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NASA NTRS1993

A Simulation Atlas of Tidal Features in Galaxies

Detailed simulations of tidally induced structure in disk galaxies have either concentrated on specific systems or consisted of a few encounters with relatively small numbers of particles and no self-gravity. Observers need a 'dictionary' of simulations that covers many encounter parameters with fine morphological resolution and includes effects of self-gravitation. Observers can then search the dictionary for the parameters that best match a particular observed morphology. Alternatively, the dictionary can be used with observational samples for statistical studies of system parameters. To fill this need, we present a survey of model tidal encounters using a self-gravitating, 180,000 particle, two-component ('stars' and 'gas') disk. A wide variety of fascinating morphologies results. There are 86 different encounters that vary orbit tilt, perigalacticon distance, galaxy to companion mass ratio, and the amount of halo dark matter relative to the disk. For morphological comparisons, over 1700 images of the entire survey are available in video form. While there is a rich variety of tidal structure covering much of this parameter space, some general patterns may be remarked. There is a strong orbital inclination dependence of the symmetry of tidal patterns, most symmetric for planar orbits and nearly one-sided for polar encounters. Retrograde encounters produce only broad fanlike global patterns, but rich small-scale internal structure. In both kinds of encounter, our numerical resolution allows us to track internal spiral structure driven by the outer material arms, especially in the lighter halo simulations. We note also that polar encounters generate series of expanding, essentially non-rotating loops resembling shell structures in some respects.

Howard, Sethanne↗

NASA NTRS2001

Observations of Circumstellar Material Around Evolved Stars With the ISI

The U.C. Berkeley Infrared Spatial Interferometer (ISI) is a stellar interferometer operating in the 9-12 micron region and has been in operation from 1988 until the present. It utilizes heterodyne detection using CO2 laser local oscillators and currently includes two 1.65 m movable telescopes mounted in semi-trailers and baselines up to about 65 m in length. A third telescope is being integrated with the other two and within the next year will operate as an imaging interferometer providing data with three simultaneous baselines and a closure phase, and baselines up to about 75 m. During the past twelve years the ISI has been used extensively for studies of circumstellar material around evolved stars. Multi-epoch observations of a sample of prototypical sources have elucidated the location and time scales for dust formation around these stars. These time scales can be as short as approx.10 years for Mira stars and as long as approx. 100 years for supergiants. For stars like Mira itself there is evidence for departure from spherical symmetry and episodes of dust formation and destruction. For some stars motion of dust has been observed -- IK Tau is one example, and NML Cyg is another. The molecules Silane and Ammonia were observed for the extreme carbon star IRC +10216 and the supergiant VY CMa pinpointing their location relative to the inner radius of the dust shell. Somewhat surprisingly, these molecules were found to form many stellar radii away from the inner radius of the dust shell, implying that they form by interactions with the surfaces of dust grains. Last year observations with the longest baselines lead to new precision diameters of $o$ Ceti and $\alpha$ Orionis, and are continuing on a somewhat larger set of Mira variable and supergiant stars.

Danchi, W. C.↗

NASA NTRS1980

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 1: Analysis

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled system of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered.

Lu, M. C.↗

NASA NTRS1983

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. I Analysis. II - Solution and results

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled systems of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered. Previously announced in STAR as N80-18428 and N80-18429

Lu, M.-C.↗

NASA NTRS1995

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Osherovich, V. A.↗

NASA NTRS1990

Crystallization of proteins by dynamic control of supersaturation

The growth of protein crystals is known to be the limiting factor in the determination of the three-dimensional structures of most proteins. It is expected that the kinetics of supersaturation, which is directly related to solvent evaporation, will affect protein crystal growth and nucleation and accordingly determine the quality, number, size, and morphology of the crystals. With a technique that controls the evaporation of solvent from a protein solution with N2(g) it is possible to determine the effect of different evaporation profiles on hen egg white lysozyme crystals. Hen egg white lysozyme was chosen as the model protein because it crystallizes easily and has solubility data available for most salt, pH, and temperature ranges. Commercially available lysozyme was further purified by a number of methods. Crystals grown with the purified lysozyme and with the unpurified lysozyme in citrate buffer were different shapes but were found to be of the same symmetry space group by precession photos. Differences were seen in the lysozyme crystals grown using different evaporation rates. At three of the four initial conditions for lysozyme crystal growth, longer evaporation times yielded better crystals. The evaporation times required to see a change in the appearance of the crystals was much longer than expected. The number of rates studied so far represent only a small fraction of the ones now available with the gas evaporation device. The technique also provides for control of both solution pH and temperature which are related to the solubilities of proteins.

Wilson, Lori June↗

NASA NTRS1984

Stability of a dual-spin spacecraft with spherical dampers

The present investigation is concerned with the stability characteristics of a specific dual-spin satellite configuration marked by a high degree of symmetry. The configuration includes a platform and a rotor. Both components contain arbitrarily located internal spherical dampers. The symmetry of the system configuration makes it possible to illustrate clearly the relationship between Routhian analysis, energy sink analysis, and digital simulation of the full nonlinear equations. Although the dual-spin spacecraft configuration contains energy dissipating devices on both platform and rotor, it is still possible to employ the rigorous, but relatively simple, Routh stability method. This method, unlike Floquet theory, has the potential of producing closed-form stability criteria. The energy sink method is capable of providing a closed-form stability criterion. Numerical simulation is a necessary requirement in the latter stages of design when the realistic perturbation environment must be considered.

Laskin, R. A.↗

NASA NTRS1992

Sines and Cosines. Part 1 of 3

Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).

Apostol, Tom M.↗

NASA NTRSDate not supplied

Metal Hydroxide and Oxyhydroxide Gas Database

In a high temperature combustion situation such as a gas turbine or rocket engine, combustion products include water vapor. This water vapor reacts with oxides in the hot-gas-path to form volatile hydroxides and oxyhydroxides. The oxides may be structural oxide components or protective oxides on alloys or non-oxide ceramics. In either case, this enhanced volatilization leads to degradation of components. Reliable thermochemical data for many metal hydroxides and oxyhydroxides has not been available. We review a database put together at NASA over many years based on experimental and ab initio computations for thermochemical data of Al, Si, Ti, Cr, Mn, Y, Zr, La, Ta, Gd, and Yb hydroxides and oxyhydroxides. Experimental methods for measuring thermodynamic quantities of metal hydroxides and oxyhydroxides are limited since the required high temperatures and high pressures preclude many conventional methods. Nonetheless, transpiration has proven a valuable tool in our laboratories for the Si-O-H, Cr-O-H, and Ti-O-H systems. Data are analyzed with second and third law methods. These data can be leveraged with quantum chemistry to provide reliable free energy functions for the third law calculation and comparison to the derived enthalpies of formation. Both wave function and DFT methods can be utilized for deriving the thermodynamic functions for the various metal hydroxides and oxyhydroxides. We have found that, in general, reasonable molecular geometries and spectroscopic data can be derived with a relatively low level of theory, i.e. DFT with the B3LYP functional. Accurate calculations of the enthalpy of formation require higher levels of theory, such as the Coupled Cluster, Singles, Doubles, and perturbative Triples CCSD(T) approach with complete basis sets (CBS). Also, corrections for hindered rotations and anharmonicity are necessary. For some symmetries, the anharmonic correction has proven to be a challenge and we have found that this is only treated properly by certain codes. The database lists the fHo(298), So(298), and Cp in the form Cp = A + BT + CT2 + D/T + E/T2, where A, B, C, D, and E are the fitting constants. Thus, it can be easily used in any of the common computational thermochemistry codes. To date, the database contains 51 gaseous species of the formula MOx(OH)y.

Metal Hydroxides↗

NASA NTRS1991

Analysis of lightning field changes produced by Florida thunderstorms

A new method is introduced for inferring the charges deposited in a lightning flash. Lightning-caused field changes (delta E's) are described by a more general volume charge distribution than is defined on a large cartesian grid system centered above the measuring networks. It is shown that a linear system of equations can be used to relate delta E's at the ground to the values of charge on this grid. It is possible to apply more general physical constraints to the charge solutions, and it is possible to access the information content of the delta E data. Computer-simulated delta E inversions show that the location and symmetry of the charge retrievals are usually consistent with the known test sources.

Koshak, William John↗

NASA NTRS2003

Models And Experiments Of Laminar Diffusion Flames In Non-Uniform Magnetic Fields

Non-uniform magnetic fields affect laminar diffusion flames as a result of the paramagnetic and diamagnetic properties of the products and reactants. Paramagnetism is the weak attraction to a magnetic field a material exhibits as a result of permanent magnetic dipole moments in the atoms of the material. Diamagnetism is the weak repulsion to a magnetic field exhibited by a material due to the lack of permanent magnetic dipole moments in the atoms of a material. The forces associated with paramagnetic and diamagnetism are several orders of magnitude less than the forces associated with the more familiar ferromagnetism. A typical example of a paramagnetic gas is oxygen while hydrocarbon fuels and products of combustion are almost always diamagnetic. The fact that magnets can affect flame behavior has been recognized for more than one hundred years. Early speculation was that such behavior was due to the magnetic interaction with the ionized gases associated with a flame. Using a scaling analysis, it was later shown that for laminar diffusion flames the magnetic field/ionized gas interaction was insignificant to the paramagnetic and diamagnetic influences. In this effort, the focus has been on examining laminar diffusion slot flames in the presence of non-uniform upward decreasing magnetic fields produced using permanent magnets. The principal reason for choosing slot flames was mathematical models of such flames show an explicit dependence on gravitational body forces, in the buoyancy-controlled regime, and an applied magnetic field would also impose a body force. In addition, the behavior of such flames was more easily visualized while maintaining the symmetry of the two-dimensional problem whereas it would have been impossible to obtain a symmetric magnetic field around a circular flame and still visually record the flame height and shape along the burner axis. The motivation for choosing permanent magnets to produce the magnetic fields was the assumption that space-related technologies based on the knowledge gained during this investigation would more likely involve permanent magnets as opposed to electromagnets. While no analysis has been done here to quantify the impact that an electric field, associated with an electromagnetic, would have relative to the paramagnetic and diamagnetic interactions, by using permanent magnets this potential effect was completely eliminated and thus paramagnetic and diamagnetic effects were isolated.

Baker, J.↗

NASA NTRS1993

Symmetries of coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).

Han, D.↗

NASA NTRS1997

Mechanical signals in plant development: a new method for single cell studies

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

NASA Discipline Number 40-50↗

NASA NTRS2012

Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime

This document introduces the exciting and fundamentally new science and astronomy that the European New Gravitational Wave Observatory (NGO) mission (derived from the previous LISA proposal) will deliver. The mission (which we will refer to by its informal name eLISA ) will survey for the first time the low-frequency gravitational wave band (about 0.1 mHz to 1 Hz), with sufficient sensitivity to detect interesting individual astrophysical sources out to z = 15. The measurements described here will address the basic scientific goals that have been captured in ESA s New Gravitational Wave Observatory Science Requirements Document ; they are presented here so that the wider scientific community can have access to them. The eLISA mission will discover and study a variety of cosmic events and systems with high sensitivity: coalescences of massive black holes binaries, brought together by galaxy mergers; mergers of earlier, less-massive black holes during the epoch of hierarchical galaxy and black-hole growth; stellar-mass black holes and compact stars in orbits just skimming the horizons of massive black holes in galactic nuclei of the present era; extremely compact white dwarf binaries in our Galaxy, a rich source of information about binary evolution and about future Type Ia supernovae; and possibly most interesting of all, the uncertain and unpredicted sources, for example relics of inflation and of the symmetry-breaking epoch directly after the Big Bang. eLISA s measurements will allow detailed studies of these signals with high signal-to-noise ratio, addressing most of the key scientific questions raised by ESA s Cosmic Vision programme in the areas of astrophysics and cosmology. They will also provide stringent tests of general relativity in the strong-field dynamical regime, which cannot be probed in any other way. This document not only describes the science but also gives an overview on the mission design and orbits. LISA s heritage in the eLISA design will be clear to those familiar with the previous proposal, as will its incorporation of key elements of hardware from the LISA Pathfinder mission, scheduled for launch by ESA in 2014. But eLISA is fundamentally a new mission, one that will pioneer the completely new science of low-frequency gravitational wave astronomy. 4 of

Amaro, Seoane, Pau↗

NASA NTRS1998

Theory of the Shape of the Heliospheric Termination Shock: Axial Symmetry

The heliospheric termination shock must exhibit asymmetry in its shape, due in part to internal latitude variations in the solar wind, and in part to the special directions defined by the external interstellar flow and/or the galactic magnetic field. This asymmetry shows up naturally in numerical simulations of the interaction between the heliosphere and local interstellar medium. However, to date only one analytical treatment of the theory has appeared, which discussed the modification of the shock shape due to solar wind latitude variations in the presence of spherically symmetric outer boundary conditions. In the present report, we discuss an extension and generalization of this theory to an axially symmetric gasdynamic system, in which departure from spherical symmetry may be due either to internal solar wind variations or to the directional properties of the external interstellar medium. It is shown that for steady flow the post-shock region is characterized by an infinite set of quantities that are conserved along streamlines; among these invariants are the stagnation pressure and a quantity closely related to vorticity. Moreover, for a given latitude profile of the (supersonic) solar wind, the geometry of the termination shock uniquely determines the valued of these invariants at the points where the streamlines emerge from the shock. A self-consistent solution of the problem thus requires a match between the shock geometry and distant boundary conditions. The theory is applied to give estimates of termination-shock asymmetry for various internal and external conditions.

Barnes, Aaron↗

NASA NTRS2004

Lightweight Deployable Mirrors with Tensegrity Supports

The upper part of Figure 1 shows a small-scale prototype of a developmental class of lightweight, deployable structures that would support panels in precise alignments. In this case, the panel is hexagonal and supports disks that represent segments of a primary mirror of a large telescope. The lower part of Figure 1 shows a complete conceptual structure containing multiple hexagonal panels that hold mirror segments. The structures of this class are of the tensegrity type, which was invented five decades ago by artist Kenneth Snelson. A tensegrity structure consists of momentfree compression members (struts) and tension members (cables). The structures of this particular developmental class are intended primarily as means to erect large segmented primary mirrors of astronomical telescopes or large radio antennas in outer space. Other classes of tensegrity structures could also be designed for terrestrial use as towers, masts, and supports for general structural panels. An important product of the present development effort is the engineering practice of building a lightweight, deployable structure as an assembly of tensegrity modules like the one shown in Figure 2. This module comprises two octahedral tensegrity subunits that are mirror images of each other joined at their plane of mirror symmetry. In this case, the plane of mirror symmetry is both the upper plane of the lower subunit and the lower plane of the upper subunit, and is delineated by the midheight triangle in Figure 2. In the configuration assumed by the module to balance static forces under mild loading, the upper and lower planes of each sub-unit are rotated about 30 , relative to each other, about the long (vertical) axis of the structure. Larger structures can be assembled by joining multiple modules like this one at their sides or ends. When the module is compressed axially (vertically), the first-order effect is an increase in the rotation angle, but by virtue of the mirror arrangement, the net first-order rotation between the uppermost and lowermost planes is zero. The need to have zero net rotation between these planes under all loading conditions in a typical practical structure is what prompts the use of the mirror configuration. Force and moment loadings other than simple axial compression produce only second-order deformations through strains in the struts and cables.

Zeiders, Glenn W.↗

NASA NTRS1972

A theoretical and experimental investigation of the hypersonic turbulent boundary layer subject to normal and longitudinal pressure gradients and cross flow along a windward plane of symmetry.

A theoretical and experimental investigation for the hypersonic turbulent boundary layer undergoing both normal and longitudinal pressure gradients and cross flow along the plane of symmetry on the windward side of a body of revolution is presented. The purpose of this investigation is to provide a method for calculating boundary layers that occur on the centerline of symmetry of an inlet. The three-dimensional compressible integral equations are written along the symmetry plane and integrated numerically, and the effect of the cross flow on the behavior of the boundary layer is also studied. The experiments were performed at Mach number 6 and Reynolds number of 44,000,000/ft for the axisymmetric case and for the case with cross flow. The velocity profiles and the boundary layer parameters agree relatively well with theoretical values with and without cross flow effects. The presence of the cross flow alters significantly the value of the profiles. Total temperature-velocity correlations deviate from the linear Crocco distribution. Heat transfer rates agree with theoretical values and values obtained by the flat plate reference enthalpy method. Cross flow influence on the heat transfer rates is of minor relevance.

Zakkay, V.↗

NASA NTRS1972

Lineaments of the Apennine Front - Apollo 15 landing site.

The well-developed systems of lineaments that suggest regional fracturing or layering of the bedrock in the mountains at the Apollo 15 site may be illusions created by oblique lighting rather than expressions of true geologic structure. Supporting evidence includes: (1) occurrence of similar dominant lineament trends on many of the slopes even though the slope orientations differ widely; (2) presence of a thick mantling regolith that should conceal bedrock structures; (3) approximate symmetry of some of the lineament sets about the sun line; (4) lack of clear-cut topographic expression for many of the lineaments; and (5) general similarity of the lunar lineaments to lineament patterns produced by low oblique lighting on model surfaces mantled by fine sifted powder. Locally, as at Silver Spur, some lineament trends are related to distinct topographic features and are more confidently interpreted to reflect underlying geologic structures.

Wolfe, E. W.↗