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NASA NTRS1998

Effect of the thickness variation and initial imperfection on buckling of composite cylindrical shells: Asymptotic analysis and numerical results by BOSOR4 and PANDA2

This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.

Li, Yi-Wei↗

NASA NTRS1998

Asymptotic Spreading Rate of Initially Compressible Jets: Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub J). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub J), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗

NASA NTRS1999

Asymptotic Stability of Interconnected Passive Non-Linear Systems

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Isidori, A.↗

NASA NTRS1998

Asymptotic Spreading Rate of Initially Compressible Jets-Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub j). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub j), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗

NASA NTRS1998

Characterization of Asymptotic Entrainment Rate for Compressible Jets

Experimental results for the spreading and centerline velocity decay rates are presented for round, compressible, submerged jets, with total temperature same as ambient temperature, covering a 'jet Mach number' (M(sub J)) range of 0.3 - 2.0. Data from a convergent and a convergent-divergent nozzle are considered. The spreading rate is determined from the total longitudinal mass fluxes measured by Pilot probe survey. Results for the far asymptotic regions show that both spreading and centerline velocity decay rates, when normalized by conditions at the nozzle exit, decrease with increasing M(sub J). Dimensional analysis and isentropic calculations predict this Mach number dependence well. The analysis also demonstrates that an increase in the 'potential core length' of the jet occurring with increasing M(sub J), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗

NASA NTRS1996

On the High-Frequency Asymptotic Evaluation of the Potentials of Elemental Sources on an Anisotropic Impedance Cylinder

In an effort to formulate the high-frequency coupling between antennas located on airframes composed of multilayer imperfectly conducting materials a general model was sought which would embody the electromagnetic properties of the layers and would apply over a broader range of separations of the antennas. Such a model is described here. This work is a generalization of the work of Pearson [1986, 1987a] concerning the high-frequency asymptotic representation of the fields of elemental sources diffracted by a multilayer cylinder. In that work the source and field points were located off the cylinder surface, and they were sufficiently separated to permit the effective use of the residue series representation of the spectral integrals involved. Here the source and field points are located on the cylinder surface and are permitted to be sufficiently close as to render the residue series poorly convergent. To obtain a more effective representation in this situation, the cylinder is modeled by an anisotropic impedance cylinder, and the resulting spectral integrals are evaluated by reduction to forms amenable to multiple applications of techniques described in the literature in connection with treatment of axially uniform sources in this context.

Pogorzelski, Ronald J.↗

NASA NTRS2001

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the transverse magnetic (TM) or the transverse electric (TE) wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3x2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.

Yang, Ping↗

NASA NTRS1991

Asymptotic expansions of the hydrogenic radial dipole integral

A method is presented for an asymptotic expansion of the hydrogenic radial dipole integral for discrete-discrete transitions from initial state n'l' to final state nl. The advantage of this simple method is that it allows all the necessary algebraic manipulations to be done by the computer programming package REDUCE-2. Expansion coefficients up to the coefficient of the l/n17 term are obtained for all initial states with n' < or = 10. However, only the coefficients which are not calculated by Klarsfeld are tabulated in this paper.

NASA Discipline Radiation Health↗

NASA NTRS2006

Asymptotic Parachute Performance Sensitivity

In 2010, the Mars Science Laboratory mission will pioneer the next generation of robotic Entry, Descent, and Landing systems by delivering the largest and most capable rover to date to the surface of Mars. In addition to landing more mass than any other mission to Mars, Mars Science Laboratory will also provide scientists with unprecedented access to regions of Mars that have been previously unreachable. By providing an Entry, Descent, and Landing system capable of landing at altitudes as high as 2 km above the reference gravitational equipotential surface, or areoid, as defined by the Mars Orbiting Laser Altimeter program, Mars Science Laboratory will demonstrate sufficient performance to land on 83% of the planet s surface. By contrast, the highest altitude landing to date on Mars has been the Mars Exploration Rover at 1.3 km below the areoid. The coupling of this improved altitude performance with latitude limits as large as 60 degrees off of the equator and a precise delivery to within 10 km of a surface target, will allow the science community to select the Mars Science Laboratory landing site from thousands of scientifically interesting possibilities. In meeting these requirements, Mars Science Laboratory is extending the limits of the Entry, Descent, and Landing technologies qualified by the Mars Viking, Mars Pathfinder, and Mars Exploration Rover missions. Specifically, the drag deceleration provided by a Viking-heritage 16.15 m supersonic Disk-Gap-Band parachute in the thin atmosphere of Mars is insufficient, at the altitudes and ballistic coefficients under consideration by the Mars Science Laboratory project, to maintain necessary altitude performance and timeline margin. This paper defines and discusses the asymptotic parachute performance observed in Monte Carlo simulation and performance analysis and its effect on the Mars Science Laboratory Entry, Descent, and Landing architecture.

Way, David W.↗

NASA NTRS2004

A chemical route to the formation of water in circumstellar envelopes around carbon-rich asymptotic branch stars: Fischer-Tropsch catalysis

Fischer-Tropsch catalysis has been suggested as a means of driving hydrocarbon chemistry in oxygen rich regions such as the protosolar nebula. In addition to producing hydrocarbons, Fischer-Tropsch catalysis also produces water, and it is therefore possible that such processes could account for the recent observations of water in the circumstellar envelope of asymptotic giant branch star IRC +10216.

astrochemistry molecular data giant branch stars↗

NASA NTRS2007

On an Asymptotically Consistent Unsteady Interacting Boundary Layer

This paper develops the asymptotic matching of an unsteady compressible boundary layer to an inviscid flow. Of particular importance is the velocity injection or transpiration boundary condition derived by this theory. It is found that in general the transpiration will contain a slope of the displacement thickness and a time derivative of a density integral. The conditions under which the second term may be neglected, and its consistency with the established results of interacting boundary layer are discussed.

Bartels, Robert E.↗

NASA NTRS2007

Asymptotic Energies and QED Shifts for Rydberg States of Helium

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.

Drake, G.W.F.↗

NASA NTRS2010

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗

NASA NTRS2013

The Contribution of Thermally-Pulsing Asymptotic Giant Branch and Red Supergiant Starts to the Luminosities of the Magellanic Clouds at 1-24 micrometers

We present the near-through mid-infrared flux contribution of thermally-pulsing asymptotic giant branch (TP-AGB) and massive red supergiant (RSG) stars to the luminosities of the Large and Small Magellanic Clouds (LMC and SMC, respectively). Combined, the peak contribution from these cool evolved stars occurs at approx 3 - 4 micron, where they produce 32% of the SMC light, and 25% of the LMC flux. The TP-AGB star contribution also peaks at approx 3 - 4 micron and amounts to 21% in both galaxies. The contribution from RSG stars peaks at shorter wavelengths, 2.2 micron, where they provide 11% of the SMC flux, and 7% for the LMC. Both TP-AGB and RSG stars are short lived, and thus potentially impose a large stochastic scatter on the near-IR derived mass-to-light (M/L) ratios of galaxies at rest-frame 1 - 4 micron. To minimize their impact on stellar mass estimates, one can use the M/L ratio at shorter wavelengths (e.g., at 0.8 - 1 micron). At longer wavelengths (much > 8 micron), emission from dust in the interstellar medium dominates the flux. In the LMC, which shows strong polycyclic aromatic hydrocarbon (PAH) emission at 8 micron, TP-AGB and RSG contribute less than 4% of the 8 micron flux. However, 19% of the SMC 8 micron flux is from evolved stars, nearly half of which is produced by the rarest, dustiest, carbon-rich TP-AGB stars. Thus, star formation rates of galaxies, based on an 8 micron flux (e.g., observed-frame 24 micron at z = 2), may be biased modestly high, especially for galaxies with little PAH emission.

Melbourne, J.↗

NASA NTRS2013

Extended Analytic Device Optimization Employing Asymptotic Expansion

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Thermoelectric Generators↗

NASA NTRS2014

A Spitzer Space Telescope Survey of Extreme Asymptotic Giant Branch Stars in M32

We investigate the population of cool, evolved stars in the Local Group dwarf elliptical galaxy M32, using Infrared Array Camera observations from the Spitzer Space Telescope. We construct deep mid-infrared colour-magnitude diagrams for the resolved stellar populations within 3.5 arcminutes of M32's centre, and identify those stars that exhibit infrared excess. Our data is dominated by a population of luminous, dustproducing stars on the asymptotic giant branch (AGB) and extend to approximately 3 magnitudes below the AGB tip. We detect for the first time a sizeable population of 'extreme' AGB stars, highly enshrouded by circumstellar dust and likely completely obscured at optical wavelengths. The total dust-injection rate from the extreme AGB candidates is measured to be 7.5 x 10 (sup −7) solar masses per year, corresponding to a gas mass-loss rate of 1.5 x 10 (sup −4) solar masses per year. These extreme stars may be indicative of an extended star-formation epoch between 0.2 and 5 billion years ago.

Space↗

DOE OSTI2022

Selected results from full-core hydrogen redistribution asymptotic analysis in YH-moderated heat-pipe cooled microreactor

Yttrium hydride is the main candidate for moderation of high temperature nuclear microreactors . This is due to its high thermal stability and relatively high hydrogen retention at temperatures exceeding 870 C. One of the main issues associated with the use of yttrium hydride is that, when exposed to temperature, stress, or concentration gradients, the hydrogen contained in the metallic matrix tends to redistribute and leak from the moderating elements, potentially leading to reactivity losses and power swings. This paper is focused on presenting selected results from the asymptotic hydrogen redistribution analysis performed on the Simplified Microreactor Benchmark Assessment (SiMBA) problem, a microreactor core conceptual design developed at INL. The analysis is based on full core analysis, relies uniquely on Bison to perform hydrogen redistribution calculations, and discusses the physical causes of the reactivity feedback. It was found that the feedback is negative, but it is one order of magnitude lower than the one found for the empire reactor unit-cell. This is due to the lower axial temperature gradient together with the effect of the reflector.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation

Here, we study reproducing kernel (RK) collocation method for peridynamic Navier equation. In the first part, we apply a linear RK approximation to both displacement and dilatation, and then back-substitute dilatation and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit for a fixed nonlocal interaction length and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. In the second part, we apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lamé parameters satisfy λ ≥ μ to avoid extra assumptions on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.

42 ENGINEERING↗