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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Mirror Instability in the Solar Wind: The Theory Revisited

"Magnetic holes", localized depressions in the interplanetary magnetic field, have been identified in Ulysses data over a range of several AU and as far as 23 degrees south in latitude by Winterhalter et al., who concluded that these structures are most likely the remnants of structures caused by occasional mirror-mode instability in the solar wind. However, these authors, like a number of previous investigators, used the mirror stability criterion derived from the kinetic theory under very special assumptions. On the other hand, theoretical investigations using the fully self-consistent kinetic theory (Vlasov-Maxwell equations) have shown that the mirror stability criterion is more complicated when electrons and ions have different anisotropies, as is normally the case in the solar wind. Winterhalter et al used an instability criterion of the form R is greater than 1, where R is a function of the thermal anisotropy; the correct criterion (for bi-Maxwellian distributions) is R R is greater than 1 - x(exp 2), where x is a real quantity that depends on both the proton anisotropy and electron anisotropy. So nonzero x would modify the Winterhalter et al results in the direction of reinforcing their conclusions. We have revisited the instability criterion in its most general form, allowing for (a) non-Maxwellian velocity distributions, (b) multiple ion species, and (c) interparticle streaming. These results should give sound theoretical grounding for future observational studies related to the mirror instability, by Ulysses and other spacecraft.

Barnes, A.↗
NASA NTRS2001

Effect of Roller Profile on Cylindrical Roller Bearing Life Prediction: Comparison of Bearing Life Theories - Part 1

Four rolling-element bearing life theories were chosen for analysis and compared for a simple roller-race geometry model. The life theories were those of Weibull; Lundberg and Palmgren; Ioannides and Harris; and Zaretsky. The analysis without a fatigue limit of Ioannides and Harris is identical to the Lundberg and Palmgren analysis, and the Weibull analysis is similar to that of Zaretsky if the exponents are chosen to be identical. The resultant predicted life a each stress condition not only depends on the life equation used but also on the Weibull slope assumed. The least variation in predicted life with Weibull slope comes with the Zaretsky equation. Except for a Weibull slope of 1.11, at which the Weibull equation predicts the highest lives, the highest lives are predicted for the Zaretsky equation. For Weibull slopes of 1.5 and 2, both the Lundherg-Palmgren and Ioannides-Harris (where tau(sub u) = 0) equations predict lower lives than the ANSI/ABMA/ISO standard. Based upon the Hertz stresses for line contact, the accepted load-life exponent of 10/3 results in a maximum Hertz stress-life exponent equal to 6.6. This value is inconsistent with that experienced in the field. The assumption of as shear stress fatigue limit tau(sub u) results in Hertz stress-life exponents greater than are experimentally verifiable.

Poplawski, Joseph V.↗
NASA NTRS2002

Applicability of the Continuum-Shell Theories to the Mechanics of Carbon Nanotubes

Validity of the assumptions relating the applicability of continuum shell theories to the global mechanical behavior of carbon nanotubes is examined. The present study focuses on providing a basis that can be used to qualitatively assess the appropriateness of continuum-shell models for nanotubes. To address the effect of nanotube structure on their deformation, all nanotube geometries are divided into four major classes that require distinct models. Criteria for the applicability of continuum models are presented. The key parameters that control the buckling strains and deformation modes of these classes of nanotubes are determined. In an analogy with continuum mechanics, mechanical laws of geometric similitude are presented. A parametric map is constructed for a variety of nanotube geometries as a guide for the applicability of different models. The continuum assumptions made in representing a nanotube as a homogeneous thin shell are analyzed to identify possible limitations of applying shell theories and using their bifurcation-buckling equations at the nano-scale.

Harik, V. M.↗
NASA NTRS2002

A Thermodynamic Theory of Solid Viscoelasticity. Part 3: Nonlinear Glassy Viscoelasticity, Stability Constraints, Specifications

This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.

Freed, Alan↗
NASA NTRS1920

Theory of Lifting Surfaces

A mathematical model is presented towards a theory of lifting and resistance on wings. It consists of a theory of multiplanes, conditions of flow at a great distance from the wing, lifting systems of minimum resistance, and free stream and stream limited by walls.

Prandtl, L.↗
NASA NTRS2003

Impact Tsunami Calculations: Hydrodynamical Simulations vs. Linear Theory

Tsunamis generated by the impacts of asteroids and comets into the Earth oceans are widely recognized as a potential catastrophic hazard to the Earth s population. Our general conclusion is that linear theory is a reasonably accurate guide to behavior of tsunamis generated by impactors of moderate size, where the initial transient impact cavity is of moderate depth compared to the ocean depth. This is particularly the case for long wavelength waves that propagate fastest and would reach coastlines first. Such tsunamis would be generated in the open ocean by impactors of 300 meters in diameter, which might be expected to strike the Earth once every few thousand years, on the average. Larger impactors produce cavities deep enough to reach the ocean floor; even here, linear theory is applicable if the starting point is chosen at a later phase in the calculation when the impact crater has slumped back to produce a cavity of moderate depth and slope.

Korycansky, E.↗
NASA NTRS2003

Solar System Test of Gravitational Theories

We are engaged in testing gravitational theory, mainly using observations of objects in the solar system and mainly on the interplanetary scale. Our goal is either to detect departures from the standard model (general relativity) - if any exist within the level of sensitivity of our data - or to place tighter bounds on such departures. For this project, we have analyzed a combination of observational data with our model of the solar system, including primarily planetary radar ranging, lunar laser ranging, and spacecraft tracking, but also including both pulsar timing and pulsar VLBI measurements. In the past year, we have included new data in the analysis, primarily tracking data from the Mars Pathfinder mission. Although these data are relatively few in number, they extend the time span of high-precision tracking on the surface of Mars from six years to over 20. As a result, the statistical standard deviation of our estimate of Mars precession rate has nearly halved, and the rest of the parameters in our solar-system model have experienced a corresponding, albeit smaller, improvement (about 20% for t,he relevant asteroid masses, 10% for the semimajor axis of Mars orbit, and smaller amounts for most other parameters). In the coming year, we plan to continue adding data to our set, as available. Ne 2 expect to use these data and improved models to obtain estimates of the gravitational- theory parameters and to publish these results.

Shapiro, Irwin I.↗
NASA NTRS2004

Thermo-Elastic Triangular Sandwich Element for the Complete Stress Field Based on a Single-Layer Theory

This study presents a new triangular finite element for modeling thick sandwich panels, subjected to thermo-mechanical loading, based on a {3,2}-order single-layer plate theory. A hybrid energy functional is employed in the derivation of the element because of a C interelement continuity requirement. The single-layer theory is based on five weighted-average field variables arising from the cubic and quadratic representations of the in-plane and transverse displacement fields, respectively. The variations of temperature and distributed loading acting on the top and bottom surfaces are non-uniform. The temperature varies linearly through the thickness.

Das, M.↗
NASA NTRS2004

Product Distribution Theory and Semi-Coordinate Transformations

Product Distribution (PD) theory is a new framework for doing distributed adaptive control of a multiagent system (MAS). We introduce the technique of "coordinate transformations" in PD theory gradient descent. These transformations selectively couple a few agents with each other into "meta-agents". Intuitively, this can be viewed as a generalization of forming binding contracts between those agents. Doing this sacrifices a bit of the distributed nature of the MAS, in that there must now be communication from multiple agents in determining what joint-move is finally implemented However, as we demonstrate in computer experiments, these transformations improve the performance of the MAS.

Airiau, Stephane↗
NASA NTRS1997

An analysis of the metabolic theory of the origin of the genetic code

A computer program was used to test Wong's coevolution theory of the genetic code. The codon correlations between the codons of biosynthetically related amino acids in the universal genetic code and in randomly generated genetic codes were compared. It was determined that many codon correlations are also present within random genetic codes and that among the random codes there are always several which have many more correlations than that found in the universal code. Although the number of correlations depends on the choice of biosynthetically related amino acids, the probability of choosing a random genetic code with the same or greater number of codon correlations as the universal genetic code was found to vary from 0.1% to 34% (with respect to a fairly complete listing of related amino acids). Thus, Wong's theory that the genetic code arose by coevolution with the biosynthetic pathways of amino acids, based on codon correlations between biosynthetically related amino acids, is statistical in nature.

NASA Discipline Exobiology↗
NASA NTRS1949

Theory of Characteristics

The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.

Tollmien, W.↗
NASA NTRS2004

Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.

Freed, alan D.↗
NASA NTRS2005

Recent Applications of the Volterra Theory to Aeroelastic Phenomena

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in experimental aeroelasticity are reviewed. These results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the Active Aeroelastic Wing (AAW) aircraft.

Silva, Walter A.↗
NASA NTRS2005

What Information Theory Says about Bounded Rational Best Response

Probability Collectives (PC) provides the information-theoretic extension of conventional full-rationality game theory to bounded rational games. Here an explicit solution to the equations giving the bounded rationality equilibrium of a game is presented. Then PC is used to investigate games in which the players use bounded rational best-response strategies. Next it is shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. It is then shown that for team (shared-payoff) games, this variant of replicator dynamics is identical to Newton-Raphson iterative optimization of the shared utility function.

Wolpert, David H.↗
NASA NTRS2005

Microwave Signatures of Melting/Refreezing Snow: Observations and Modeling Using Dense Medium Radiative Transfer Theory

Microwave brightness temperatures of snow covered terrains can be modeled by means of the Dense Radiative Transfer Medium Theory (DMRT). In a dense medium, such as snow, the assumption of independent scattering is no longer valid and the scattering of correlated scatterers must be considered. In the DMRT, this is done considering a pair distribution function of the particles position. In the electromagnetic model, the snowpack is simulated as a homogeneous layer having effective permittivity and albedo calculated through the DMRT. In order to account for clustering of snow crystals, a model of cohesive particles can be applied, where the cohesion between the particles is described by means of a dimensionless parameters called stickiness (z), representing a measure of the inversion of the attraction of the particles. The lower the z the higher the stickiness. In this study, microwave signatures of melting and refreezing cycles of seasonal snowpacks at high altitudes are studied by means of both experimental and modeling tools. Radiometric data were collected 24 hours per day by the University of Michigan Tower Mounted Radiometer System (TMRS). The brightness temperatures collected by means of the TMRS are simulated by means of a multi-layer electromagnetic model based on the dense medium theory with the inputs to the model derived from the data collected at the snow pits and from the meteorological station. The paper is structured as follows: in the first Section the temperature profiles recorded by the meteorological station and the snow pit data are presented and analyzed; in the second Section, the characteristics of the radiometric system used to collect the brightness temperatures are reported together with the temporal behavior of the recorded brightness temperatures; in the successive Section the multi-layer DMRT-based electromagnetic model is described; in the fourth Section the comparison between modeled and measured brightness temperatures is discussed. We dedicate the last Section to the conclusions and future works.

Tedesco, Marco↗
NASA NTRS1997

A Simplified Theory of Coupled Oscillator Array Phase Control

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

Pogorzelski, R. J.↗
NASA NTRS2006

Magneto-thermo-elastokinetics of Geometrically Nonlinear Laminated Composite Plates. Part 1: Foundation of the Theory

A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.

Hasanyan, Davresh↗