedures is described. The technique represents in some respects a generalization of the method of base and comparison solutions for flows depending on a parameter. For the generalized problem, the input variable is no longer a parameter but a function that is incremented over its entire domain. After performing calculations for a base configuration and a small number of variations of it, solutions for a large class of configurations can be obtained by forming linear combinations of the solution increments. For a restricted class of problems, approximate solutions can be obtained for general variations of a base configuration by using a function-space derivative estimate obtained from a base solution and a single variation.

Barger, R. L.↗
NASA NTRS1986

Analysis and measurement of electromagnetic scattering by pyramidal and wedge absorbers

By modifying the reflection coefficients in the Uniform Geometrical Theory of Diffraction a solution that approximates the scattering from a dielectric wedge is found. This solution agrees closely with the exact solution of Rawlins which is only valid for a few minor cases. This modification is then applied to the corner diffraction coefficient and combined with an equivalent current and geometrical optics solutions to model scattering from pyramid and wedge absorbers. Measured results from 12 inch pyramid absorbers from 2 to 18 GHz are compared to calculations assuming the returns add incoherently and assuming the returns add coherently. The measured results tend to be between the two curves. Measured results from the 8 inch wedge absorber are also compared to calculations with the return being dominated by the wedge diffraction. The procedures for measuring and specifying absorber performance are discussed and calibration equations are derived to calculate a reflection coefficient or a reflectivity using a reference sphere. Shaping changes to the present absorber designs are introduced to improve performance based on both high and low frequency analysis. Some prototypes were built and tested.

Dewitt, B. T.↗
NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗
NASA NTRS1959

Some Basic Aspects of Magnetohydrodynamic Boundary-Layer Flows

An appraisal is made of existing solutions of magnetohydrodynamic boundary-layer equations for stagnation flow and flat-plate flow, and some new solutions are given. Since an exact solution of the equations of magnetohydrodynamics requires complicated simultaneous treatment of the equations of fluid flow and of electromagnetism, certain simplifying assumptions are generally introduced. The full implications of these assumptions have not been brought out properly in several recent papers. It is shown in the present report that for the particular law of deformation which the magnetic lines are assumed to follow in these papers a magnet situated inside the missile nose would not be able to take up any drag forces; to do so it would have to be placed in the flow away from the nose. It is also shown that for the assumption that potential flow is maintained outside the boundary layer, the deformation of the magnetic lines is restricted to small values. The literature contains serious disagreements with regard to reductions in heat-transfer rates due to magnetic action at the nose of a missile, and these disagreements are shown to be mainly due to different interpretations of reentry conditions rather than more complicated effects. In the present paper the magnetohydrodynamic boundary-layer equation is also expressed in a simple form that is especially convenient for physical interpretation. This is done by adapting methods to magnetic forces which in the past have been used for forces due to gravitational or centrifugal action. The simplified approach is used to develop some new solutions of boundary-layer flow and to reinterpret certain solutions existing in the literature. An asymptotic boundary-layer solution representing a fixed velocity profile and shear is found. Special emphasis is put on estimating skin friction and heat-transfer rates.

Hess, Robert V.↗
NASA NTRS2017

Smoothing-Based Relative Navigation and Coded Aperture Imaging

This project will develop an efficient smoothing software for incremental estimation of the relative poses and velocities between multiple, small spacecraft in a formation, and a small, long range depth sensor based on coded aperture imaging that is capable of identifying other spacecraft in the formation. The smoothing algorithm will obtain the maximum a posteriori estimate of the relative poses between the spacecraft by using all available sensor information in the spacecraft formation.This algorithm will be portable between different satellite platforms that possess different sensor suites and computational capabilities, and will be adaptable in the case that one or more satellites in the formation become inoperable. It will obtain a solution that will approach an exact solution, as opposed to one with linearization approximation that is typical of filtering algorithms. Thus, the algorithms developed and demonstrated as part of this program will enhance the applicability of small spacecraft to multi-platform operations, such as precisely aligned constellations and fractionated satellite systems.

Relative positioning↗
NASA NTRS1986

Methods for the solution of radiative transfer equation

To obtain an exact solution of the radiative-transfer equation in media where both absorption and scattering are significant, the usual approach is to use a numerical method. Three methods are known in the literature: invariant imbedding, eigenvalue-eigenfunction, and matrix doubling. This paper examines the practical application of these methods to the problem of emission from an inhomogeneous (Rayleigh) layer, the effects of layer parameters on the stability. It is found that invariant imbedding is most suitable for computing emission from an inhomogeneous layer with a temperature profile but tends to be unstable as the optical thickness of the layer increases beyond 0.5. On the other hand, the matrix-doubling method is stable for arbitrary optical thickness but is not suitable for handling multilayers. The eigenvalue-eigenfunction method is more stable than the invariant imbedding as optical thickness increases up to 2.0. It also permits temperature profile in the layer, but the computation is much more complicated. It is less stable than the matrix-doubling method when optical thickness is larger than 2.0. In general, the choice of a method is dependent on the nature of the problem.

Chen, M. F.↗
NASA NTRS2024

Revisiting Optimal Guidance Solution for Vertical Landing and Take-Off

The vertical landing and take-off are crucial phases of a rocket-powered spacecraft's powered descent and ascent trajectories, during which its motion is confined to a single (vertical) axis. It is well-known that the minimum-propellant guidance solutions for vertical landing and take-off in a vacuum, consist of only one coast and one full-thrust arc and no singular arc exists in these problems. However, an exact solution for the vertical descent problem is not found in the literature. In the present work, exact guidance solutions for the optimal vertical landing and take-off are presented that are valid for arbitrary boundary conditions. The time-based and switching function-based guidance law implementations are discussed and their performance is compared using lunar descent and ascent simulations.

powered descent↗