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Results for “symmetry transformations”

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 NTRS1990

On the partitioning strategy based on symmetry transformations

A computational procedure is presented for the analysis of unsymmetric structures. The procedure is based on a modified version of the symmetry-transformation partitioning strategy, in which the response of the structure is approximated by a linear combination of symmetric/antisymmetric response vectors, each obtained by using only a fraction of the degrees of freedom of the original FEM model. The three key elements of the procedure are: (1) mixed (or primitive-variable) formulation with independent shape functions for the different fields; (2) restructuring of the governing discrete equations of the structure into uncoupled sets in the symmetric and antisymmetric response vectors; and (3) a stable and efficient iterative process for generating the response of the structure. The effectiveness of the proposed procedure and its advantages over classical substructuring are demonstrated by means of numerical examples.

Noor, Ahmed K.↗
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 NTRS2002

The Statistical Mechanics of Ideal Homogeneous Turbulence

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Shebalin, John V.↗
NASA NTRS1990

Computational technology for flight vehicles; Proceedings of the Symposium, Washington, DC, Nov. 5-7, 1990

Recent advances in computational fluid mechanics are discussed in reviews and reports. Sections are devoted to (1) the modeling of local phenomena and edge effects in solids, (2) stochastic modeling and simulation of fracture toughness, and (3) partitioning strategy and new finite elements. Particular attention is given to global and local finite-element/spectral-boundary-element techniques for failure analysis, simulations of microfracture in metal-matrix composites, fatigue analysis of cracked anisotropic plates under stochastic loading, mathematical modeling for the analysis of nonlinear aircraft dynamics, physical and mathematical modeling of wave propagation in the Ariane 5 VEB structure, partitioning based on symmetry transformations, an FEM approach to adaptive reliability assurance, and time-domain FEMs for the large rotational dynamics of multibody systems.

Noor, Ahmed K.↗
NASA NTRS1981

Effective constitutive relations for large repetitive frame-like structures

Effective mechanical properties for large repetitive framelike structures are derived using combinations of strength of material and orthogonal transformation techniques. Symmetry considerations are used in order to identify independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified; (2) effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods; and (3) orthogonal transformations are used to determine the contribution of each basic set to the overall effective continuum properties of the structure.

Nayfeh, A. H.↗
NASA NTRS1965

Beyond su/3/plus

Symmetry approach to particle physics - review of transformation properties, mixed symmetries and extensions, and bootstrap philosophy in high energy interactions

HIGH ENERGY INTERACTION↗
NASA NTRS1986

Geometric Representations for Discrete Fourier Transforms

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

Cambell, C. W.↗
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 NTRS1994

Some Aspects of the Implementation of Double Group Symmetry and Electron Correlation in Molecular 4-Component Calculations

The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.

Dyall, Kenneth G.↗
NASA NTRS2001

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Pawloski, Janice S.↗
NASA NTRS2013

On the Use of Quartic Force Fields in Variational Calculations

The use of quartic force fields (QFFs) has been shown to be one of the most effective ways to efficiently compute vibrational frequencies for small molecules. In this paper we outline and discuss how the simple-internal or bond-length bond-angle (BLBA) coordinates can be transformed into Morse-cosine(-sine) coordinates which produce potential energy surfaces from QFFs that possess proper limiting behavior and can effectively describe the vibrational (or rovibrational) energy levels of an arbitrary molecular system. We investigate parameter scaling in the Morse coordinate, symmetry considerations, and examples of transformed QFFs making use of the MULTIMODE, TROVE, and VTET variational vibrational methods. Cases are referenced where variational computations coupled with transformed QFFs produce accuracies compared to experiment for fundamental frequencies on the order of 5 cm(exp −1) and often as good as 1 cm(exp −1).

quartic force field↗
NASA NTRS1975

The thermal expansion and high temperature transformation of GeSe

The thermal expansion of GeSe has been studied above room temperature up to the melting point of 670 plus or minus 5 C by X-ray diffraction techniques using a 190 mm Unicam high temperature camera. The thermal expansion of the crystallographic axes is linear with a distinct change in the expansion coefficients for all axes above 400 C. The relative changes in the axes indicate a rearrangement of the structure towards cubic symmetry with increasing temperature. The transformation of GeSe from the orthorhombic to a normal NaCl-type structure is observed at 651 plus or minus 5 C. The lattice parameter of the cubic form of GeSe is a 0 ? 5.730 plus or minus 0.003 A at 656 C. The GeSe lattice remains cubic up to the melting point.

Wiedemeier, H.↗
NASA NTRS1976

Ray propagation in oblate atmospheres

Phinney and Anderson's (1968) exact theory for the inversion of radio-occultation data for planetary atmospheres breaks down seriously when applied to occultations by oblate atmospheres because of departures from Bouguer's law. It has been proposed that this breakdown can be overcome by transforming the theory to a local spherical symmetry which osculates a ray's point of closest approach. The accuracy of this transformation procedure is assessed by evaluating the size of terms which are intrinsic to an oblate atmosphere and which are not eliminated by a local spherical approximation. The departures from Bouguer's law are analyzed, and it is shown that in the lowest-order deviation from that law, the plane of refraction is defined by the normal to the atmosphere at closest approach. In the next order, it is found that the oblateness of the atmosphere 'warps' the ray path out of a single plane, but the effect appears to be negligible for most purposes. It is concluded that there seems to be no source of serious error in making an approximation of local spherical symmetry with the refraction plane defined by the normal at closest approach.

Hubbard, W. B.↗
NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
NASA NTRS2007

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Rubinstein, Robert↗
NASA NTRS1979

Design of a 24-channel transmultiplexer

The design of a transmultiplexer capable of performing the bilateral conversion between one 1544 kbit/s digital signal (which represents 24 PCM coded voice channels) and two analog group signals (each one containing 12 voice channels in the 60-108 kHz band) is investigated. It is shown that an FIR filter bank required as part of such a transmultiplexer can be realized efficiently by cascading a discrete cosine transform processor and a weighting network. Fast convolution algorithms are derived for evaluating the cosine transform. A method of using the symmetry conditions to reduce the computation rate in the weighting network and an elegant hardware configuration for implementing it are also discussed.

Narasimha, M. J.↗
NASA NTRS1984

Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Campbell, C. W.↗