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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Asymptotic forms for the energy of force-free magnetic field ion figurations of translational symmetry

It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.

Sturrock, P. A.↗
NASA NTRS1993

Model-based automatic generation of grasping regions

The problem of automatically generating stable regions for a robotic end effector on a target object, given a model of the end effector and the object is discussed. In order to generate grasping regions, an initial valid grasp transformation from the end effector to the object is obtained based on form closure requirements, and appropriate rotational and translational symmetries are associated with that transformation in order to construct a valid, continuous grasping region. The main result of this algorithm is a list of specific, valid grasp transformations of the end effector to the target object, and the appropriate combinations of translational and rotational symmetries associated with each specific transformation in order to produce a continuous grasp region.

Bloss, David A.↗
NASA NTRS1977

Statistical properties of the sound and source fields of an axisymmetric jet

It is shown, by measurements and analysis, that the sound field radiated from subsonic jets as well as the source field are statistically axially symmetric at lower frequencies. In this range, the source field behaves like a line-quadrupole. The sources are coherent with respect to phase and compact with respect to acoustic wavelength. The results are developed in terms of correlation, coherence, and phase. A new and simpler form of the source integral is obtained in the range where the phases are linear functions of frequency through symmetry, translation, and rotation of the axis.

Maestrello, L.↗
NASA NTRS1987

Nonlinear susceptibilities of finite conjugated organic polymers

Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

Beratan, David N.↗
NASA NTRS1989

Steps toward interstellar silicate dust mineralogy

One of the most certain facts on interstellar dust is that it contains grains with silicon oxygen tetrahedra (SOT), the internal vibrations of which cause the well known silicate bands at 10 and 18 microns. The broad and almost structureless appearance of them demonstrates lack of translation symmetry in these solids that must be considered amorphous or glassy silicates. There is no direct information on the cations in these interstellar silicates and on the number of bridging oxygens per tetrahedron (NBO). Comparing experimental results gained on amorphous silicates, e.g., silicate glasses, of cosmically most abundant metals (Mg, Fe, Ca, Al) with the observations is the only way to investigate interstellar silicate dust mineralogy (cf, Dorschner and Henning, 1986). At Jena University Observatory IR spectra of submicrometer-sized grains of pyroxene glasses (SSG) were studied. Pyroxenes are common minerals in asteroids, meteorites, interplanetary, and supposedly also cometary dust particles. Pyroxenes consist of linearly connected SOT (NBO=2). In the vitreous state reached by quenching melted minerals, the SOT remain nearly undistorted (Si-O bond length unchanged); the Si-O-Si angles at the bridging oxygens of pyroxenes, however, scatter statistically. Therefore, the original cation oxygen symmetry of the crystal (octahedral and hexahedral coordination by O) is completely lost. The blended bands at 10 and 18 microns lose their diagnostic differences and become broad and structureless. This illustrates best the basic problem of interstellar silicate mineral diagnostics. Optical data of glasses of enstatite, bronzite, hypersthene, diopside, salite, and hedenbergite have been derived. Results of enstatite (E), bronzite (B), and hypersthene (H) show very good agreement with the observed silicate features in the IR spectra of evolutionarily young objects that show P-type silicate signature according to the classification by Gurtler and Henning (1986). Compositional parameters and main characteristics of experimental SSG spectra in IR for the glasses E, B, and H are shown in tabular form. Results fit excellently the relations derived by Koike and Hasegawa (1987) and suggest that the band ratio of the astronomical silicate by Draine and Lee (1984) is too low.

Dorschner, J.↗
NASA NTRS1993

A new class of exact, nonlinear solutions to the Grad-Shafranov equation

We have constructed a new class of exact, nonlinear solutions to the Grad-Shafranov equation, representing force-free magnetic fields with translational symmetry. These exact solutions are pertinent to the study of magnetic structures in the solar corona that are subjected to photospheric shearing motions.

Roumeliotis, George↗
NASA NTRS1983

A simple example of a classical gauge transformation

Attention is given to the manner in which the interaction of a gravitational field with a diffusing gas is induced by a gauge transformation. Since the gas can be thought of as a field, the diffusion process may be represented by a Lagrangian density with the symmetry property of invariance under translation. While this property is lost when the field interacts with a static gravitational field, it is formally restored when an appropriate gauge transformation is performed. This ascription of field properties to a gas offers an illuminating illustration of the coupling of matter to a gauge field within the context of classical mechanics.

Whitten, R. C.↗
NASA NTRS2003

Transient Evolution of a Planar Diffusion Flame Aft of a Translating Flat Plate

The high degree of spatial symmetry of a planar diffusion flame affords great simplifications for experimental and modeling studies of gaseous fuel combustion. Particularly, in a microgravity environment, where buoyancy effects are negligible, an effectively strain-rate-free, vigorous flame may be obtained. Such a flame can also provide long residence times and large length scales for practical probing of flame structures and soot processes. This 2-D numerical study explores the feasibility of establishing such a planar diffusion flame in an enclosed container utilizing a realistic test protocol for a microgravity experiment. Fuel and oxygen mixtures, initially segregated into two half-volumes of a squat rectangular container by a thin separator, are ignited as soon as a flammable mixture is formed in the wake of the separator withdrawn in the centerplane. A triple-flame ensues that propagates behind the trailing edge of the separator. The results of calculations show that the mechanically- and thermally-induced convection decays in about two seconds. The establishment of a planar diffusion flame after this period seems feasible in the central region of the container with sufficient quantities of reactants left over for subsequent studies. An analysis of the flame initiation and formation process suggests how the feasibility of creating such a flame can be further improved.

Gokoglu, Suleyman A.↗
NASA NTRS1979

Coupled motion of rigid bodies about their center of mass

Nontrivial analytical solutions for the coupled motion of two rigid bodies about their center of mass are obtained on the assumptions that the rigid bodies are coupled by a massless rigid boom and that no external forces are acting on the system. Both relative rotational and translational motions of the two bodies are considered. General equations of motion are derived by regarding the two bodies as consisting of two distinct systems of particles and by applying the principle of conservation of angular momentum. It is shown that a basic nontrivial solution can be obtained for the translational problem if an assumption is made concerning the relative orientation of one principal axis of inertia of each body and that fundamental nontrivial solutions are readily obtained for the rotational problem if an additional assumption is made with respect to the symmetry of one body. Certain stability criteria are found for some of these motions by defining regions of constraint for the relative translational and rotational elements.

Jezewski, D. J.↗
NASA NTRS1983

NASTRAN forced vibration analysis of rotating cyclic structures

Theoretical aspects of a new capability, developed and added to the general purpose finite element program NASTRAN Level 17.7, to conduct forced vibration analysis of turned cyclic structures rotating about their axis of symmetry, are presented. The effects of Coriolis and centripetal accelerations as well as those due to the translational acceleration of the axis of rotation, are included. The equations of motion are first derived for an arbitrary grid point of the cyclic sector finite element model and then extended for the complete model. The equations are solved by four principal steps: (1) transformation of applied loads at frequency-dependent circumferential harmonic components; (2) application of circumferential harmonic-dependent intersegment compatibility constraints; (3) solution of frequency-dependent circumferential harmonic components of displacements; and (4) recovery of frequency-dependent response in various segments of the total structure. Five interrelated examples are presented to illustrate the various features of the development.

Elchuri, V.↗
NASA NTRS1983

NASTRAN forced vibration analysis of rotating cyclic structures

Theoretical aspects of a new capability developed and implemented in NASTRAN level 17.7 to analyze forced vibration of a cyclic structure rotating about its axis of symmetry are presented. Fans, propellers, and bladed shrouded discs of turbomachines are some examples of such structures. The capability includes the effects of Coriolis and centripetal accelerations on the rotating structure which can be loaded with: (1) directly applied loads moving with the structure and (2) inertial loas due to the translational acceleration of the axis of rotation (''base' acceleration). Steady-state sinusoidal or general periodic loads are specified to represent: (1) the physical loads on various segments of the complete structure, or (2) the circumferential harmonic components of the loads in (1). The cyclic symmetry feature of the rotating structure is used in deriving and solving the equations of forced motion. Consequently, only one of the cyclic sectors is modelled and analyzed using finite elements, yielding substantial savings in the analysis cost. Results, however, are obtained for the entire structure. A tuned twelve bladed disc example is used to demonstrate the various features of the capability.

Elchuri, V.↗
NASA NTRS1989

Inertial corrections by dynamic estimation

The highlights are presented of an Engineering Memorandum, Dynamic Estimation for Floated Gradiometers. The original impetus for the work was that gradiometers, in principle, measure components of the gravity gradient tensor, plus rotation effects, similar to centrifugal and Coriolis effects in accelerometers. The problem is that the rotation effects are often quite large, compared to the gradient, and that available inertial instruments can't measure them to adequate accuracy. The paper advances the idea that, if the instruments can be floated in a package subject to very low disturbances, a dynamic estimation, based on the Euler and translational equations of motion, plus models of all the instruments, can be used to greatly strengthen the estimates of the gradient and the rotation parameters. Moreover, symmetry constraints can be imposed directly in the filter, further strengthening the solution.

Sonnabend, David↗
NASA NTRS1983

Prediction of structures and magnetic orientations in solid alpha and beta-O2

A quasi-harmonic-lattice-dynamics method coupled with a pattern-recognition optimization scheme is used to determine the minimum energy structures and magnetic orientations of solid oxygen. It is shown that the magnetic interaction is responsible for the stability of alpha-O2 with respect to beta-O2 at zero temperature and pressure. The calculated alpha-O2 lattice parameters, magnetic orientations, and sublimation energy are in good agreement with experiment. Phonon dispersion curves are calculated at vector k not equal to zero and the acoustic sound velocities are determined. The rms translational and orientational fluctuations from equilibrium are also calculated. The beta-O2 phase is described by constraining the magnetic moments so that the magnetic Hamiltonian preserves the hexagonal symmetry of the crystal. The calculated lattice parameters are in good agreement with the experiments, and a three-sublattice, quasi-helical magnetic orientation is predicted from structural and energetic considerations.

Etters, R. D.↗
NASA NTRS2004

Improved Phase-Mask Fabrication of Fiber Bragg Gratings

An improved method of fabrication of Bragg gratings in optical fibers combines the best features of two prior methods: one that involves the use of a phase mask and one that involves interference between the two coherent laser beams. The improved method affords flexibility for tailoring Bragg wavelengths and bandwidths over wide ranges. A Bragg grating in an optical fiber is a periodic longitudinal variation in the index of refraction of the fiber core. The spatial period (Bragg wavelength) is chosen to obtain enhanced reflection of light of a given wavelength that would otherwise propagate relatively unimpeded along the core. Optionally, the spatial period of the index modulation can be made to vary gradually along the grating (such a grating is said to be chirped ) in order to obtain enhanced reflection across a wavelength band, the width of which is determined by the difference between the maximum and minimum Bragg wavelengths. In the present method as in both prior methods, a Bragg grating is formed by exposing an optical fiber to an ultraviolet-light interference field. The Bragg grating coincides with the pattern of exposure of the fiber core to ultraviolet light; in other words, the Bragg grating coincides with the interference fringes. Hence, the problem of tailoring the Bragg wavelength and bandwidth is largely one of tailoring the interference pattern and the placement of the fiber in the interference pattern. In the prior two-beam interferometric method, a single laser beam is split into two beams, which are subsequently recombined to produce an interference pattern at the location of an optical fiber. In the prior phase-mask method, a phase mask is used to diffract a laser beam mainly into two first orders, the interference between which creates the pattern to which an optical fiber is exposed. The prior two-beam interferometric method offers the advantage that the period of the interference pattern can be adjusted to produce gratings over a wide range of Bragg wavelengths, but offers the disadvantage that success depends on precise alignment and high mechanical stability. The prior phase-mask method affords the advantages of compactness of equipment and relative insensitivity to both misalignment and vibration, but does not afford adjustability of the Bragg wavelength. The present method affords both the flexibility of the prior two-beam interferometric method and the compactness and stability of the prior phase-mask method. In this method (see figure), a laser beam propagating along the x axis is normally incident on a phase mask that lies in the (y,z) plane. The phase of light propagating through the mask is modulated with a spatial periodicity, p, along the y axis chosen to diffract the laser light primarily to first order at the angle . (The zero-order laser light propagating along the x axis can be used for alignment and thereafter suppressed during exposure of the fiber.) The diffracted light passes through a concave cylindrical lens, which converts the flat diffracted wave fronts to cylindrical ones, as though the light emanated from a line source. Then two parallel flat mirrors recombine the diffracted beams to form an interference field equivalent to that of two coherent line sources at positions A and B (virtual sources). The interference pattern is a known function of the parameters of the apparatus and of position (x,y) in the interference field. Hence, the tilt, wavelength, and chirp of the Bragg grating can be chosen through suitable adjustments of the apparatus and/or of the position and orientation of the optical fiber. In particular, the Bragg wavelength can be adjusted by moving the fiber along the x axis, and the bandwidth can be modified over a wide range by changing the fiber tilt angle or by moving the phase mask and/or the fiber. Alignment is easy because the zero-order beam defines the x axis. The interference is relatively stable and insensitive to the mechanical vibration because of the gh symmetry and compactness of the apparatus, the fixed positions of the mirrors and lens, and the consequent fixed positions of the two virtual line sources, which are independent of the translations of the phase mask and the laser relative to the lens.

Grant, Joseph↗
NASA NTRS2016

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Trajectory models↗
NASA NTRS2004

Science Using an Electrostatic Levitation Furnace in the MUCAT Sector at the APS

The original motivation for the construction of the BESL prototype was to obtain the first proof of a 50-year-old hypothesis regarding the solidification of liquid metals. Since the 1950s it has been known that under proper conditions liquid metals can be cooled below their melting temperature (undercooled) without crystallizing to the stable solid phase. In 1952 Frank proposed that this was because the atoms in the metallic liquid were arranged with the symmetry of an icosahedron, a Platonic solid consisting of 20 tetrahedra (4-sided pyramid-shaped polyhedra) arranged around a common center. Since this local atomic order is incompatible with the long-range translational periodicity of crystal phases, a barrier is formed to the formation of small regions of the crystal phase, the nucleation barrier. A proof of Frank's hypothesis required a direct correlation between measured icosahedral order in the undercooled liquid and the nucleation barrier. The tendency of sample containers to catalyze nucleation obscured this relation, requiring containerless techniques. Combining containerless processing techniques for electrostatically levitated droplets (ESL) with x-ray synchrotron methods, a team from Washington University, St. Louis, MO, NASA Marshall Space Flight Center, and MUCAT at the APS demonstrated an increasing icosahedral order in TiZrNi liquids with decreasing temperature below the melting temperature. The increased icosahedral order caused the transformation of the liquid to a metastable icosahedral quasicrystal phase, instead of the stable tetrahedrally-coordinated crystal intermetallic, giving the first clear demonstration of the connection between the nucleation barrier and the local structure of the liquid, verifying Frank's hypothesis for this alloy.

Goldman, A.↗
NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
NASA NTRS1977

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Geddes, K. O.↗