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NASA NTRS1986

A multiaxial theory of viscoplasticity for isotropic materials

Many viscoplastic constitutive models for high temperature structural alloys are based exclusively on uniaxial test data. Generalization to multiaxial states of stress is made by assuming the stress dependence to be on the second principal invariant (J sub 2) of the deviatoric stress, frequently called the effective stress. If such a J sub 2 theory, based on uniaxial testing, is called upon to predict behavior under conditions other than uniaxial, e.g., pure shear, and it does so poorly, nothing is left to adjust in the theory. For a fully isotropic material whose inelastic deformation behavior is relatively independent of hydrostatic stress, the most general stress dependence is on the two (non-zero) principal invariants of the deviatoric stress, J sub 2 and J sub 3. These invariants constitute what is known as an integrity basis for the material. A time dependent constitutive theory with stress dependence on J sub 2 and J sub 3 is presented, that reduces to a known J sub 2 theory as a special case.

Robinson, D. N.↗

NASA NTRS1989

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗

NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗

NASA NTRS1989

Fractals in geology and geophysics

The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

Turcotte, Donald L.↗

NASA NTRS1990

The magnetic pumping of plasmas with sawtooth waveforms

The pumping of plasmas by sawtooth-waveform magnetic induction variations is studied theoretically and by means of computer simulations. A sawtooth is a cycle waveform that is characterized by a slow increase in the magnetic induction followed by a rapid drop in the induction. Two types of sawtooth pumping are analyzed, and the types classified as to whether or not the first adiabatic invariants of the plasma particles are conserved during the rapid drops in the magnetic induction. When the invariants are conserved, the sawtooth waveforms are found to be less efficient than square waves for pumping plasmas. When the adiabatic invariations are not conserved, the pumping efficiency is found to be a slight improvement over square waves. Both types of pumping are applied to a hypothetical tokamak plasma and it is concluded that neither type of sawtooth pumping is practical for heating magnetically confined fusion plasmas.

Borovsky, Joseph E.↗

NASA NTRS1990

Multi-level modulation codes and multi-stage decoding

Multi-level method is a powerful technique for constructing bandwidth efficient modulation codes. It allows the construction of modulation codes systematically with arbitrary large minimum squared Euclidean distance from component codes in conjunction with proper bits-to-signal mapping. If the component codes are chosen properly, the resultant modulation code not only has good minimum squared Euclidean distance but is also rich in structural properties such as: linear structure, phase invariant property, and trellis structure. A modulation code with linear structure has invariant distance distribution. Phase invariant property is useful in resolving carrier-phase ambiguity and ensuring rapid carrier-phase resynchronization after temporary loss of synchronization. It the component codes have trellis structure, the resultant multi-level modulation code also has trellis structure. Trellis structure allows decoding of a multi-level modulation code with the soft-decision Viterbi decoding algorithm. Furthermore, the multi-level structure allows decoding of a multi-level modulation code with the multi-stage decoding. This type of decoding reduces the decoding complexity. Multi-stage decoding is not optimum even though the decoding of each component is optimum. Based on the analysis and simulation results, the difference in error performance between the optimum decoding of the overall multi-level modulation code and the suboptimum multi-stage decoding of the code is very little, a fraction of dB loss.

Lin, Shu↗

NASA NTRS1990

Rapid traversal of an image database using binary synthetic discriminant filters

Pattern recognition invariant to image rotations of up to 75 deg, using a single filter, has been demonstrated for binary synthetic discriminant function (BSDF) optical filters, suggesting their use in directed graph-arranged data bases which can be rapidly traversed by means of a filter-plane programmable spatial light modulator (SLM). The filter data base is arranged as a tree structure in which the root node filters are invariant to over 60 deg rotation, while the leaves are 5-deg invariant. Results are presented from experiments with BSDFs designed to recognize in-plane-rotated views of a Space Shuttle Orbiter. Using a magnetooptic SLM that is driven at 350 Hz in the filter plane, orientation identifications requiring less than 30 msec have been achieved after sequencing through only 10 BSDFs.

Reid, Max B.↗

NASA NTRS1991

Robustness analysis of multirate and periodically time varying systems

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Berg, Martin C.↗

NASA NTRS1991

Energy functions for regularization algorithms

Regularization techniques are widely used for inverse problem solving in computer vision such as surface reconstruction, edge detection, or optical flow estimation. Energy functions used for regularization algorithms measure how smooth a curve or surface is, and to render acceptable solutions these energies must verify certain properties such as invariance with Euclidean transformations or invariance with parameterization. The notion of smoothness energy is extended here to the notion of a differential stabilizer, and it is shown that to void the systematic underestimation of undercurvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. A set of stabilizers is proposed that meet this condition as well as invariance with rotation and parameterization.

Delingette, H.↗

NASA NTRS1994

Kinetic and thermodynamic properties of a convecting plasma in a two-dimensional dipole field

Charged particle guiding center motion is considered in the magnetic field of a two-dimensional ('line') dipole on which is superimposed a small, static, perpendicular electric field. The parallel equation of motion is that of a simple harmonic oscillator for cos theta, the cosine of magnetic colatitude theta. Equations for the perpendicular electric and magnetic drifts are derived as well as their bounce-averaged forms. The latter are solved to yield a bounce-averaged guiding center trajectory, which is the same as that obtained from conversation of magnetic moment mu, longitudinal invariant J, and total (kinetic plus electrostatic) energy K. The algebraic simplicity of the trajectory equations is also manifest in the forms of the invariants. An interesting result is that guiding centers drift in such a way that they preserve the values of their equatorial pitch angles and (equivalently) mirror latitudes. The most general Maxwellian form of the equilibrium one-particle distribution function f is constructed from the invariants, and spatially varying density and pressure moments, parallel and perpendicular to the magnetic field, are identified. Much of the paper deals with the more restricted problem in which f is specified as a bi-Maxwellian over a straight line of finite length in the equatorial plane of the dipole and perpendicular to field lines. This might be thought of as specifying a cross-tail ion injection source; our formalism then describes the subsequent spatial development. The distribution away from the source is a scaled bi-Maxwellian but one that is cut off at large and small kinetic energies, which depend on position. Density and pressure components are reduced from the values they would have if the total content of individual flux tubes convected intact. The equatorial and meridional variations of density and pressure components are examined and compared systematically for the isotropic and highly anisotropic situations. There appears to be little qualitative difference due to anisotropy. An anisotropy measure is defined, and its spatial variation determined as a signature of possible MHD instability. Extreme values are found, larger than at the source, but the plasma beta in such regions is probably so low as to render the effect inconsequential energetically. Finally, the possible consequence of 'nonadia- batic' pressure profiles on electrostatic interchanges is considered, and a boundary delineating stabilizing and destabilizing regions determined.

Huang, T. S.↗

NASA NTRS1996

Symmetries in Turbulent Boundary Layer Flows

The objective is the development of a new theory which enables the algorithmic computation of all self-similar mean velocity profiles. The theory is based on Liegroup analysis and unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the middle of a Couette flow and in the middle of a rotating channel flow, and a new exponential mean velocity profile not previously reported. Experimental results taken in the outer parts of a high Reynolds number flat-plate boundary layer, strongly support the exponential profile. From experimental as well as from DNS data of a turbulent channel flow the algebraic scaling law could be confirmed in both the center region and in the near wall region. In the case of the logarithmic law of the wall, the scaling with the wall distance arises as a result of the analysis and has not been assumed in the derivation. The crucial part of the derivation of all the different mean velocity profiles is to consider the invariance of the equation for the velocity fluctuations at the same time as the invariance of the equation for the velocity product equations. The latter is the dyad product of the velocity fluctuations with the equation for the velocity fluctuations. It has been proven that all the invariant solutions are also consistent with similarity of all velocity moment equations up to any arbitrary order.

Oberlack, M.↗

NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

NASA NTRS2001

Cloud Structure and Cloud-Radiation Interaction: From Smallest Observable Scales (Less than 10 m) to GCM Grid Scales (More than 100 km)

In this presentation we review the fractal nature of internal cloud structure from cm- to km-scales as captured by in-situ probes during long horizontal penetrations by aircraft. We uncover the non-Poissonian spatial distribution of cloud droplets at submeter scales and confirm scale-invariant behavior for large scales. Based on these structural characteristics, we generate simple fractal cloud models that reproduce statistical scaling properties of real clouds. These stochastic models represent a link between nonlinear science, in general, and cloud-radiation interaction, in particular. Next we run three-dimensional radiative transfer computations on these synthetic fractal clouds and compare the structure of the resulting radiation fields with the known structure of the cloud model and with satellite images of real clouds. The different behaviors observed for small and large-scale variabilities will be discussed in detail. We find that while the large-scale fluctuations of the resulting radiation fields resemble those in the original scale-invariant cloud structure, the radiation at small scales is much smoother than its cloud liquid water counterpart. This violates scale-invariance and produces a scale-break at 0.2-0.5 km that is clearly observed in high-resolution satellite data such as from Landsat. Finally, we show how radiative transfer Green function theory in the photon diffusion limit explains (and predicts) the above phenomena of "radiative smoothing."

Marshak, Alexander↗

NASA NTRS1995

Secondary structure in solution of two anti-HIV-1 hammerhead ribozymes as investigated by two-dimensional 1H 500 MHz NMR spectroscopy in water

Two hammerhead chimeric RNA/DNA ribozymes (HRz) were synthesized in pure form. Both were 30 nucleotides long, and the sequences were such that they could be targeted to cleave the HIV-1 gag RNA. Named HRz-W and HRz-M, the former had its invariable core region conserved, the latter had a uridine in the invariable region replaced by a guanine. Their secodary structures were determined by 2D NOESY 1H 500 MHz NMR spectroscopy in 90% water and 10% D2(0), following the imino protons. The data show that both HRz-M and HRz-W form identical secondary structures with stem regions consisting of continuous stacks of AT and GT pairs. An energy minimized computer model of this stem region is provided. The results suggest that the loss of catalytic activity that is known to result when an invariant core residue is replaced is not related to the secondary structure of the ribozymes in the absence of substrate.

NASA Discipline Exobiology↗

NASA NTRS2003

Strength Differential Measured in Inconel 718: Effects of Hydrostatic Pressure Studied

Aeropropulsion components, such as disks, blades, and shafts, are commonly subjected to multiaxial stress states at elevated temperatures. Experimental results from loadings as complex as those experienced in service are needed to help guide the development of accurate viscoplastic, multiaxial deformation models that can be used to improve the design of these components. During a recent study on multiaxial deformation (ref. 1) on a common aerospace material, Inconel 718, it was shown that the material in the aged state exhibits a strength differential effect (SDE), whereby the uniaxial compressive yield and subsequent flow behavior are significantly higher than those in uniaxial tension. Thus, this material cannot be described by a standard von Mises yield formulation. There have been other formulations postulated (ref. 2) that involve other combinations of the stress invariants, including the effect of hydrostatic stress. The question remained as to which invariants are necessary in the flow model. To capture the physical mechanisms occurring during deformation and reflect them in the plasticity formulation, researchers examined the flow of Inconel 718 under various amounts of hydrostatic stress to determine whether or not hydrostatic stress is needed in the formulation. Under NASA Grant NCC3-464, monitored by the NASA Glenn Research Center, a series of tensile tests were conducted at Case Western Reserve University on aged (precipitation hardened) Inconel 718 at 650 C and with superimposed hydrostatic pressure. Dogbone shaped tensile specimens (3-mm-diameter gauge by 16-mm gauge length) and cylindrical compression specimens (3-mm-diameter gauge by 6-mm gauge length) were strain gauged and loaded in a high-pressure testing apparatus. Hydrostatic pressures were obtained with argon and ranged from 210 to 630 MPa. The aged Inconel 718 showed a pronounced difference in the tension and compression yield strength (i.e., an SDE), as previously observed. Also, there were no significant effects of hydrostatic pressure on either the tensile and compressive yield strength (see the graph) or on the magnitude of the SDE. This behavior is not consistent with the pressure-dependent theory of the SDE, which postulates that the SDE is associated with pressure-dependent and/or internal friction dependent deformation associated with non-Schmid effects at the crystal level (refs. 3 and 4). Flow in Inconel 718 appears to be independent of hydrostatic pressure, suggesting that this invariant may be removed from the phenomenological constitutive model. As part of an ongoing effort to develop advanced constitutive models, Glenn s Life Prediction Branch coordinated this work with that of research on the multiaxial deformation behavior of Inconel 718 being conducted at Pennsylvania State University under NASA Grant NCC597.

Lewandowski, John J.↗

NASA NTRS2009

Searching for New Physics with Ultrahigh Energy Cosmic Rays

Ultrahigh energy cosmic rays that produce giant extensive showers of charged particles and photons when they interact in the Earth's atmosphere provide a unique tool to search for new physics. Of particular interest is the possibility of detecting a very small violation of Lorentz invariance such as may be related to the structure of space-time near the Planck scale of approximately 10 (exp -35) m. We discuss here the possible signature of Lorentz invariance violation on the spectrum of ultrahigh energy cosmic rays as compared with present observations of giant air showers. We also discuss the possibilities of using more sensitive detection techniques to improve searches for Lorentz invariance violation in the future. Using the latest data from the Pierre Auger Observatory, we derive a best fit to the LIV parameter of 3 .0 + 1.5 - 3:0 x 10 (exp -23) ,corresponding to an upper limit of 4.5 x 10-23 at a proton Lorentz factor of approximately 2 x 10(exp 11) . This result has fundamental implications for quantum gravity models.

Stecker, Floyd W.↗

NASA NTRS2007

Physical Interpretation of the Correlation Between Multi-Angle Spectral Data and Canopy Height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally

Schull, M. A.↗

NASA NTRS2012

A Traceable Ground to On-Orbit Radiometric Calibration System for the Solar Reflective Wavelength Region

This paper describes the combination of a Mie scattering spectral BSDF and BTDF albedo standard whose calibration is traceable to the NIST SIRCUS Facility or the NIST STARR II Facility. The Space-based Calibration Transfer Spectroradiometer (SCATS) sensor uses a simple, invariant optical configuration and dedicated narrow band spectral channel modules to provide very accurate, polarization-insensitive, stable measurements of earth albedo and lunar disk albedo. Optical degradation effects on calibration stability are eliminated through use of a common optical system for observations of the Sun, Earth, and Moon. The measurements from space would be traceable to SI units through preflight calibrations of radiance and irradiance at NIST's SIRCUS facility and the invariant optical system used in the sensor. Simultaneous measurements are made in multiple spectral channels covering the solar reflective wavelength range of 300 nm to 2.4 microns. The large dynamic range of signals is handled by use of single-element, highly-linear detectors, stable discrete electronic components, and a non imaging optical configuration. Up to 19 spectral modules can be mounted on a single-axis drive to give direct pointing at the Earth and at least once per orbit view of the Sun and Moon. By observing the Sun on every orbit, the most stringent stability requirements of the system are limited to short time periods. The invariant optical system for both radiance and irradiance measurements also give excellent transfer to-orbit SI traceability. Emerging instrumental requirements for remotely sensing tropospheric trace species have led to a rethinking by some of the paradigm for Systeme International d'Unites (SI) traceability of the spectral irradiance and radiance radiometric calibrations to spectral albedo (sr(exp -1)) which is not a SI unit. In the solar reflective wavelength region the spectral albedo calibrations are tied often to either the spectral albedo of a solar diffuser or the Moon. This new type of Mie scattering diffuser (MSD) is capable of withstanding high temperatures, and is more Lambertian than Spectralon(tm). It has the potential of covering the entire solar reflective wavelength region. Laboratory measurements have shown that the specular reflectance component is negligible, and indicate that internal absorption by multiple scattering is small. This MSD, a true volume diffuser, exhibits a high degree of radiometric stability which suggests that measurements at the National Institute of Standards and Technology (NIST) could provide a spectral albedo standard. Measurements have been made of its radiometric stability under a simulated space environment of high energy gamma rays, high energy protons, and UV radiation from ambient down to the vacuum ultraviolet H Lyman alpha at 121.6 nm for its eventual use in space as a solar diffuser.

Heath, Donald F.↗