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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

Spiridonov, Vyacheslav↗
NASA NTRS1992

Structural relations for time-dependent intermediate shocks

A quantitative description of time-dependent (MHD) intermediate shocks is formulated. In non-coplanar Riemann problems, time-dependent 2 yields 3 intermediate shocks evolve in time as a localized self-similar structure whose strength decreases as 1/sq rt t, and whose width expands as sq rt t. We derive structural relations, similar to Rankine-Hugoniot relations, between the plasma properties and the magnitude of the transverse magnetic field, which we hope can help identify time-dependent 2 yields 3 intermediate shocks at the magnetopause, in the solar wind, and elsewhere in space. The analytic forms of the structural relations agree with our numerical results.

Wu, C. C.↗
NASA NTRS1993

Streamwise vortex meander in a plane mixing layer

Previous measurements in a two-stream plane mixing layer have shown that the mean streamwise vorticity decays monotonically with downstream distance such that it is absent in the far-field (self-similar) region. It was not clear at that time if this measured decay was a result of actual vortex diffusion or increasing vortex meander within the mixing layer. The present experimental study was conducted in order to determine the existence of streamwise vortex meander in a mixing layer, and if present, its significance on the measured properties. The dependence of the velocity cross-correlation on the fixed probe location is considered a good indicator of the stationarity of the streamwise vortex location. The cross-correlation measurements obtained here indicate that the spanwise meander is negligible while the transverse apparent meander (normal to the plane of the mixing layer) is relatively large.

Leboeuf, Richard L.↗
NASA NTRS1993

Centrifugally driven winds from protostellar disks. I - Wind model and thermal structure

The thermal structure of a wind that is centrifugally driven from the surface of a protostellar disk is studied. A generalized version of the Blandford and Payne self-similar wind model is introduced, and the temperature and ionization distributions in the outflow are investigated. For the evolution of atomic winds, the heat equation and the rate equations that describe the ionization and excitation state of hydrogen are solved self-consistently. Ambipolar diffusion is found to be a robust mechanism for heating the gas. In the more powerful outflows, molecular hydrogen is collisionally dissociated close to the disk surface, and hydrogen is mainly atomic within a few astronomical units from the central source. It is also demonstrated that these outflows have enough momentum to lift dust grains from the disk surface.

Safier, Pedro N.↗
NASA NTRS1992

Search for deterministic pulse trends in gamma ray burst temporal profiles

Most cosmic gamma-ray burst temporal profiles appear to be comprised of several individual pulses, many of which overlap. It is advantageous to deconvolve the temporal structures into their constituent pulses, and thereby investigate the shape, intensity and temporal distributions of the pulses as a function of energy. Such fundamental pulse descriptors would provide constraints for theoretical modeling of the burst emission process, such as indications of source size, optical depth and geometry, as a function of time. We have developed a deconvolution algorithm which treats sequences of pulse shapes that change deterministically. The algorithm, a generalization of autoregressive techniques, has been applied to a few bright bursts observed by BATSE. Results indicate that, even within short intervals, constituent pulses are not self-similarly shaped, nor do pulse shapes evolve in a simple manner throughout a burst. Hence, the direction of our future work on pulse deconvolution will focus on analysis methods which allow pulse shape to vary.

Norris, J. P.↗
NASA NTRS1993

Real group velocity in a medium with dissipation

In order to clarify the role of the imaginary term Im(d(omega)/dk), the motion of a wave packet in a dissipative, homogeneous medium is examined. The integral representation of the packet is analyzed by means of a saddle-point method. It is shown that in a moving frame attached to its maximum the packet looks self-similar. A Gaussian packet keeps its Gaussian identity, as is typical for the case of a nondissipative medium. The central wave number of the packet slowly changes because of a different damping among the Fourier components. Simple 'ray-tracing equations' are derived to follow the packet centers in coordinate and Fourier spaces. The analysis is illustrated with a comparison to geometric optics, and with two applications: the case of a medium with some resonant damping (or growth) and the propagation of whistler waves in a collisional plasma.

Muschietti, L.↗
NASA NTRS1991

Wave interactions with continuous fractal layers

Many natural structures possess self-similar multiscales which can be characterized by power law spectra. Under appropriate conditions, knowledge of the strength of these scale sizes provides information on the physical processes which formed these objects. In this paper, we investigate wave interactions with continuous fractal layers which model geological and variegated structures. Since fractal characteristics of the layers are embedded in the scattered field, they can be retrieved under appropriate conditions. This inversion can be performed in either the frequency or the time domain as desired.

Kim, Y.↗
NASA NTRS1993

A small-scale turbulence model

A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2D cross section flow, which may be obtained numerically. Examples are given in which a k exp -5/3 spectrum is obtained by this method. The k exp -5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.

Lundgren, T. S.↗
NASA NTRS1993

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Degani, A. T.↗
NASA NTRS1988

Fatigue damage criteria - Matrix, fibers and interfaces of continuous fiber reinforced metal matrix composites

Continuous fiber reinforced metal matrix composites (MMC) are projected for use in high temperature, stiffness critical parts that will be subjected to cyclic loadings. Depending on the relative fatigue behavior of the fiber and matrix, and the interface properties, the failure modes of MMC can be grouped into four catagories: (1) matrix dominated, (2) fiber dominated, (3) self-similar damage growth, and (4) fiber/matrix interfacial failures. These four types of damage are discussed and illustrated by examples. The emphasis is on the fatigue of unnotched laminates.

Johnson, W. S.↗
NASA NTRS1993

The small amplitude magnetohydrodynamic Riemann problem

The small-amplitude MHD Riemann problem is studied using the Cohen-Kulsrud-Burgers equations. Unlike the coplanar Riemann problem, the evolution of noncoplanar Riemann problems is not self-similar and its flow structures could change in time. But its large-time behavior is very simple and a time-dependent 2 - 3 intermediate shock is always involved for the noncoplanar field rotations. The time-dependent 2 - 3 intermediate shock has a well-defined structure and exists for any degree of field rotation.

Wu, C. C.↗
NASA NTRS1993

Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere

The nonlinear evolution of an emerging magnetic flux tube or sheet in the solar atmosphere is studied through 3D MHD simulations. In the initial state, a horizontal magnetic flux sheet or tube is assumed to be embedded at the bottom of MHD two isothermal gas layers, which approximate the solar photosphere/chromosphere and the corona. The magnetic flux sheet or tube is unstable against the undular mode of the magnetic buoyancy instability. The magnetic loop rises due to the linear and then later nonlinear instabilities caused by the buoyancy enhanced by precipitating the gas along magnetic field lines. We find by 3D simulation that during the ascendance of loops the bundle of flux tubes or even the flux sheet develops into dense gas filaments pinched between magnetic loops. The interchange modes help produce a fine fiber flux structure perpendicular to the magnetic field direction in the linear stage, while the undular modes determine the overall buoyant loop structure. The expansion of such a bundle of magnetic loops follows the self-similar behavior observed in 2D cases studied earlier. Our study finds the threshold flux for arch filament system (AFS) formation to be about 0.3 x 10 exp 20 Mx.

Matsumoto, R.↗
NASA NTRS1993

Fractal dimensions of rampart impact craters on Mars

Ejecta blanket morphologies of Martian rampart craters may yield important clues to the atmospheric densities during impact, and the nature of target materials (e.g., hard rock, fine-grained sediments, presence of volatiles). In general, the morphologies of such craters suggest emplacement by a fluidized, ground hugging flow instead of ballistic emplacement by dry ejecta. We have quantitatively characterized the shape of the margins of the ejecta blankets of 15 rampart craters using fractal geometry. Our preliminary results suggest that the craters are fractals and are self-similar over scales of approximately 0.1 km to 30 km. Fractal dimensions (a measure of the extent to which a line fills a plane) range from 1.06 to 1.31. No correlations of fractal dimension with target type, elevation, or crater size were observed, though the data base is small. The range in fractal dimension and lack of correlation may be due to a complex interplay of target properties (grain size, volatile content), atmospheric pressure, and crater size. The mere fact that the ejecta margins are fractals, however, indicates that viscosity and yield strength of the ejecta were at least as low as those of basalts, because silicic lava flows are not generally fractals.

Ching, Delwyn↗
NASA NTRS1992

A small-scale turbulence model

A model for the small-scale structure of turbulence is reformulated in such a way that it may be conveniently computed. The model is an ensemble of randomly oriented structured two dimensional vortices stretched by an axially symmetric strain flow. The energy spectrum of the resulting flow may be expressed as a time integral involving only the enstrophy spectrum of the time evolving two-dimensional cross section flow, which may be obtained numerically. Examples are given in which a k(exp -5/3) spectrum is obtained by this method without using large wave number asymptotic analysis. The k(exp -5/3) inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the two-dimensional enstrophy spectrum. The results are insensitive to time dependence of the strain-rate, including even intermittent on-or-off strains.

Lundgren, T. S.↗
NASA NTRS1992

Multi-resolution processing for fractal analysis of airborne remotely sensed data

Fractal geometry is increasingly becoming a useful tool for modeling natural phenomenon. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Since they are characterized by self-similarity, an ideal fractal surface is scale-independent; i.e. at different scales a fractal surface looks the same. This is not exactly true for natural surfaces. When viewed at different spatial resolutions parts of natural surfaces look alike in a statistical manner and only for a limited range of scales. Images acquired by NASA's Thermal Infrared Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension - Schelberg's line-divider method, the variogram method, and the triangular prism method. A description of these methods and the results of applying these methods to a remotely-sensed image is also presented. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected was the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. This corresponds to 3 different pixel sizes - 5m, 15m, and 30m. After, simulating different spatial sampling intervals within the same image for each of the 3 image sets, the results are cross-correlated to compare the extent of detail and complexity that is obtained when data is taken at lower spatial intervals.

Jaggi, S.↗
NASA NTRS1993

Investigation of the asymptotic state of rotating turbulence using large-eddy simulation

Study of turbulent flows in rotating reference frames has long been an area of considerable scientific and engineering interest. Because of its importance, the subject of turbulence in rotating reference frames has motivated over the years a large number of theoretical, experimental, and computational studies. The bulk of these previous works has served to demonstrate that the effect of system rotation on turbulence is subtle and remains exceedingly difficult to predict. A rotating flow of particular interest in many studies, including the present work, is examination of the effect of solid-body rotation on an initially isotropic turbulent flow. One of the principal reasons for the interest in this flow is that it represents the most basic turbulent flow whose structure is altered by system rotation but without the complicating effects introduced by mean strains or flow inhomogeneities. The assumption of statistical homogeneity considerably simplifies analysis and computation. The principal objective of the present study has been to examine the asymptotic state of solid-body rotation applied to an initially isotropic, high Reynolds number turbulent flow. Of particular interest has been to determine the degree of two-dimensionalization and the existence of asymptotic self-similar states in homogeneous rotating turbulence.

Squires, Kyle D.↗
NASA NTRS1992

Buckling behavior of long symmetrically laminated plates subjected to combined loads

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are axial tension and compression, transverse tension and compression, and shear. Results obtained using a special purpose analysis, well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered, it is found that the buckling coefficients of infinitely long plates are independent of the bending stiffness ratio (D sub 11/D sub 22) sup 1/4.

Nemeth, Michael P.↗
NASA NTRS1989

Cross correlation and length scales in turbulent flows near surfaces

Two kinds of length scales are used in turbulent flows; 'functional length scales' such as mixing length, dissipation length L(sub epsilon), etc., and 'flow-field length scales' derived from cross correlations of velocity, pressure, etc. in the flow. Some connection between these scales are derived here. We first consider the cross correlation R(sub vv)(y,y(sub 1)) of the normal components u at two heights y, y(sub 1) above a rigid surface, normalized by the velocity y(sub 1) (greater than y). For shear-free boundary layers it is found theoretically, and in field and numerical experiments that R(sub vv) approximately equals y/y(sub 1). For shear layers it is also found that R(sub vv) approximately equals f(y/y(sub 1)) less than or equal to y,y(sub 1). This function f differs slightly between low Reynolds number numerical simulations and field experiments. The lateral structure defined by R(sub vv)(y,r(sub 3); y(sub 1),0) is also self similar and shows that the eddies centered at about y(sub 1) appear to have constant lateral width a(sub 3) above and below y(sub 1), where a(sub 3, sup +) approximately equals 7+1/(1.4dU(sup +)/dy(sup +)), when normalized on u(sub *) and v, where U is the mean velocity. Results for L(sub epsilon, sup -1) from direct numerical simulation are found to compare well with the formula L(sub epsilon, sup -1) = A(sub B)/y + A(sub S)dU/dy/v, for unidirectional and reversing turbulent boundary layers and channel flow, except near where dU/dy approximately equals 0. The conclusion is that the large-scale eddy structure and length scales in these flows are determined by a combination of shear and blocking, and that the vertical component of turbulence has a self-similar structure in both kinds of boundary layer.

Hunt, J. C. R.↗