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NASA NTRS1974

Optimal filter design subject to output sidelobe constraints - Theoretical considerations

The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and duality theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures.

Fortmann, T. E.↗
NASA NTRS1975

A sudden increase in the X-ray flux from Centaurus A

Observations from OSO-7 show that the X-ray flux from Cen A increased by a factor of at least 1.6 over a six-day period in April 1973. Long-term observations indicate greater increases and a hardening of the spectrum. The maximum flux exceeded that measured by Tucker et al. and Lampton et al. in 1970 and 1971 by factors of 6.7 in the 2- to 10-keV range and 14 in the 10- to 50-keV range. Both rapid variability and a harder spectrum are consistent with a model proposed by Grindlay (1975). At maximum brightness, the best-fit spectrum leads to a luminosity of 1.1 x 10 to the 43rd power ergs/s in the 2- to 10-kev range.

Winkler, P. F., Jr.↗
NASA NTRS1976

Radiative cooling of a low-density plasma

The paper extends and improves the radiative cooling coefficient calculations of Cox and Tucker (1969) and Cox and Daltabuit (1971) for a low-density optically thin plasma with no molecules or dust, of cosmic abundances in the range from 10,000 to 100,000,000 K. Earlier rates applied to a plasma containing H, He, C, N, O, Ne, Mg, Si, and S; the present study added Ca, Fe, and Ni. For the elements included, many individual lines are calculated which previously has been averaged together. The cooling processes considered are permitted, forbidden, and semiforbidden line transitions, including contributions from dielectronic recombination and bremsstrahlung, radiative recombination, and two-photon continua. The ionization balance is calculated in collisional equilibrium using an approximate auto-ionization following inner-shell excitation and the low-density limit for the dielectronic recombination rate. Cooling in various observational bands in the soft X-ray region is determined.

Raymond, J. C.↗
NASA NTRS1976

Optimization of multi-constrained structures based on optimality criteria

A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Rizzi, P.↗
NASA NTRS1976

Accretion by galaxy clusters and the relationship between X-ray luminosity and velocity dispersion

A relationship between X-ray luminosity and cluster velocity dispersion is derived, which improves on the results of Solinger and Tucker (1972) in several important respects, and a simple model for primordial gas accretion by a cluster of galaxies is described. It is argued that the accreted gas may be causally related to the occurrence of a central active radio or giant cD or galaxy in X-ray clusters. Accretion and subsequent dissipation lead to a decrease with time in the amount of hot gas and in the X-ray luminosity as well as to an increase in mass of the dominant central galaxy.

Silk, J.↗
NASA NTRS1977

Computation of transonic boattail flow with separation

The relaxation procedure of South and Jameson for the full potential transonic flow equation was coupled to a modified Reshotko-Tucker integral boundary-layer technique with an empirical model for separated flow. The viscous and inviscid flows were solved iteratively until convergence was obtained. This iterative method was then applied to the subsonic and transonic flow over a series of axisymmetric circular-arc boattails with solid jet plume simulators. Comparisons of theoretical and experimental surface pressures and boattail drag are presented over a free-stream Mach numbers below 0.90. The qualitative variation of boattail drag with free-stream Mach number and boattail angle well into the region of transonic drag rise was correctly predicted; however, the absolute drag levels were significantly underpredicted. For separated flows, the empirical discriminating streamline model gives good results up to a free-stream Mach number of about 0.90 and allows reasonable predictions for shock-induced separation if the proper separation location and separation turning angle are known.

Wilmoth, R. G.↗
NASA NTRS1978

Curvilinear projection developments

Gradient projection is a powerful algorithm for minimization of a function subject to constraints. Constraint nonlinearities hamper projection computations. The constraints must then be restored before another projection cycle. The restoration steps taken in the process of following nonlinear constraint surfaces can be used as a guide to the construction of a curve which more nearly follows the constraints than does the straight line in the projected gradient direction. This scheme, termed 'curvilinear projection', was explored in earlier research. The study presently reported carries out some computational experiments using a related version of the technique. Some other details of projection computations which turn out to be practically important are taken up: rules for updating the variable metric in projection when early termination of the one-dimensional search on constraint violation occurs, and active-constraint logic for screening inequalities that makes use of the Kuhn-Tucker necessary conditions.

Kelley, H. J.↗
NASA NTRS1978

An algorithm for optimal structural design with frequency constraints

The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.

Kiusalaas, J.↗
NASA NTRS1978

Utilization of independent solar flux measurements to eliminate nongeochemical variation in X-ray fluorescence data

It is shown that the direct method of solar activity correction for lunar XRF data produces XRF data with better statistics than uncorrected data. Direct measurements of the solar flux made by Solrad 10 are converted to emissions of the sun from two assumed temperature regions. These emissions are ratioed to produce emission measure ratios, sensitive indicators of shifts in solar activity. The Tucker-Koren model (1971) of the solar flux is used in the calculation of EMRs and in the calculation of theoretical lunar Si, Al, and Mg fluorescence of maria and highland soils. Al/Si(Mg/Si) ratios calculated at a 'normal' EMR of 0.030 are divided by Al/Si(Mg/Si) ratios at particular EMRs. The relationship between EMR and the quotients of this division, called 'correction factors', is well explained by empirically derived power law functions.

Clark, P. E.↗
NASA NTRS1980

Predicting propulsion system drag

DONBOL computer program analytically predicts axisymmetric nozzle afterbody pressure distributions and drag. Predictions are based on Neumann solution for inviscid external flow coupled with modified Reshotko-Tucker integral boundary layer technique, control volume method of Presz for calculating flow in separated region, and inviscid one dimensional solution for jet exhaust flow. Comparisons with experimental data indicate program accurately predicts pressure distributions of boattail afterbodies for which jet exhaust plume can be simulated by solid body. For other configurations, nozzle pressure drag seems to be significantly underpredicted. Method is limited to subsonic free stream mach numbers below those for which flow over body becomes sonic.

Putnam, L. E.↗
NASA NTRS1980

HEAO 1 observations of active coronae in main-sequence and subgiant stars

The HEAO 1 data has been searched for evidence of X-ray emission from 105 bright late-type stars of luminosity classes IV and V, selected on the basis of indirect optical evidence of the presence of a hot corona. Six of the target stars were detected at the 3-standard deviation level and 15 were coincident with 2-standard deviation X-ray sources. On a statistical basis no more than 5 of these 21 sources are spurious, and the probability that the identification with the class of active chromosphere stars is spurious is less than 0.00001. The sources lie near a line of X-ray/bolometric luminosity ratio = 0.0001, similar to a solar plage, and it is concluded that the most active coronae of late-type stars which are not members of close binary systems are being observed. The RS CVn systems discovered to date seem to form a distinct class of coronal X-ray sources, but the lowest X-ray luminosity members of the group, of which Capella may be the prototype, appear to overlap the domain of these single stars with active coronae. The data do not fit the coronal model of Gorenstein and Tucker (1976), but they are consistent with the coronal loop model of Rosner et al. (1978) as extended by Walter et al. (1980).

Walter, F. M.↗
NASA NTRS1980

Magnetic fields and coronal heating

General considerations concerning the scaling properties of magnetic-field-related coronal heating mechanisms are used to build a two-parameter model for the heating of closed coronal regions. The model predicts the way in which coronal temperature and electron density are related to photospheric magnetic field strength and the size of the region, using the additional constraint provided by the scaling law of Rosner, Tucker, and Vaiana. The model duplicates the observed scaling of total thermal energy content with total longitudinal flux; it also predicts a relation between the coronal energy density (or pressure) and the longitudinal field strength modified by the region scale size.

Golub, L.↗
NASA NTRS1981

Effect of thermal conduction and radiation on the dynamics of a flaring coronal loop

A systematic study of the effects of thermal conduction and radiation (Cox-Tucker type) on the dynamic response of a coronal loop is presented. The study is based on a one-fluid hydrodynamic description of a magnetic flux loop subject to a sudden localized heating, simulating the flare energy release. Numerical results are obtained for the heating of a full loop at one end and symmetrical heating at both ends. The results show that: (1) the basic response is the propagation of a hydrodynamic shock; (2) thermal conduction (Coulomb type) has significant effects; and radiation has only minor influence unless the density exceeds 10 to the 11th per cu cm. It is noted that the uniform flaring of a loop is associated with heating of long duration. Short pulse-like heating results in the nonuniform brightening and propagation of luminous fronts similar to that sometimes observed in flare loops.

Wu, S. T.↗
NASA NTRS1981

Discovery of X-ray emission lines from the RS CVn binary sigma CrB

X-ray observations of the RS CVn binary sigma CrB were carried out with a solid state spectrometer on board the Einstein Observatory in 1979. X-ray emission lines due to Mg XI, Si XIII, S XV and a blend of L-transition lines due to Fe XVII and Fe XVIII were detected in the sigma CrB spectrum. The observed X-ray spectrum is described by a two-temperature coronal X-ray emission model: the dominant low temperature component originates in a plasma at a temperature of 5.9 + or 0.5 x 10 to the 6th K; the weaker higher temperature arises from a plasma of not less than 35 x 10 to the 6th K. Intensity variations over a period of a few hours are also recorded and thought to be due to a variation in the number of loops concentrated around active regions on the star surface. Implications of the results are discussed in terms of the constant-pressure coronal loop model (Rosner, Tucker, Vaiana, 1978).

Agrawal, P. C.↗
NASA NTRS1979

DONBOL: A computer program for predicting axisymmetric nozzle afterbody pressure distributions and drag at subsonic speeds

A Neumann solution for inviscid external flow was coupled to a modified Reshotko-Tucker integral boundary-layer technique, the control volume method of Presz for calculating flow in the separated region, and an inviscid one-dimensional solution for the jet exhaust flow in order to predict axisymmetric nozzle afterbody pressure distributions and drag. The viscous and inviscid flows are solved iteratively until convergence is obtained. A computer algorithm of this procedure was written and is called DONBOL. A description of the computer program and a guide to its use is given. Comparisons of the predictions of this method with experiments show that the method accurately predicts the pressure distributions of boattail afterbodies which have the jet exhaust flow simulated by solid bodies. For nozzle configurations which have the jet exhaust simulated by high-pressure air, the present method significantly underpredicts the magnitude of nozzle pressure drag. This deficiency results because the method neglects the effects of jet plume entrainment. This method is limited to subsonic free-stream Mach numbers below that for which the flow over the body of revolution becomes sonic.

Putnam, L. E.↗
NASA NTRS1982

Collaborative research in tunneling and field emission pumped surface wave local oscillators and amplifiers for infrared and submillimeter wavelengths under director's discretionary fund

Progress is reported in work towards the development of surface wave sources for the infrared and sub-millimeter portion of the spectrum to be based upon electron pumping by tunneling electrons in metal-barrier-metal or metal-barrier-semiconductor devices. Tunneling phenomena and the coupling of radiation to tunnel junctions were studied. The propagation characteristics of surface electro-magnetic modes in metal-insulator-p(++) semiconductor structures as a function of frequency were calculated. A model for the gain process based upon Tucker's formalism was developed and used to estimate what low frequency gain might be expected from such structures. The question of gain was addressed from a more fundamental viewpoint using the method of Lasher and Stern.

Gustafson, T. K.↗
NASA NTRS1984

Efficient calculation of optimum design sensitivity

Two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented. The first-order method uses gradient information to estimate the required sensitivity. The second-order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter. It is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter. This discontinuity is accounted for in the present methods. These methods are compared to a previous approach based on the Kuhn-Tucker necessary conditions for optimality. It is shown that the present methods provide the appropriate sensitivity information in an efficient manner. The methods are demonstrated by a structural synthesis example.

Vanderplaats, G. N.↗
NASA NTRS1985

A general numerical analysis of the superconducting quasiparticle mixer

For very low noise millimeter-wave receivers, the superconductor-insulator-superconductor (SIS) quasiparticle mixer is now competitive with conventional Schottky mixers. Tucker (1979, 1980) has developed a quantum theory of mixing which has provided a basis for the rapid improvement in SIS mixer performance. The present paper is concerned with a general method of numerical analysis for SIS mixers which allows arbitrary terminating impedances for all the harmonic frequencies. This analysis provides an approach for an examination of the range of validity of the three-frequency results of the quantum mixer theory. The new method has been implemented with the aid of a Fortran computer program.

Hicks, R. G.↗