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NASA NTRS1987

Algebra and topology for applications to physics

The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.

Rozhkov, S. S.↗

NASA NTRS1986

Two-step excitation and blue fluorescence under continuous-wave pumping in Nd:YLF

Near-UV and blue fluorescence from the 4D3/2 and 4D5/2 manifolds in Nd:YLF has been observed at room temperature under CW pumping by a rhodamine 590 dye laser. Excitation to these manifolds is attributed to two-step excitation involving excited-state absorption from the 4F3/2 metastable level. A similar phenomenon has also been observed in Nd:YAG and Nd:glass. The effective excited-state absorption cross section is measured to be (2 + or - 1) x 10 to the -20th sq cm at 587.4 nm in the pi polarization, and the peak effective stimulated emission cross section is measured to be 5 x 10 to the -20th sq cm at 411.7 nm, also in the pi polarization. Estimated laser threshold at 411.7 nm for two-step pumping at 587.4 nm is 70 mW.

Fan, T. Y.↗

NASA NTRS1988

Quickly Removable Valve

Unit removed with minimal disturbance. Valve inlet and outlet ports adjacent to each other on same side of valve body. Ports inserted into special manifold on fluid line. Valve body attached to manifold by four bolts or, alternatively, by toggle clamps. Electromechanical actuator moves in direction parallel to fluid line to open and close valve. When necessary to clean valve, removed simply by opening bolts or toggle clamps. No need to move or separate ports of fluid line. Valve useful where disturbance of fluid line detrimental or where fast maintenance essential - in oil and chemical industries, automotive vehicles, aircraft, and powerplants.

Robbins, John S.↗

NASA NTRS1987

Analysis of internal flows relative to the space shuttle main engine

Cooperative efforts between the Lockheed-Huntsville Computational Mechanics Group and the NASA-MSFC Computational Fluid Dynamics staff has resulted in improved capabilities for numerically simulating incompressible flows generic to the Space Shuttle Main Engine (SSME). A well established and documented CFD code was obtained, modified, and applied to laminar and turbulent flows of the type occurring in the SSME Hot Gas Manifold. The INS3D code was installed on the NASA-MSFC CRAY-XMP computer system and is currently being used by NASA engineers. Studies to perform a transient analysis of the FPB were conducted. The COBRA/TRAC code is recommended for simulating the transient flow of oxygen into the LOX manifold. Property data for modifying the code to represent LOX/GOX flow was collected. The ALFA code was developed and recommended for representing the transient combustion in the preburner. These two codes will couple through the transient boundary conditions to simulate the startup and/or shutdown of the fuel preburner. A study, NAS8-37461, is currently being conducted to implement this modeling effort.

Source record↗

NASA NTRS1987

Coherent structures and dynamical systems

Any flow of a viscous fluid has a finite number of degrees of freedom, and can therefore be seen as a dynamical system. A coherent structure can be thought of as a lower dimensional manifold in whose neighborhood the dynamical system spends a substantial fraction of its time. If such a manifold exists, and if its dimensionality is substantially lower that that of the full flow, it is conceivable that the flow could be described in terms of the reduced set of degrees of freedom, and that such a description would be simpler than one in which the existence of structure was not recognized. Several examples are briefly summarized.

Jimenez, Javier↗

NASA NTRS1988

The determination of energy transfer rates in the Ho:Tm:Cr:YAG laser material

Energy transfer processes occurring between atomic, ionic, or molecular systems are very widespread in nature. The applications of such processes range form radiation physics and chemistry to biology. In the field of laser physics, energy transfer processes have been used to extend the lasing range, increase the output efficiency, and influence the spectral and temporal characteristics of the output pulses of energy transfer dye lasers or solid-state laser materials. Thus in the development of solid state lasers, it is important to investigate the basic energy transfer (ET) mechanisms and processes in order to gain detailed knowledge so that successful technical utilization can be achieved. The aim of the present research is to measure the ET rate from a given manifold associated with the chromium sensitizer atom to a given manifold in the holmium activator atom via the thulium transfer atom, in the Ho:Cr:YAG laser material.

Koker, Edmond B.↗

NASA NTRS1989

Analysis of regularized Navier-Stokes equations, 2

A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung↗

NASA NTRS1989

Dynamics of a class of vortex rings

The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows.

Shariff, Karim↗

NASA NTRS1990

Space shuttle main engine computed tomography applications

For the past two years the potential applications of computed tomography to the fabrication and overhaul of the Space Shuttle Main Engine were evaluated. Application tests were performed at various government and manufacturer facilities with equipment produced by four different manufacturers. The hardware scanned varied in size and complexity from a small temperature sensor and turbine blades to an assembled heat exchanger and main injector oxidizer inlet manifold. The evaluation of capabilities included the ability to identify and locate internal flaws, measure the depth of surface cracks, measure wall thickness, compare manifold design contours to actual part contours, perform automatic dimensional inspections, generate 3D computer models of actual parts, and image the relationship of the details in a complex assembly. The capabilities evaluated, with the exception of measuring the depth of surface flaws, demonstrated the existing and potential ability to perform many beneficial Space Shuttle Main Engine applications.

Sporny, Richard F.↗

NASA NTRS1989

Dielectric image-resonator multiplexer

A two, three or four channel multiplexer can be operated in the TE 01δ or HE 11δ modes, each channel of the multiplexer has one bandpass filter, with each filter usually having a plurality of cavities. One cavity of each filter is a common cavity with all of the other filters of the multiplexer. The common cavity contains one independent dielectric quarter-cut or half-cut image resonator for each filter representing a channel- of the multiplexer. Each resonator is mounted on a suitable support the common cavity provides a common junction and contains a loop coupling to couple electromagnetic energy between the various· channels. The multiplexer has at least one input and at least one output. Previous microwave multiplexers have a plurality of bandpass filters arranged on a coaxial manifold. With the multiplexer of the present invention, the manifold can be eliminated. Further, at the S-band or L-band, substantial weight and volume savings can be achieved using the multiplexer of the present invention without sacrificing performance. This can be very important for space applications.

Wai-Cheung Tang↗

NASA NTRS1991

Analysis of regularized Navier-Stokes equations. I, II

A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung↗

NASA NTRS1992

Non-Hamiltonian perturbations of integrable systems and resonance trapping

This paper studies general, non-Hamiltonian perturbations of integrable systems with two degrees of freedom and derives conditions for temporary and permanent resonance trapping. The analysis involves a noncanonical transformation of variables near the resonant manifold and averaging with respect to the fast phase to investigate oscillatory behavior on the intermediate timescale. The resulting reduced system is Hamiltonian to leading order and permits, after averaging on the intermediate, or libration, timescale, a canonical transformation to action-angle variables in the oscillation zone. The final system so obtained reveals the possible existence of two- and three-dimensional invariant tori in the vicinity of the resonant manifold. An explicit divergence condition for general perturbations to be dissipative on the slow timescale follows from the analysis. An application of this approach to the problem of resonant trapping and escape is outlined for the restricted problem of three bodies subject to dissipative perturbations with a radial symmetry.

Ghil, M.↗

NASA NTRS1991

Theoretical temperature-dependent branching ratios and laser thresholds of the 3F4 to 3H6 levels of Tm(3+) in ten garnets

The calculated energy levels, the branching ratios, and the estimated thresholds for thulium operating on the 3F4 to 3H6 transitions are reported. Garnet materials with the general formula A3B2C3O12 are evaluated. Calculations are performed for the A side under the assumption of D2 symmetry. X-ray data available in the literature are used to evaluate the crystal-field components, A sub nm. Even-n components are employed to calculate the crystal-field splittings within the manifold. Thermal occupation factors are determined in a straightforward manner using a Boltzmann distribution for the respective manifolds. Odd-n components are applied to calculate the transition probabilities for electric field transitions. It is determined that the magnetic dipole contributions to the transition probability are comparable to the electric dipole contributions in some cases. Thresholds as a function of the density of thulium atoms are calculated.

Filer, Elizabeth D.↗

NASA NTRS1993

Application of incremental unknowns to the Burgers equation

In this article, we make a few remarks on the role that attractors and inertial manifolds play in fluid mechanics problems. We then describe the role of incremental unknowns for approximating attractors and inertial manifolds when finite difference multigrid discretizations are used. The relation with direct numerical simulation and large eddy simulation is also mentioned.

Choi, Haecheon↗

NASA NTRS1993

Heat pipe cooled heat rejection subsystem modelling for nuclear electric propulsion

NASA LeRC is currently developing a FORTRAN based computer model of a complete nuclear electric propulsion (NEP) vehicle that can be used for piloted and cargo missions to the Moon or Mars. Proposed designs feature either a Brayton or a K-Rankine power conversion cycle to drive a turbine coupled with rotary alternators. Both ion and magnetoplasmodynamic (MPD) thrusters will be considered in the model. In support of the NEP model, Rocketdyne is developing power conversion, heat rejection, and power management and distribution (PMAD) subroutines. The subroutines will be incorporated into the NEP vehicle model which will be written by NASA LeRC. The purpose is to document the heat pipe cooled heat rejection subsystem model and its supporting subroutines. The heat pipe cooled heat rejection subsystem model is designed to provide estimate of the mass and performance of the equipment used to reject heat from Brayton and Rankine cycle power conversion systems. The subroutine models the ductwork and heat pipe cooled manifold for a gas cooled Brayton; the heat sink heat exchanger, liquid loop piping, expansion compensator, pump and manifold for a liquid loop cooled Brayton; and a shear flow condenser for a K-Rankine system. In each case, the final heat rejection is made by way of a heat pipe radiator. The radiator is sized to reject the amount of heat necessary.

Moriarty, Michael P.↗

NASA NTRS1993

Scientific goals of the Cooperative Multiscale Experiment (CME)

Mesoscale Convective Systems (MCS) form the focus of CME. Recent developments in global climate models, the urgent need to improve the representation of the physics of convection, radiation, the boundary layer, and orography, and the surge of interest in coupling hydrologic, chemistry, and atmospheric models of various scales, have emphasized the need for a broad interdisciplinary and multi-scale approach to understanding and predicting MCS's and their interactions with processes at other scales. The role of mesoscale systems in the large-scale atmospheric circulation, the representation of organized convection and other mesoscale flux sources in terms of bulk properties, and the mutually consistent treatment of water vapor, clouds, radiation, and precipitation, are all key scientific issues concerning which CME will seek to increase understanding. The manner in which convective, mesoscale, and larger scale processes interact to produce and organize MCS's, the moisture cycling properties of MCS's, and the use of coupled cloud/mesoscale models to better understand these processes, are also major objectives of CME. Particular emphasis will be placed on the multi-scale role of MCS's in the hydrological cycle and in the production and transport of chemical trace constituents. The scientific goals of the CME consist of the following: understand how the large and small scales of motion influence the location, structure, intensity, and life cycles of MCS's; understand processes and conditions that determine the relative roles of balanced (slow manifold) and unbalanced (fast manifold) circulations in the dynamics of MCS's throughout their life cycles; assess the predictability of MCS's and improve the quantitative forecasting of precipitation and severe weather events; quantify the upscale feedback of MCS's to the large-scale environment and determine interrelationships between MCS occurrence and variations in the large-scale flow and surface forcing; provide a data base for initialization and verification of coupled regional, mesoscale/hydrologic, mesoscale/chemistry, and prototype mesoscale/cloud-resolving models for prediction of severe weather, ceilings, and visibility; provide a data base for initialization and validation of cloud-resolving models, and for assisting in the fabrication, calibration, and testing of cloud and MCS parameterization schemes; and provide a data base for validation of four dimensional data assimilation schemes and algorithms for retrieving cloud and state parameters from remote sensing instrumentation.

Cotton, William↗

NASA NTRS1994

The galactic globular cluster system

We explore correlations between various properties of Galactic globular clusters, using a database on 143 objects. Our goal is identify correlations and trends which can be used to test and constrain theoretical models of cluster formation and evolution. We use a set of 13 cluster parameters, 9 of which are independently measured. Several arguments suggest that the number of clusters still missing in the obscured regions of the Galaxy is of the order of 10, and thus the selection effects are probably not severe for our sample. Known clusters follow a power-law density distribution with a slope approximately -3.5 to -4, and an apparent core with a core radius approximately 1 kpc. Clusters show a large dynamical range in many of their properties, more so for the core parameters (which are presumably more affected by dynamical evolution) than for the half-light parameters. There are no good correlations with luminosity, although more luminous clusters tend to be more concentrated. When data are binned in luminosity, several trends emerge: more luminous clusters tend to have smaller and denser cores. We interpret this as a differential survival effect, with more massive clusters surviving longer and reaching more evolved dynamical states. Cluster core parameters and concentrations also correlate with the position in the Galaxy, with clusters closer to the Galactic center or plane being more concentrated and having smaller and denser cores. These trends are more pronounced for the fainter (less massive) clusters. This is in agreement with a picture where tidal shocks form disk or bulge passages accelerate dynamical evolution of clusters. Cluster metallicities do not correlate with any other parameter, including luminosity and velocity dispersion; the only detectable trend is with the position in the Galaxy, probably reflecting Zinn's disk-halo dichotomy. This suggests that globular clusters were not self-enriched systems. Velocity dispersions show excellent correlations with luminosity and surface brightness. Their origin is not well understood, but they may well reflect initial conditions of cluster formation, and perhaps even be used to probe the initial density perturbation spectrum on a approximately 10(exp 6) solar mass scale. Core radii and concentrations play a role of a 'second parameter' in these correlations. While a global manifold of cluster properties has a high statistical dimensionality (D greater than 4), a subset of structural, photometric, and dynamical parameters forms a statistically three-dimensional family, as expected from objects following King models; we propose to call this set of quantities the King Manifold. Some of the observed correlations may be usable as distance indicator relations for globular clusters.

Djorgovski, S.↗

NASA NTRS2000

Microgravity Isolation Control System Design Via High-Order Sliding Mode Control

Vibration isolation control system design for a microgravity experiment mount is considered. The controller design based on dynamic sliding manifold (DSM) technique is proposed to attenuate the accelerations transmitted to an isolated experiment mount either from a vibrating base or directly generated by the experiment, as well as to stabilize the internal dynamics of this nonminimum phase plant. An auxiliary DSM is employed to maintain the high-order sliding mode on the primary sliding manifold in the presence of uncertain actuator dynamics of second order. The primary DSM is designed for the closed-loop system in sliding mode to be a filter with given characteristics with respect to the input external disturbances.

Shkolnikov, Ilya↗