SEARCH · Engineering Papers

Results for “Matrix elements”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

NASA NTRS1991

Cross section for production of low-energy electron-positron pairs by relativistic heavy ions

Starting with the lowest-order unscreened QED matrix element for electron-positron pair production by heavy charged particles, the paper calculates the cross section for this process differential in all independent variables and valid for all pair energies small compared to the incident particle energy. Integration over the possible emission angles of one of the pair members gives an expression that is valid for low-energy pairs that can be compared with previous work based on the Weizsaecker-Williams method. Integration over the possible angles of the other pair member then yields an expression identical to one derived by Racah. The high energy-transfer limit of the expression for the cross section integrated over electron and positron angles is found to be identical to that of Kelner in the unscreened case.

Eby, P. B.↗

NASA NTRS1990

Accounting for crustal magnetization in models of the core magnetic field

The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.

Jackson, Andrew↗

NASA NTRS1992

Application of edge-based finite elements and vector ABCs in 3D scattering

A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation.

Chatterjee, A.↗

NASA NTRS1991

The electronic Hamiltonian for cuprates

A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.

Annett, James F.↗

NASA NTRS1991

External calibration of polarimetric radars using point and distributed targets

Polarimetric calibration algorithms using combinations of point targets and reciprocal distributed targets are developed. From the reciprocity relations of distributed targets, and equivalent point target response is derived. Then the problem of polarimetric calibration using two point targets and one distributed target reduces to that using three point targets, which has been previously solved. For calibration using one point target and one reciprocal distributed target, two cases are analyzed with the point target being a trihedral reflector or a polarimetric active radar calibrator (PARC). For both cases, the general solutions of the system distortion matrices are written as a product of a particular solution and a matrix with one free parameter. For the trihedral-reflector case, this free parameter is determined by assuming azimuthal symmetry for the distributed target. For the PARC case, knowledge of one ratio of two covariance matrix elements of the distributed target is required to solve for the free parameter. Numerical results are simulated to demonstrate the usefulness of the developed algorithms.

Yueh, S. H.↗

NASA NTRS1991

Radiative transition probabilities for all vibrational levels in the X 1Sigma(+) state of HF

Recent analyses have led to an experimentally-based potential energy curve for the ground state of HF which includes nonadiabatic corrections and which joins smoothly to the long-range potential at an accurately determined dissociation limit. Using this potential curve and a new ab initio dipole moment function, accurate radiative transition probabilities among all vibrational levels of the ground state of HF have been calculated for selected rotational quantum numbers. Comparisons of Einstein A spontaneous emission coefficients, dipole moment absorption matrix elements, and Herman-Wallis factors for absorption bands are presented.

Zemke, Warren T.↗

NASA NTRS1991

The application of time-dependent wavepacket methods to reactive scattering

Several methods for performing numerically exact reactive scattering calculations using time-dependent wavepackets are reviewed. The basic idea is to take the multiarrangement reactive problem and reformulate it as one or more inelastic ones. In the simplest method, total reaction probabilities are extracted by calculating the flux of the wavepacket as it leaves the interaction region in the direction of the reactive arrangement. To make this practical, complex potentials that absorb the wavepacket before it reaches the numerical grid boundary are used. Methods that generate observables ranging from total, energy-averaged reaction probabilities up to energy- and state-resolved S-matrix elements are used. Techniques for efficiently performing the necessary inelastic wavepacket propagation are also reviewed.

Neuhauser, Daniel↗

NASA NTRS1992

Transition operators in electromagnetic-wave diffraction theory - General theory

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Hahne, G. E.↗

NASA NTRS1992

Electron impact polarization of atomic spectral lines. I - A general theoretical scheme

A suitable theoretical scheme able to describe, in a wide variety of astrophysical situations, the phenomenon of atomic line polarization by electron impact is developed. Starting from the general principles of quantum mechanics and assuming the Born approximation, the rate equations for the density matrix elements of a multilevel atomic system, interacting with a nonrelativistic electron beam having any kind of angular distribution, are derived in full generality. The resulting theory generalizes the previous ones by accounting for the collisional rates and the cross sections concerning both inelastic and superelastic collisions (in any geometrical situation), and, moreover, by taking into account the coherences among Zeeman sublevels split by a magnetic field. As an example of particular relevance, the general formulas derived in the first sections of the paper are subsequently particularized to the case of the electric dipole interaction.

Fineschi, Silvano↗

NASA NTRS1992

Sufficient conditions for a local minimum of the Bolza problem with a scalar terminal point constraint

Sufficient conditions for a weak relative minimum for a form of the Bolza problem of variational calculus are derived. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of most previously published sets of conditions. The derivation is felt to be more complete and straightforward than previous derivations. The variational problem considered is relatively simple, with just a scalar constraint to implicitly or explicitly determine the final time, in order to avoid the complexities associated with controllability considerations. Sufficient conditions for a local minimum for more general optimal control problems can be approached by building upon the derivation and results presented here.

Wood, Lincoln J.↗

NASA NTRS1991

Sufficient conditions for a local minimum of the Bolza problem with multiple terminal point constraints

Sufficient conditions for a weak relative minimum are derived for a form of the Bolza problem of variational calculus. The derivation ties together first-order and second-order conditions in a unified consistent manner, addresses controllability considerations in some detail, and clarifies some small inconsistencies in earlier work. The resulting second-order conditions of optimality involve the integration of fewer backward-sweep matrix elements than the standard conditions in the literature for problems with an unspecified final time. As a result, the backward-sweep matrices have the same general structure and dimensionality whether the final time is specified or free, with the terminal values of two of three sweep matrices being more complicated in the latter case.

Wood, Lincoln J.↗

NASA NTRS1992

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

Volakis, J. L.↗

NASA NTRS1993

Quons, an interpolation between Bose and Fermi oscillators

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics, and infinite statistics, I discuss the statistics of 'quons' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the q-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi, and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter q for electrons due to the Ramberg-Snow experiment.

Greenberg, O. W.↗

NASA NTRS1992

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Macfarlane, J. J.↗

NASA NTRS1991

nu-2 band of H2 O-16 - Line strengths and transition frequencies

High-resolution spectra of H2 O-16 were recorded with a Fourier-transform spectrometer covering transitions in the (010)-(000) band from 1066 to 2582/cm. The measured line frequencies were used along with additional data taken from studies at microwave and far-infrared frequencies in an analysis to obtain rotational energies of levels in the (000) and (010) states. Measurements of the line strengths were fitted by least squares to a model in which the dipole moment matrix elements were represented by as many as 19 expansion coefficients. The results produced computed line strength values that are in excellent agreement, on the average, with the 874 experimental transitions included in the analysis. These results provide a more accurate representation of the line positions and strengths for the (010)-(000) band than are currently available on the HITRAN absorption line parameter compilation.

Toth, Robert A.↗

NASA NTRS1992

Performance characterization of polarimetric active radar calibrators and a new single antenna design

Three aspects of a polarimetric active radar calibrator (PARC) are treated: (1) experimental measurements of the magnitudes and phases of the scattering-matrix elements of a pair of PARCs operating at 1.25 and 5.3 GHz; (2) the design, construction, and performance evaluation of a PARC; and (3) the extension of the single-target-calibration technique (STCT) to a PARC. STCT has heretofore been limited to the use of reciprocal passive calibration devices, such as spheres and trihedral corner reflectors.

Sarabandi, Kamal↗

NASA NTRS1993

A fast method of numerical quadrature for p-version finite element matrices

A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.

Hinnant, Howard E.↗

NASA NTRS1993

Photoionization of the hydrogen atom in strong magnetic fields

The photoionization of the hydrogen atom in magnetic fields B about 10 exp 11 - 10 exp 13 G typical of the surface layers of neutron stars is investigated analytically and numerically. We consider the photoionization from various tightly bound and hydrogen-like states of the atom for photons with arbitrary polarizations and wave-vector directions. It is shown that the length form of the interaction matrix elements is more appropriate in the adiabatic approximation than the velocity form, at least in the most important frequency range omega much less than omega(B), where omega(B) is the electron cyclotron frequency. Use of the length form yields nonzero cross sections for photon polarizations perpendicular to the magnetic field at omega less than omega(B); these cross sections are the ones that most strongly affect the properties of the radiation escaping from an optically thick medium, e.g., from the atmosphere of a neutron star. The results of the numerical calculations are fitted by simple analytical formulas.

Potekhin, Aleksandr IU.↗