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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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NASA NTRS1972

Chemical nonequilibrium effects on the flow in the windward plane of symmetry of a blunted delta orbiter

The extent, and some of the consequences, of nonequilibrium effects in the inviscid orbiter flow field are examined. Calculations have been made for the reacting flow along selected streamlines in the windward plane of symmetry of a blunted delta shape representative of a shuttle orbiter. An approximate model of the pressure field in the windward plane of symmetry of a blunted delta wing was constructed from wind tunnel measurements of the body surface pressure distribution and approximate calculations of the shock shape and streamline locations. Numerical solutions for the flow along streamlines were obtained for this pressure distribution, and solutions were obtained for both equilibrium and finite-reaction rate, nonequilibrium chemical reactions. Since the streamtube solutions are much easier to compute than fully three-dimensional, reacting flows, results were obtained for a wide range of conditions. The validity of this approach is based on the assumptions that the pressure field is insensitive to nonequilibrium effects and that the flow along streamlines is quasi-one dimensional. Numerical solutions have been used to verify this approach for other blunted slender shapes such as spherically blunted cones.

Lordi, J. A.↗
NASA NTRS1973

Laminar boundary layer on a cone near a plane of symmetry.

The three-dimensional laminar boundary layer near the planes of symmetry of a cone with either outflow or inflow is studied in supersonic and hypersonic flow. Solutions are presented for a variety of values of three parameters, namely those of cross flow, external Mach number, and wall enthalpy ratio. Also asymptotic solutions for ranges of pertinent similarity variables are developed and used in numerical analyses so as to assure exponential behavior as the similarity variables approach infinity. Of special interest in the results is the existence for outflow, i.e., for the windward plane of symmetry, of a new solution branch and for inflow of four solution branches. The physical significance of the new solutions is discussed.

Wu, P.↗
NASA NTRS1973

NASTRAN cyclic symmetry capability

A development for NASTRAN which facilitates the analysis of structures made up of identical segments symmetrically arranged with respect to an axis is described. The key operation in the method is the transformation of the degrees of freedom for the structure into uncoupled symmetrical components, thereby greatly reducing the number of equations which are solved simultaneously. A further reduction occurs if each segment has a plane of reflective symmetry. The only required assumption is that the problem be linear. The capability, as developed, will be available in level 16 of NASTRAN for static stress analysis, steady state heat transfer analysis, and vibration analysis. The paper includes a discussion of the theory, a brief description of the data supplied by the user, and the results obtained for two example problems. The first problem concerns the acoustic modes of a long prismatic cavity imbedded in the propellant grain of a solid rocket motor. The second problem involves the deformations of a large space antenna. The latter example is the first application of the NASTRAN Cyclic Symmetry capability to a really large problem.

Macneal, R. H.↗
NASA NTRS1974

Note on the symmetry of perturbed Hartree-Fock and X-alpha wavefunctions

An objection to the effect that the first-order orbitals describing the perturbation of Hartree-Fock or X-alpha closed shell atoms by a multipole electric field may not have the required symmetry properties is acknowledged and answered. It is shown that the assumption of the expected symmetry is a self-consistent one.

Eaves, J. O.↗
NASA NTRS1975

Quantization and symmetry in periodic coverage patterns with applications to earth observation

Analytical approaches based on an idealized physical model and concepts from number theory show that in periodic coverage patterns, uniquely defined by their revolution numbers R (orbital) and N (rotational), the subnodal points are earth-fixed, and they divide the equator into R equal segments of length s. The ascending subsatellite trace crosses each point once (only) each period. The descending subnodal points coincide with the ascending points if the integers N and R have like parity, and bisect the intervals between them if opposite. The interval between consecutive unidirectional crossings is Ns. Symmetries extend the equatorial results to all parallels of latitude. Complete periodic patterns of traces exhibit an overall symmetry, with trace intersections confined to discrete coordinate values which are quantized in longitude (basic s-unit) and symmetric in latitude.

King, J. C.↗
NASA NTRS1976

Exploiting symmetries for efficient post-buckling analysis of composite plates

Two aspects of the post-buckling analysis of composite plates are considered in this paper. The first pertains to identifying the different types of symmetry exhibited by the pre- and post-buckling responses of rectangular and skewed composite plates. A procedure is presented for exploiting these symmetries in finite-element and finite-difference analyses. The procedure can be used with existing programs having multipoint constraint capability. The second aspect pertains to the post-buckling response of biaxially loaded composite plates. Numerical results from finite-element analysis are presented which show the range of parameters for which shear deformation and/or anisotropy are important in buckling and post-buckling analysis.

Noor, A. K.↗
NASA NTRS1979

Globally baryon symmetric cosmology, GUT spontaneous symmetry breaking, and the structure of the universe

Grand unified theories (GUT) such as SU(5), with spontaneous symmetry breaking, can lead more naturally to a globally baryon symmetric big bang cosmology with a domain structure than to a totally asymmetric cosmology. The symmetry is broken at random in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Because of the additional freedom in the high-energy physics allowed by such GUT gauge theories, new observational tests may be possible. Arguments in favor of this cosmology and various observational tests are discussed.

Stecker, F. W.↗
NASA NTRS1979

Cosmological baryon number domain structure from symmetry-breaking in grand unified field theories

It is suggested that grand unified field theories with spontaneous symmetry breaking in the very early big-bang can lead more naturally to a baryon symmetric cosmology with a domain structure than to a totally baryon asymmetric cosmology. The symmetry is broken in a randomized manner in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Arguments in favor of this cosmology and observational tests are discussed.

Brown, R. W.↗
NASA NTRS1979

Cosmological baryon-number domain structure from symmetry breaking in grand unified field theories

It is suggested that grand unified field theories with spontaneous symmetry breaking in the very early big bang can lead more naturally to a baryon-symmetric cosmology with a domain structure than to a totally baryon-asymmetric cosmology. The symmetry is broken in a randomized manner in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Arguments in favor of this cosmology and observational tests are discussed.

Brown, R. W.↗
NASA NTRS1980

Common time in a four-dimensional symmetry framework

Following the ideas of Poincare, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, clock systems and light propagation are analyzed within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporating common time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail.

Hsu, J. P.↗
NASA NTRS1980

Determination of the orientation symmetry axis of graphite specimens

A technique is described for determining the true orientation symmetry axis of graphite specimens from conventional X-ray diffraction data. The technique, although developed for graphite, is applicable to any material exhibiting crystalline orientation which is symmetric about some axis. The requisite equations are derived for applying the procedure to both Bacon transmission data and rotating specimen reflection data. Results are presented which show that the symmetry axis of eleven molded graphites tested differed significantly from their nominal pressing directions.

Schryer, D. R.↗
NASA NTRS1982

Low energy, left-right symmetry restoration in SO(N) GUTS

A general n step symmetry breaking pattern of SO(4K+2) down to SU sub C (3)xSU sub L (2)xU sub Y (1), which uses regular subgroups only, does not allow low energy left right symmetry restoration. In these theories, the smallest mass scale at which such restoration is possible is approximately one billion GeV as in the SO(10) case. The unification mass in SO(4K+2) GUTS must be at least as large as that in SU(5). These results assumed standard values of the Weinberg angle and strong coupling constant.

Holman, R.↗
NASA NTRS1985

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗
NASA NTRS1986

Symmetry and stability in Taylor-Couette flow

The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.

Golubitsky, M.↗
NASA NTRS1987

Exploiting symmetries in the modeling and analysis of tires

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Noor, Ahmed K.↗
NASA NTRS1988

Symmetry and equivalence restrictions in electronic structure calculations

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1988

Iterates of maps with symmetry

Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.

Chossat, Pascal↗
NASA NTRS1990

The symmetry properties of planetary magnetic fields

This paper provides a comparative study of the geometrical structures of the magnetic fields of earth, Jupiter, Saturn, and Uranus, starting from the traditional multipolar representations of these fields. For earth, Jupiter, and Saturn, the centered dipole, quadrupole, and octupole contributions are included, while at Uranus only the dipole and quadrupole contributions are considered. It is found that there are a number of common features of the magnetic fields of earth and Jupiter. Compared to earth and Jupiter, the Saturnian field exhibits not only a high degree of symmetry about the rotation axis but also a high degree of antisymmetry about the equatorial plane. The Uranian field shows strong deviations from both such symmetries. Nevertheless, there remain features common to all four planets.

Raedler, Karl-Heinz↗