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At least 1,567 records · Page 87
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

On the passage of radiation through inhomogeneous, moving media. VIII - Ray paths and fluxes in a plane differentially sheared medium

We give a detailed discussion of the group-velocity ray paths in a plane differentially sheared medium with constant index of refraction as measured by a local inertial observer. For a given velocity profile the numerical ray paths are presented graphically for several representative cases. Assuming that the medium has a volume emissivity and that a given flux of radiation is incident at the base of the medium, the flux of radiation leaving the slab as a function of exit angle is calculated and presented in the same representative cases. Peaks and discontinuities in the flux generally appear at given exit angles, but their locations and the half-widths of the peaks depend sensitively on the index of refraction.

Lee, M. A.↗
NASA NTRS1974

Rigid and differential rotation driven by oscillations within the sun

Long-period oscillations involving the entire mass of the sun rotate like rigid bodies, and their oscillatory power is distributed nonuniformly across the solar surface. A mostly qualitative theory is constructed showing how the oscillations drive convective flows of global scale, which then organize photospheric and coronal magnetic fields into patterns which rotate rigidly. The convection rises along long graceful curves, creating the magnetic-arcade structures in the corona and unipolar photospheric regions on each side by dynamo action. These are thought to be the origin of the sector structure in the solar wind. The rigid patterns of convective upwelling also force nonrigid horizontal winds on the solar surface. Under the action of the Coriolis force, the main horizontal motions are converted into polar and equatorial wind currents which have the proper directions to drive the differential rotation long observed on the sun's surface.

Wolff, C. L.↗
NASA NTRS1974

Discretized partial differential equations - Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Brockett, R. W.↗
NASA NTRS1975

On an integro-differential equation model for the study of the response of an acoustically coupled panel

The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.

Yen, D. H. Y.↗
NASA NTRS1975

Differential spectra and phase space densities of trapped electrons at Jupiter

Using Pioneer 10 data, differential spectra and phase-space densities have been constructed for trapped electrons at Jupiter. These quantities should assist in calculating synchrotron radiation from these particles and in evaluating the diffusion mechanisms that accelerate the particles. Absorption by the moons Io and Europa is evident, and injection by Io is demonstrated by a density peak in phase space, which demands a local source. There is also a rapid decrease in density between the moons, which could call for either a local loss mechanism or nonlocal losses fed by diffusion.

Mcilwain, C. E.↗
NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗
NASA NTRS1975

Some properties of extremal solutions of zero-sum differential games

Necessary conditions for infinite-time linear-quadratic two-player differential games with perfect state information are examined in the light of Willems' work on the algebraic Riccati equation. Necessary conditions for the nonzero-sum game do not always reduce precisely to those of the zero-sum game, when the weighting parameters of the cost index are taken as those of a zero-sum game. Formulation of zero-sum game problems in extended L2-spaces reveals the existence of nonstabilizing but infimal controls, and explicit frequency-domain conditions for existence of solutions and stabilizing solutions are established through the algebraic Riccati equation (ARE).

Johnson, T. L.↗
NASA NTRS1975

Curved branching crystals and differentiation in comb-layered rocks

An investigation is conducted concerning two common features of comb layered rocks. Attention is given to the curvature of oriented, elongate, branching crystals and the tendency to form highly differentiated layers. Crystallization studies of plagioclase show that some degree of supercooling is necessary to produce the skeletal, curved, and branching plagioclase crystal morphologies found in comb-layered rocks and that curved crystals can be grown without the presence of a directed stress.

Lofgren, G. E.↗
NASA NTRS1974

Apollo 17 petrology and experimental determination of differentiation sequences in model moon compositions

Experimental studies of model moon compositions are discussed, taking into account questions related to the differentiation of the outer layer of the moon. Phase relations for a series of proposed lunar compositions have been determined and a petrographic and electron microprobe study was conducted on four Apollo 17 samples. Two of the samples consist of high-titanium mare basalts, one includes crushed anorthosite and gabbro, and another contains blue-gray breccia.

Hodges, F. N.↗
NASA NTRS1977

Differential-optoacoustic absorption detector

Two-cell spectrophone detects trace amounts of atmospheric pollutants by measuring absorption coefficients of gases with various laser sources. Device measures pressure difference between two tapered cells with differential manometer. Background signal is reduced by balanced window heating and balanced carrier gas absorption in two cells.

Shumate, M. S.↗
NASA NTRS1975

Study of viscous flow about airfoils by the integro-differential method

An integro-differential method was used for numerically solving unsteady incompressible viscous flow problems. A computer program was prepared to solve the problem of an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000. Some of the results obtained for this problem were discussed and compared with related work completed previously. Two numerical procedures were used, an Alternating Direction Implicit (ADI) method and a Successive Line Relaxation (SLR) method. Generally, the ADI solution agrees well with the SLR solution and with previous results are stations away from the trailing edge. At the trailing edge station, the ADI solution differs substantially from previous results, while the vorticity profiles obtained from the SLR method there are in good qualitative agreement with previous results.

Wu, J. C.↗
NASA NTRS1975

Computer simulation of an aircraft-based differential absorption and scattering system for retrieval of SO2 vertical profiles

The feasibility of using the differential absorption and scattering technique from aircraft altitudes for remotely measuring the vertical distribution of SO2 was studied via a computer simulation. Particular care was taken in this simulation to use system parameters (i.e., laser energy, telescope size, etc.) which can be accommodated on an aircraft and can be realized with commercially available technology. The vertical molecular and aerosol profiles were chosen to simulate the types of profiles which might be experienced over a large city. Results are presented on the retrieval of the assumed SO2 profile which show the effects of systematic errors due to interfering gases and aerosols, as well as random errors due to shot noise in the return signal, detector and background noise, and instrument-generated noise.

Hoell, J. M., Jr.↗
NASA NTRS1976

The reduction of aileron operating force by differential linkage

It is shown that the control force of ordinary ailerons may be reduced to zero over a range of deflections and at a given flight condition by the use of an appropriate differential movement. Approximations to the ideal motion obtainable with a simple linkage are discussed and a chart that enables the selection of an appropriate crank arrangement is presented. Various aspects of the practical application of the system are discussed and it is concluded that a small fixed tab, deflected to trim both ailerons upward, would be advantageous.

Jones, R. T.↗
NASA NTRS1976

Proton and deuteron double differential cross sections at angles from 10 deg to 60 deg from Be, C, Al, Fe, Cu, Ge, W, and Pb under 558-MeV-proton irradiation

The double differential cross sections for the production of protons and deuterons from targets of Be, C, Al, Fe, Cu, Ge, W, and Pb were obtained at laboratory angles of scatter of 10, 20, 30, 40, 50, and 60 degrees for 558-MeV incident protons. The position of the quasi-elastic peak, discernible in the cross sections up to approximately 40 degrees, corresponded closely to the theoretical predictions for proton-proton elastic scattering at 558 MeV. The mean ratio of deuteron to proton energy-integrated cross sections was 0.056 + or - 0.008. The dependence of energy-integrated cross sections for both protons and deuterons on target mass number A varied from A to the 1/3 power at 10 degrees to A to the 2/3 power above approximately 30 degrees. The ratio of energy-integrated deuteron cross sections for quasielastic processes to that for reactions yielding a deuteron-pi-meson pair was approximately 10 percent.

Beck, S. M.↗
NASA NTRS1976

The Adams formulas for numerical integration of differential equations from 1st to 20th order

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

Kirkpatrick, J. C.↗
NASA NTRS1976

Solution to the differential equation for combined radiative and convective cooling for a heated sphere

A solution is presented for the differential equation relating the combined effects of radiative and forced convective cooling for a heated sphere. The equation has the form where T and t are the variables temperature and time, respectively, and K sub o, T sub o, and H are constants. The solution can be used as a guideline for the design and understanding of space processing phenomena.

Wills, F. D.↗
NASA NTRS1976

Application of a helicopter mathematical model to the Langley differential maneuvering simulator for use in a helicopter/fighter evasive maneuver study

A real time simulation study was conducted using a differential maneuvering simulator to determine and evaluate helicopter evasive maneuvers when attacked by fighter aircraft. A general helicopter mathematical model was modified to represent an H-53 helicopter. The helicopter model was compared to H-53 flight test data to determine any differences between the simulated and actual vehicles. The simulated helicopter was also subjectively validated by participating pilots. Two fighter mathematical models validated in previous studies were utilized for the attacking aircraft. The results of this simulation study have been verified in a flight test program conducted by the U. S. Air Force and were found to closely match the flight results.

Houck, J. A.↗