Search NASA⌕ Search

SEARCH · Search NASA

Results for “conjugation”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Design and breadboard evaluation of the SPS reference phase control system concept

Efficient operation of a very large phased array such as the proposed solar power satellite, requires precision focusing and pointing of the power beam; i.e., the power beam must have a planar wavefront directed precisely at the center of the target antenna (rectenna). To maintain such a power beam requires real-time phase compensation at each subaperture in order to adjust for structural deformations and other transitory factors. In the current solar power satellite (SPS) baseline, the spaceborne antenna (Spacetenna) is an active retrodirective array. A pilot signal transmitted from the center of the rectenna is phase-conjugated at each subaperture (power module) of the spacetenna, thereby assuring that the radiated composite wave is focused on the target. This scheme requires a large amount of precision electronic circuitry on the spacetenna. Specifically, pilot receivers must be located at each power module and an adaptive distribution network is required in order to provide a properly phased reference signal at each conjugator.

Hopkins, P. M.↗
NASA NTRS1981

Surface conforming thermal/pressure seal

An assembly is disclosed for sealing a variable gap between the surface of element and a second element in movable relation to it. A seal housing is attached to the second element for movement therewith and has a sealing surface. At least one elongated seal member carried by the housing has first and second conjugate sealing surfaces. The first sealing surface is for rubbing and sealing engagement with the first element surface and the second sealing surface is for sliding and sealing engagement with the housing sealing surface. A biasing assembly may be carried by the housing for biasing the first and second conjugate sealing surfaces of the sealing member toward sealing engagement with the first element surface and housing sealing surface, respectively.

Stevens, M. L.↗
NASA NTRS1980

Phase control system concepts and simulations

A phase control system concept for a solar power satellite is proposed which partitions the system into three major levels. The first level of phase control consists of a reference phase distribution system implemented in the form of phase distribution tree structure. The major purpose of the tree structure is to electronically compensate for the phase shift due to the transition path lengths from the center of the spacetenna to each phase control center located in each subarray. In the reference system, this is accomplished using the master slave returnable timing system technique. The second level of phase control consists of the beam steering and microwave power generating system which houses the power transponders. This transponder consists of a set of phase conjugation multipliers driven by the reference phase distribution system output and the output of a pilot spread spectrum receiver which accepts the received pilot via a diplexer connected to a separate receive horn or the subarray itself. The output of the phase conjugation circuits serve as inputs to the third level of the phase control system. The third level of phase control is associated with maintaining an equal and constant phase shift through the microwave power amplifier devices while minimizing the associated phase noise effects on the generated power beam. This is accomplished by providing a phase locked loop around each high power amplifier.

Lindsay, V. C.↗
NASA NTRS1983

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗
NASA NTRS1982

The use of artificial electron beams as probes of the distant magnetosphere

Experiments are reported in which electron beams were injected into the magnetosphere (with up to 40 kev energy and at current up to 0.8 A) to diagnose the plasma processes at great distance by measurements made in the ionosphere. In some of the experiments, the conjugate region atmosphere was used to detect the electron beam; in others, conjugate echoes were detected near the injection region. The echoes were found to respond to changes in the convection fields and to reflect auroral zone activity. Theoretical and experimental echo patterns are discussed. Evidence for beam pitch angle scattering and altered mirror heights is presented. The use of the atmospheric response to electron beams in the loss cone as a detector has been achieved using optical, X-ray, and radar techniques.

Winckler, J. R.↗
NASA NTRS1984

Microprocessor implementation of an FFT for ionospheric VLF observations

A fast Fourier transform algorithm is implemented on a CMOS microprocessor for application to very low-frequency electric fields (less than 10 kHz) sensed on high-altitude scientific balloons. Two FFT's are calculated simultaneously by associating them with conjugate symmetric and conjugate antisymmetric results. One goal of the system was to detect spectral signatures associated with fast time variations present in natural signals such as whistlers and chorus. Although a full evaluation of the system was not possible for operational reasons, a measure of the system's success has been defined and evaluated.

Elvidge, J.↗
NASA NTRS1984

Modeling algorithm execution time on processor arrays

An approach to modelling the execution time of algorithms on parallel arrays is presented. This time is expressed as a function of the number of processors and system parameters. The resulting model has been applied to a parallel implementation of the conjugate-gradient algorithm on NASA's FEM. Results of experiments performed to compare the model predictions against actual behavior show that the floating-point arithmetic, communication, and synchronization components of the parallel algorithm execution time were correctly modelled. The results also show that the overhead caused by the interaction of the system software and the actual parallel hardware must be reflected in the model parameters. The model has been used to predict the performance of the conjugate gradient algorithm on a given problem as the number of processors and machine characteristics varied.

Adams, L. M.↗
NASA NTRS1986

Synthesis and Optimization of Spiral Bevel Gears

Two mathematical models help in optimizing design of spiral bevel gears. In essence, replace actual generated tooth surface with mathematical conjugate approximation. Tooth surfaces of spiral bevel gears replaced (or approximated) by conjugate tooth surfaces. Surfaces generated by two conical surface's rigidly connected with each other and in linear tangency along common generatrix of tool cones and by conical surface and surface of revolution in linear tangency along circle. Gears have widespread applications in transmission systems of helicopters, airplanes, trucks, automobiles, tanks, and many other machines.

Litvin, F. L.↗
NASA NTRS1984

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Ehlers, F. E.↗
NASA NTRS1984

Augmented weak forms and element-by-element preconditioners: Efficient iterative strategies for structural finite elements. A preliminary study

A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.

Muller, A.↗
NASA NTRS1984

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Padeapproximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗
NASA NTRS1985

GMRES acceleration of computational fluid dynamics codes

The generalized minimal residual algorithm (GMRES) is a conjugate-gradient like method that applies directly to nonsymmetric linear systems of equations. In this paper, GMRES is modified to handle nonlinear equations characteristic of computational fluid dynamics. Attention is devoted to the concept of preconditioning and the role it plays in assuring rapid convergence. A formulation is developed that allows GMRES to be preconditioned by the solution procedures already built into existing computer codes. Examples are provided that demonstrate the ability of GMRES to greatly improve the robustness and rate of convergence of current state-of-the-art fluid dynamics codes. Theoretical aspects of GMRES are presented that explain why it works. Finally, the advantage GMRES enjoys over related methods such as conjugate gradients are discussed.

Wigton, L. B.↗
NASA NTRS1986

Larger Convergence Zones for Newton's Method

Iterative technique applies over wider range of initial guesses. New theorem describes convergence zone of Newton's iterative method for finding zeros of real function. Involves two points, Xp and Xp*, called primary conjugate points. If exact solution lies between these points (Xp is less than Xz is less than Xp*) and no other conjugate points in interval, then according to theorem, subsequent iterations will converge upon exact solution if initial guess lies in interval.

Campbell, C. W.↗
NASA NTRS1985

Cell Partition in Two Polymer Aqueous Phases

Partition of biological cells in two phase aqueous polymer systems is recognized as a powerful separation technique which is limited by gravity. The synthesis of new, selective polymer ligand conjugates to be used in affinity partition separations is of interest. The two most commonly used polymers in two phase partitioning are dextran and polyethylene glycol. A thorough review of the chemistry of these polymers was begun, particularly in the area of protein attachment. Preliminary studies indicate the importance in affinity partitioning of minimizing gravity induced randomizing forces in the phase separation process. The PEG-protein conjugates that were prepared appear to be ideally suited for achieving high quality purifications in a microgravity environment. An interesting spin-off of this synthetic work was the observation of catalytic activity for certain of our polymer derivatives.

Harris, J. M.↗
NASA NTRS1985

Directivity optimization of a reflector antenna with cluster feeds - A closed-form solution

The directivity of a reflector antenna deteriorates as the feed moves away from the focal point for beam scanning. This deterioration can be substantially reduced if a cluster feed instead of single feed is used to control a beam. A closed-form solution is presented for the cluster excitation to achieve the optimum directivity. For an offset 108 lambda parabolic reflector scanning 10 beamwidths, the optimum directivity achieved by a 19-element (seven-element) cluster is 12 dB (8 dB) higher than that of a single element. Comparison of the optimum-directivity design and the popular conjugate field matching design is made. When the cluster spacing d is greater than 1 lambda, it is found that the optimum directivity is higher than that of conjugate field matching (CFM) scheme by an insignificant amount, although the excitations of two designs can be quite different. For d less than 0.5 lambda, the optimum design may exhibit the supergain phenomenon, namely extremely high directivities achieved by an oscillatory cluster excitation.

Lam, P. T.↗
NASA NTRS1987

Solving Finite-Element Problems on a Concurrent Processor

By use of "conjugate gradients" technique, concurrent efficiency greater than 90 percent. Algorithm applies method of conjugate gradients to iterative solution of finite-element problems on concurrent processor. With algorithm, iteration rates nearly proportional to number of processors. For sufficiently large problems, fraction of proportional speedup achieved, called concurrent efficiency, exceeds 90 percent. Results indicate future application of this and related algorithms to large finite-element problems depend primarily upon applicability of iteratiave techniques, not upon issues of concurrency or efficiency.

Lyzenga, G. A.↗
NASA NTRS1986

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Nicolaides, R. A.↗
NASA NTRS1987

Experience in grid optimization

Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.

Mastin, C. W.↗