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NASA NTRS1990

Astrophysical fractals - An overview and prospects

Different astrophysical circumstances under which fractal structures have been identified so far, or are likely to be identified in the future, are reviewed. The observed fractals can be classified into 2 main groups: (1) fractal configurations in space-time, materializing as fractals defined over the time axis at a given position in space, or over the physical configuration space at a fixed instant in time; and (2) fractals in parameter spaces. The theoretical interpretation of the origin of the spatial fractal geometry of the most conspicuous 'irregular' astronomical bodies is still wanting in the context of standard continuum models. In contrast, the less conventional discrete models (cellular automata) naturally produce such spatially fractal structures.

Perdang, J.↗

NASA NTRS1991

A fully Galerkin method for the recovery of stiffness and damping parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness and damping parameters in Euler-Bernoulli beam models is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which converges exponentially and is valid on the infinite time interval. Hence the method avoids the time-stepping which is characteristic of many of the forward schemes which are used in parameter recovery algorithms. Tikhonov regularization is used to stabilize the resulting inverse problem, and the L-curve method for determining an appropriate value of the regularization parameter is briefly discussed. Numerical examples are given which demonstrate the applicability of the method for both individual and simultaneous recovery of the material parameters.

Smith, R. C.↗

NASA NTRS1978

Photoelectrons in the upper atmosphere - A formulation incorporating effects of transport

A technique for solving the problem of photoelectron spatial transport and spectral degradation is presented. The developed model, which allows for a relatively complete description of the relevant transport and collisional physics, can be applied to study processes at either low or high altitude, and may be used to investigate interhemispheric transport. The technique involves dividing the spatial dimension into a set of discrete ordinates and calculating the photoelectron intensity for a specific energy at each point in space and at a set of angle points. The selected range of the energy spectrum was covered completely by a set of energy bins, and the photoelectron intensity in the highest energy bin was calculated first by assuming that the only source term was derived from photoionization. The method is similar to a method used in radiative transfer theory. Spatial and angular redistribution of electrons play a dominant role at heights above 400 km.

Prather, M. J.↗

NASA NTRS1975

Application of spatial features to satellite land-use analysis

A Level I land-use analysis of selected training areas of the Colorado Front Range was carried out using digital ERTS-A satellite imagery. Level I land-use categories included urban, agriculture (irrigated and dryland farming), rangeland, and forests. The spatial variations in spectral response for these land-use classes were analyzed using discrete two-dimensional Fourier transforms to isolate and extract spatial features. Analysis was performed on ERTS frame 1352-17134 (July 10, 1973) and frame number 1388-17131 (August 15, 1973). On training sets, spatial features yielded 80 to 100 percent classification accuracies with commission errors ranging from 0 to 20 percent.

Smith, J.↗

NASA NTRS1974

Efficient stream distributions in radiative transfer theory

This paper discusses a new, computationally-efficient method for approximating the integro-differential equation of radiative transfer with a finite set of coupled differential equations for discrete streams. The method uses recommended spatial distributions of streams that are quite different from those typically used in that they are based on the symmetry of several regular Platonic solids. To facilitate the use of such distributions, an explicit, one-parameter relationship between the physical radiance and the abstract stream is formulated. The parameter is used to determine the minimum number of streams required in the radiative transfer model. Accuracy and computational efficiency are shown to be served best by choosing a stream distribution that is invariant to a large number of three space rotations. For various values of the above-mentioned parameter, the resulting recommended stream distribution is shown to be more computationally efficient than more conventional stream distributions. Finally, the incorporation of polarization in the stream definition is described.

Whitney, C.↗

NASA NTRS1978

Application of the finite element method to rotary-wing aeroelasticity

Recent research in rotary-wing aeroelasticity has indicated that all fundamental problems in this area are inherently nonlinear. The non-linearities in this problem are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration the method is applied to the coupled flap-lag problem of a helicopter rotor blade in hover. Comparison of the solutions with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary-wing aeroelastic stability or response problems.

Friedmann, P.↗

NASA NTRS1982

Infrared array detectors

Arrays of detectors sensitive to infrared radiation will enable astronomical observations to be made with shorter observing times than with discrete detectors and with good relative spatial accuracy. Systems using such arrays are being developed for astronomy in several regions of the electromagnetic spectrum. An example of an infrared system is given here consisting of a 32x32 element bismuth doped silicon charge injection device array that has been used in an astronomical camera.

Arens, J. F.↗

NASA NTRS1988

Geodetic measurement of deformation in California

The very long baseline interferometry (VLBI) measurements made in the western U.S. since 1979 as part of the NASA Crustal Dynamics Project provide discrete samples of the temporal and spatial deformation field. The interpretation of the VLBI-derived rates of deformation requires an examination of geologic information and more densely sampled ground-based geodetic data. In the first two of three related studies embodying this thesis triangulation and trilateration data measured on two regional networks are processed, one in the central Mojave Desert and one in the Coast Ranges east of the San Andreas fault. At the spatial scales spanned by these local geodetic networks, auxiliary geologic and geophysical data have been utilized to examine the relation between measured incremental strain and the accommodation of strain seen in local geological structures, strain release in earthquakes, and principal stress directions inferred from in situ measurements. In the third study, VLBI data from stations distributed across the Pacific - North American plate boundary zone in the western United States are processed. The VLBI data have been used to constrain the integrated rate of deformation across portions of the continental plate boundary in California and to provide a tectonic framework to interpret regional geodetic and geologic studies.

Sauber, Jeanne Marie↗

NASA NTRS1989

Plate motions and deformations from geologic and geodetic data

The very long baseline interferometry (VLBI) measurements made in the western U.S. since 1979 provide discrete samples of the temporal and spatial deformation field. The interpretation of the VLBI derived rates of deformation requires an examination of geologic information and more densely sampled ground based geodetic data. Triangulation and trilateration data measured on two regional networks, one in the central Mojave Desert and one in the Coast Ranges east of the San Andreas fault, were processed. At the spatial scales spanned by these local geodetic networks, auxiliary geologic and geophysical data were utilized to examine the relation between measured incremental strain and the accommodation of strain seen in local geologic structures, strain release in earthquakes, and principal stress directions inferred from in situ measurements. VLBI data was also processed from stations distributed across the Pacific-North America plate boundary zone in the western U.S. The VLBI data were used to constrain the integrated rate of deformation across portions of the continental plate boundary in California and to provide a tectonic framework to interpret regional geodetic and geologic studies.

Jordan, Thomas H.↗

NASA NTRS1989

Geodetic measurement of deformation in California

The very long baseline interferometry (VLBI) measurements made in the western U.S. since 1979 as part of the NASA Crustal Dynamics Project provide discrete samples of the temporal and spatial deformation field. The interpretation of the VLBI-derived rates of deformation requires an examination of geologic information and more densely sampled ground-based geodetic data. In the first two of three related studies, triangulation and trilateration data measured on two regional networks, one in the central Mojave Desert and one in the Coast Ranges east of the San Andreas fault, have been processed. At the spatial scales spanned by these local geodetic networks, auxiliary geologic and geophysical data have been utilized to examine the relation between measured incremental strain and the accommodation of strain seen in local geological structures, strain release in earthquakes, and principal stress directions inferred from in situ measurements. In a third study, the geocentric position vectors from a set of 77 VLBI experiments beginning in October 1982 have been used to estimate the tangential rate of change of station positions in the western U.S. in a North-America-Fixed reference frame.

Sauber, Jeanne↗

NASA NTRS1988

A general association between discrete auroras and ion precipitation from the tail

Observations from the spinning polar-orbiting S3-3 satellite were used to compare the locations of discrete auroral arcs (defined to be regions containing particle distributions consistent with field-aligned potential drops of not less than 0.5 kV) with regions of isotropic ion precipitation. It was found that the regions of discrete aurora are almost exclusively confined to the region of isotropic ion precipitation at all local times studied (polar cap arcs and local times near noon were not considered). It was also found that, throughout the local time interval studied, the discrete aurora was generally associated with spatial structure and boundaries in the precipitating ions, indicating that arc generation may be associated with structure in the particle population within the tail current sheet.

Lyons, L. R.↗

NASA NTRS1990

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Bates, J. R.↗

NASA NTRS1991

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗

NASA NTRS1994

Ground based studies of thermocapillary flows in levitated drops

Analytical studies along with ground-based experiments are presently being carried out in connection with thermocapillary phenomena associated with drops and bubbles in a containerless environment. The effort here focuses on the thermal and the fluid phenomena associated with the local heating of acoustically levitated drops, both at 1-g and at low-g. In particular, the Marangoni effect on drops under conditions of local spot-heating and other types of heating are being studied. With the experiments conducted to date, fairly stable acoustic levitation of drops has been achieved and successful flow visualization by light scattering from smoke particles has been carried out. The results include situations with and without heating. As a preliminary qualitative interpretation of these experimental results, we consider the external flow pattern as a superposition of three discrete circulation cells operating on different spatial scales. The observations of the flow fields also indicate the existence of a steady state torque induced by the streaming flows. The theoretical studies have been concentrated on the analysis of streaming flows in a gaseous medium with the presence of a spherical particle undergoing periodic heating. A matched asymptotic analysis was carried out for small parameters derived from approximations in the high frequency range. The heating frequency being 'in tune' with the acoustic frequency results in a nonzero time-averaged thermal field. This leads to a steady heat flow across the equatorial plane of the sphere.

Sadhal, Satwindar Singh↗

NASA NTRS1994

Performance of customized DCT quantization tables on scientific data

We show that it is desirable to use data-specific or customized quantization tables for scaling the spatial frequency coefficients obtained using the Discrete Cosine Transform (DCT). DCT is widely used for image and video compression (MP89, PM93) but applications typically use default quantization matrices. Using actual scientific data gathered from divers sources such as spacecrafts and electron-microscopes, we show that the default compression/quality tradeoffs can be significantly improved upon by using customized tables. We also show that significant improvements are possible for the standard test images Lena and Baboon. This work is part of an effort to develop a practical scheme for optimizing quantization matrices for any given image or video stream, under any given quality or compression constraints.

Ratnakar, Viresh↗

NASA NTRSDate not supplied

Mapping Process Model Results to Fracture Model Initial Conditions for Adhesive Bonding

A systematic approach is proposed for mapping adhesive bonding process outcomes to initial conditions for progressive damage analysis (PDA). Herein, two mapping procedures are developed: 1) direct mapping for residual stresses, strains, and deformations obtained from a process model; and 2) functional mapping for quantities such as bondline thickness, degree of cure, and porosity that are assumed to have a functional relationship with fracture toughness but are not discretely modeled in the PDA. The spatial distribution of functionally mapped quantities may be determined by process modeling or inspection. The functional maps between the quantity of interest and fracture toughness may be obtained from independent lower-scale numerical simulations or empirical test campaigns. The proposed mapping procedure links the adhesive bonding process to the structural performance. Therefore, by accounting for the effects of bondline nonuniformities in structural analysis, analytical predictive accuracy can be improved, and off-nominal conditions can be evaluated. The mapping procedures are demonstrated and verified with example problems.

Andrew C Bergan↗

NASA NTRSDate not supplied

Mapping Process Model Results to Fracture Model Initial Conditions for Adhesive Bonding

Andrew Bergan↗

NASA NTRS1993

Two-dimensional radiative transfer in cloudy atmospheres - The spherical harmonic spatial grid method

A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.

Evans, K. F.↗