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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Synthesis of vibration systems, having group symmetry or quasi-symmetry, according to the frequency spectrum

Torsional vibration systems, with finite numbers of degrees of freedom are investigated. In designing such systems, it is important to select parameters, so that the frequency spectrum of the natural vibrations is beyond the limits of the resonance danger region. In the case when the system has a large number of degrees of freedom, calculation of its natural frequencies, as well as tuning out the resonance danger zones is laborious. When the system being investigated has one group symmetry or another, solution of the problem mentioned above is facilitated, as a consequence of breaking down the frequency equations into several, which are smaller in size. An algorithm is given for tuning out the natural frequency spectrum from the forbidden region, by means of varying the rigidity of systems having group symmetries or group quasi-symmetries.

Andryushkevichyus, A. I.↗
NASA NTRS1989

Novel local symmetries and chiral-symmetry-broken phases in S = 1/2 triangular-lattice Heisenberg model

Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.

Baskaran, G.↗
NASA NTRS1993

Symmetry in polarimetric remote sensing

Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is observed that e and e(sub 0) are increasing with incident angle and e is greater than e(sub 0) at L-band because of the directional feature of sea surface waves. Symmetry properties of geophysical media can also be used to calibrate polarimetric radars.

Nghiem, S. V.↗
NASA NTRS1992

Application of symmetry properties to polarimetric remote sensing with JPL AIRSAR data

Based on symmetry properties, polarimetric remote sensing of geophysical media is studied. From the viewpoint of symmetry groups, media with reflection, rotation, azimuthal, and centrical symmetries are considered. The symmetries impose relations among polarimetric scattering coefficients, which are valid to all scattering mechanisms in the symmetrical configurations. Various orientation distributions of non-spherical scatterers can be identified from the scattering coefficients by a comparison with the symmetry calculations. Experimental observations are then analyzed for many geophysical scenes acquired with the Jet Propulsion Laboratory (JPL) airborne polarimetric SAR at microwave frequencies over sea ice and vegetation. Polarimetric characteristics of different ice types are compared with symmetry behaviors. The polarimetric response of a tropical rain forest reveals characteristics close to the centrical symmetry properties, which can be used as a distributed target to relatively calibrate polarimetric radars without any deployment of manmade calibration targets.

Nghiem, S. V.↗
NASA NTRS1992

Symmetry properties in polarimetric remote sensing

This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.

Nghiem, S. V.↗
NASA NTRS2012

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Nemeth, Michael P.↗
NASA NTRS1976

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗
NASA NTRS1986

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Golubitsky, Martin↗
NASA NTRS1994

Symmetry breaking in O4(+): An application of the Brueckner coupled-cluster method

A recent calculation of the antisymmetric stretch frequency for the rectangular structure of quartet O4(+) using the singles and doubles quadratic configuration interaction method with a perturbational estimate of connected triple excitations (QCISD(T)) method gave a value of 3710 cm(exp -1). This anomalous frequency is shown to be a consequence of symmetry breaking effects, which occur even though the QCISD(T) solution derived from a delocalized SCF reference function lies energetically well below the two localized (symmetry-broken) solutions at the equilibrium geometry. The symmetry breaking is almost eliminated at the CCSD level of theory, but the small remaining symmetry breaking effects are magnified at the CCSD(T) level of theory so that the antisymmetric stretch frequency is still significantly in error. The use of the Brueckner coupled cluster method, however, leads to a symmetrical solution which is free of symmetry breaking effects, with an antisymmetric stretch frequency of 1322 cm(exp -1), in good agreement with our earlier calculations using the complete active space self consistent field/complete active space state interaction (CASSCF/CASSI) method.

Barnes, Leslie A.↗
NASA NTRS1995

Spatial symmetry breaking in rapidly rotating convective spherical shells

Many problems in geophysical and astrophysical convection systems are characterized by fast rotation and spherical shell geometry. The combined effects of Coriolis forces and spherical shell geometry produce a unique spatial symmetry for the convection pattern in a rapidly rotating spherical shell. In this paper, we first discuss the general spatial symmetries for rotating spherical shell convection. A special model, a spherical shell heated from below, is then used to illustrate how and when the spatial symmetries are broken. Symmetry breaking occurs via a sequence of spatial transitions from the primary conducting state to the complex multiple-layered columnar structure. It is argued that, because of the dominant effects of rotation, the sequence of spatial transitions identified from this particular model is likely to be generally valid. Applications of the spatial symmetry breaking to planetary convection problems are also discussed.

Zhang, Keke↗
NASA NTRS1990

The calculation of the contributions to low energy e+H2 scattering from sigma u+ and Pion u symmetries using the Kohn variational method

Above incident energies of about 2 eV, the contribution to the total cross section in positron+H2 scattering from the sigma g+ symmetry is insufficient to account for the experimental value. Calculations carried out of the lowest partial waves of sigma u+ symmetry and Pion u symmetry using the Kohn variational method are described. The contributions to the total cross section from the two equivalent partial waves of Pion u symmetry significantly reduce the discrepancy with experiment up to incident energies of 4 to 5 eV. Comparisons are made with recent R-matrix calculations performed by Danby and Tennyson.

Armour, E. A. G.↗
NASA NTRS1990

Symmetry assessment of an air-blast atomizer spray

This study represents an evaluation of the extent to which conventional and recently introduced modern diagnostics can assess the symmetry of sprays formed by three atomizers of identical design. The conventional diagnostics include sheet-lit photography, patternation, and laser diffraction. The modern diagnostic is laser interferometry (phase Doppler). Symmetry is assessed in ambient conditions for four atomizer orientations, and comparisons are made between the diagnostic techniques. The results demonstrate that conventional and modern diagnostics are consistent in the assessment of symmetry, patternation and phase Doppler are most effective in establishing symmetry of mass flux, and phase Doppler, although more tedious to employ, provides the additional information necessary to establish the sources of detected asymmetries in terms of nonuniformities in droplet velocities, size distributions, volume flux, and concentration.

Mcdonnell, V. G.↗
NASA NTRS1994

Crystalline structure and symmetry dependence of acoustic nonlinearity parameters

A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born-Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.

Cantrell, John H.↗
NASA NTRS2000

Effect of Medium Symmetries in Limiting the Number of Parameters Estimated with Polarimetric Interferometry

The addition of interferometric backscattering pairs to the conventional polarimetric SAR data over forests and other vegetated areas increases the dimensionality of the data space, in principle enabling the estimation of a larger number of vegetation parameters. Without regard to the sensitivity of these data to vegetation scattering parameters, this paper poses the question: Will increasing the data channels as such result in a one-to-one increase in the number of parameters that can be estimated, or do vegetation and data properties inherently limit that number otherwise? In this paper, the complete polarimetric interferometric covariance matrix is considered and various symmetry properties of the scattering medium are used to study whether any of the correlation pairs can be eliminated. The number of independent pairs has direct consequences in their utility in parameter estimation schemes, since the maximum number of parameters that can be estimated cannot exceed the number of unique measurements. The independent components of the polarimetric interferometric SAR (POL/INSAR) data are derived for media with reflection, rotation, and azimuth symmetries, which are often encountered in vegetated surfaces. Similar derivations have been carried out before for simple polarimetry, i.e., zero baseline. This paper extends those to the interferometric case of general nonzero baselines. It is shown that depending on the type of symmetries present, the number of independent available measurements that can be used to estimate medium parameters will vary. In particular, whereas in the general case there are 27 mathematically independent measurements possible from a polarimetric interferometer, this number can be reduced to 15, 9, and 6 if the medium has reflection, rotation, or azimuthal symmetries, respectively. The results can be used in several ways in the interpretation of SAR data and the development of parameter estimation schemes, which will be discussed at the presentation. Recent POL/INSAR data from the JPL AIRSAR over a forested area will be used to demonstrate the results of this derivation. This work was performed by the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, under contract from the National Aeronautics and Space Administration.

Moghaddam, Mahta↗
NASA NTRS1995

The MCH2+ Systems: Do ScCH2+ and TiCH2+ Have C(sub s) or C(sub 2v) Symmetry and A Comparison of the B3LYP Method to Other Approaches

ScCH2(+) and TiCH2(+) are found to have C(sub s) symmetry, while the remaining systems have the expected C(sub 2v) symmetry. The C(sub s) symmetry structure is favored for ScCH2(+) and TiCH2(+) because it allows donation from one of the CH bonds into an empty 3d orbital. This distortion stabilizes the systems by less than 2 kcal/mol at the B3LYP, CASSCF, and CCSD(T) levels of theory. The SCF and B3LYP approaches find the C2(sub v) structure to be a saddle point, while the CASSCF approach finds the C(sub 2v) structure to be a stationary point. For V-Cu there are no empty 3d orbitals of the correct symmetry, and therefore the distortion to C(sub s), is unfavorable. The B3LYP binding energies are in good agreement with experiment and our previous best estimates.

Ricca, Alessandra↗
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.↗