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NASA NTRS1988

Interior impedance wedge diffraction with surface waves

The exact impedance wedge solution is evaluated asymptotically using the method of steepest descents for plane wave illumination at normal incidence. Uniform but different impedances on each face are considered for both soft and hard polarizations. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, and surface wave fields. Multiply reflected fields of any order are permitted. The multiply reflected fields from the exact solution are written as ratios of auxiliary Maliuzhinets functions, whereas a geometrical analysis gives the reflected fields as products of reflection coefficients. These two representations are shown to be identical in magnitude, phase and the angular range over which they exist. The diffracted field includes four Fresnel transition functions as in the perfect conductor case, and the expressions for the appropriate discontinuities at the shadow boundaries are presented. The surface wave exists over a finite angular range and only for certain surface impedances. A surface wave transition field is included to retain continuity. Computations are presented for interior wedge diffractions although the formulation is valid for both exterior and interior wedges.

Balanis, Constantine A.↗

NASA NTRS1988

The decay of highly excited open strings

The decay rates of leading edge Regge trajectory states are calculated for very high level number in open bosonic string theories, ignoring tachyon final states. The optical theorem simplifies the analysis while enabling identification of the different mass level decay channels. The main result is that (in four dimensions) the greatest single channel is the emission of a single photon and a state of the next mass level down. A simple asymptotic formula for arbitrarily high level number is given for this process. Also calculated is the total decay rate exactly up to N=100. It shows little variation over this range but appears to decrease for larger N. The formalism is checked in examples and the decay rate of the first excited level calculated for open superstring theories. The calculation may also have implications for high spin meson resonances.

Mitchell, D.↗

NASA NTRS1991

On the strain energy of laminated composite plates

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Atilgan, Ali R.↗

NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗

DOE OSTI2023

Spectroscopic survey of faint planetary-nebula nuclei – II. The subdwarf O central star of Fr 2-30

Fr 2-30 = PN? G126.8−15.5 is a faint emission nebula, hosting a 14th-mag central star that we identify here for the first time. Deep Hα and [O III ] images reveal a roughly elliptical nebula with dimensions of at least 22 arcmin × 14 arcmin, fading into a surrounding network of even fainter emission. Optical spectrograms of the central star show it to have a subdwarf O spectral type, with a Gaia parallax distance of 890 pc. A model-atmosphere analysis gives parameters of T eff = 60 000 K, log g = 6.0, and a low helium content of n He /n H = 0.0017. The location of the central star in the log g–T eff plane is inconsistent with a post-asymptotic-giant-branch evolutionary status. Two alternatives are that it is a helium-burning post-extreme-horizontal-branch object, or a hydrogen-burning post-red-giant-branch star. In either case, the evolutionary ages are so long that a detectable planetary nebula (PN) should not be present. We find evidence for a variable radial velocity (RV), suggesting that the star is a close binary. However, there are no photometric variations, and the spectral-energy distribution rules out a companion earlier than M2 V. The RVs of the star and surrounding nebula are discordant, and the nebula lacks typical PN morphology. We suggest that Fr 2-30 is a ‘PN mimic’ – the result of a chance encounter between the hot sdO star and an interstellar cloud. However, we note the puzzling fact that there are several nuclei of genuine PNe that are known to be in evolutionary states similar to that of the Fr 2-30 central star.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1971

Unsteady flow through compressor stages

The application of the nonsteady Lax-Wendroff technique to problems with asymptotically periodic solution which offers a potentially powerful method for the investigation of the interaction of rotating and stationary blade rows in turbomachinery is reported. A technique for specifying boundary conditions with phase lag was developed to accomplish this. A complete nonlinear analysis is carried out numerically to determine the entire flow field without recourse to the assumption of small disturbances of linear equations which underlie the previous acoustic theories. The result, obtained for the case of equal number of rotor and stator blades shows that transonic flow can be handled without difficulty. In addition, the program is not limited with regard to blade thickness, camber or loading. Extension of this method to incorporate viscous wakes and to analysis of fully three dimensional configuration is feasible, and would greatly expand its utility in practical applications.

Alzner, E.↗

NASA NTRS1976

Orbital elements of dust particles intercepted by Pioneers 8 and 9

Results of analysis of the orbital elements of interplanetary dust particles collected by Pioneers 8 and 9 are presented in tabular form. The following conclusions are drawn from the analysis: (1) statistical analysis confirms that the nature of the nominal trajectories is essentially correct, with the most probable elements close to the nominal ones, (2) the elliptic or hyperbolic nature of most orbits is not affected by reasonable density assumptions, and (3) the incoming asymptote of the hyperbolic orbits is consistent with the particles arriving from the apex of the solar motion.

Wolf, H.↗

NASA NTRS1985

Backward boundary layers in downward flame spread

The gas-phase combustion of a vertical fuel slab pyrolyzing at a finite rate under downward flame spread conditions is investigated theoretically. The backward boundary layer character of the flow is exploited, and a transformation that shifts the singularity associated with boundary-layer equations to a location, upstream of flame lift-off, where the surface temperature is nearly ambient, is employed. The boundary-layer flow is matched asymptotically for large Grashof number to a potential flow that allows the flow induced by the flame and along the upstream surface of the fuel bed to be calculated. Gas-phase temperature and velocity predictions are compared to experiment, and although analysis of the gas phase is emphasized, an approximate spread rate, based on a solid-phase energy balance, is calculated.

Vedha-Nayagam, M.↗

NASA NTRS1994

Time-dependent evolution of cosmic-ray-modified shock structure: Transition to steady state

Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.

Donohue, D. J.↗

NASA NTRS1999

Cyclin E-p27 opposition and regulation of the G1 phase of the cell cycle in the murine neocortical PVE: a quantitative analysis of mRNA in situ hybridization

We have analyzed the expression patterns of mRNAs of five cell cycle related proteins in the ventricular zone of the neocortical cerebral wall over the course of the neuronogenetic interval in the mouse. One set of mRNAs (cyclin E and p21) are initially expressed at high levels but expression then falls to a low asymptote. A second set (p27, cyclin B and cdk2) are initially expressed at low levels but ascend to peak levels only to decline again. These patterns divide the overall neuronogenetic interval into three phases. In phase 1 cyclin E and p21 levels of mRNA expression are high, while those of mRNAs of p27, cdk2 and cyclin B are low. In this phase the fraction of cells leaving the cycle after each mitosis, Q, is low and the duration of the G1 phase, TG1, is short. In phase 2 levels of expression of cyclin E and p21 fall to asymptote while levels of expression of mRNA of the other three proteins reach their peaks. Q increases to approach 0.5 and TG1 increases even more rapidly to approach its maximum length. In phase 3 levels of expression of cyclin E and p21 mRNAs remain low and those of the mRNAs of the other three proteins fall. TG1 becomes maximum and Q rapidly increases to 1.0. The character of these phases can be understood in part as consequences of the reciprocal regulatory influence of p27 and cyclin E and of the rate limiting functions of p27 at the restriction point and of cyclin E at the G1 to S transition.

NASA Discipline Cell Biology↗

DOE OSTI2022

Determination of asymptotic normalization coefficients for the channel 16 O→ α+ 12 C: excited state 16 O(0 + ; 6.05 MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1976

Analysis of transonic flow over lifting and oscillating airfoils

Finite element procedures are presented for the numerical solution of transonic flow over lifting and oscillating airfoils based on small disturbance theory. The algorithm is simple and effective in handling the mixed flow problem and, for airfoil in free air, treats the entire flow domain by making use of the far field asymptotic solution. Numerical results are presented and compared with experimental data and those obtained by finite difference relaxation techniques.

Chan, S. T. K.↗

NASA NTRS1982

Numerical analysis of Weyl's method for integrating boundary layer equations

A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.

Najfeld, I.↗

NASA NTRS1972

Stability of large-scale systems with stable and unstable subsystems.

The purpose of this paper is to develop new methods for constructing vector Liapunov functions and broaden the application of Liapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. With minor technical adjustments, the same criterion can be used to determine connective asymptotic stability of large-scale systems subject to structural perturbations. By redefining the constraints imposed on the interconnections among the subsystems, the considered class of systems is broadened in an essential way to include composite systems with unstable subsystems. In this way, the theory is brought substantially closer to reality since stability of all subsystems is no longer a necessary assumption in establishing stability of the overall composite system.

Grujic, Lj. T.↗

DOE OSTI2020

Application of Detectability Analysis for Power System Dynamic State Estimation

To guide the measurement placement and selection for dynamic state estimation in power systems, it is important to determine the existence of an observer that can estimate the dynamic states. Past studies have been focused on observability analysis, which determines whether the initial states can be uniquely determined. In this paper, detectability analysis is proposed to determine whether the current states can be estimated as time involving. Through the proposed detectability analysis, the states of an unobservable system can be categorized into the detectable states and undetectable states. It is shown that if the eigenvalues corresponding to the unobservable states are stable, the states are detectable and their estimates will converge to the true ones asymptotically. The study can be used to guide measurement placement and selection.

Detectability, dynamic state estimation↗

NASA NTRS1992

Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators

A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.

Sicard, Pierre↗

NASA NTRS1973

Analysis of a model for transport of charged particles in a random magnetic field

A model for the transport of charged particles in a random magnetic field is a Volterra integrodifferential equation with a long-range kernel. The integrodifferential equation is solved numerically with the method of Bellman, Kalaba, and Lockett (1966). The results are shown to be in excellent agreement with analytical asymptotic results.-

Hanson, F. B.↗

NASA NTRS1976

Economic analysis of low cost silicon sheet produced from Czochralski grown material

This study shows that the lower limits for manufacturing add-on costs to convert polysilicon to wafers is in the range of $22 to $26/sq m with the cost about equally divided between the crystal growth and wafering processes. However, the $22 to $26/sq m cost limit should be viewed as an asymptote since it is based on multicharge or continuous growth configurations, solidification rates in excess of 2 Kg/hr, multiblade wafering and a slice plus kerf of .045 cm. It should also be emphasized that the results of this study are based on as-sawn wafers, 100% yields (growth and slicing) and no profit. To the first approximation, the limiting cost factors are crucible material and furnace parts for growth and blade material and slurry for slicing.

Koliwad, K. M.↗