Search NASA⌕ Search

SEARCH · Search NASA

Results for “Inversion symmetry”

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.

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

At least 19 records

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↗

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Mixing Effects in the V1 Band of NH3 - II

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

Boulet, C.↗

Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Coupling and Line Mixing Effects on NH3 Lines in the V4 Band

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular v4 band. As in the pure rotational and the parallel v1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the v1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 equals K2 equals 0, whose matrix elements require the selection rule delta k equals 0, the formalism is applicable for the v4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

Absorption coefficient↗

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.↗

Solitons in superfluid (He-3)-A - Bound states on domain walls

The effects of solitons on the spectrum of fermion excitations in superfluid (He-3)-A are investigated. It is found that there is a two-dimensional manifold of bound states with energies within the gap of the bulk superfluid. The bound-state spectrum lacks inversion symmetry parallel to the wall.

Ho, T. L.↗

Optical Characterization and 2,525 micron Lasing of Cr(2+):Cd(0.85)Mn(0.15)Te

Transition metal doped solids are of significant current interest for the development of tunable solid-state lasers for the near and mid-infrared (1-4 pm) spectral region. Applications of these lasers include basic research in atomic, molecular, and solid-state physics, optical communication, medicine, and environmental studies of the atmosphere. In transition metal based laser materials, absorption and emission of light arises from electronic transitions between crystal field split energy levels of 3d transition metal ions. The optical spectra generally exhibit broad bands due to the strong interaction between dopant and host (electron-phonon coupling). Broad emission bands offer the prospect of tunable laser activity over a wide wavelength range, e.g. the tuning range of Ti:Sapphire extends from 700-1100 run. The only current transition metal laser operating in the mid-infrared wavelength region (1.8-2.4 micro-m) is CO(2+):MgF2, but its performance is severely limited due to strong nonradiative decay at room temperature. Based on lifetime data, the quantum efficiency is estimated to be less than 3 deg/0 11,21. In general, the probability for non-radiative decay via multi-phonon relaxation increases with decreasing energy gap between ground and excited state. Therefore, efficient transition metal lasers beyond -1.6 micro-m are rare. Recently, tunable laser activity around 2.3 micro-m was observed from Cr doped ZnS and ZnSe. The new lasing center in these materials was identified as Cr(2+) occupying the tetrahedral Zn site. Tetrahedrally coordinated optical centers are rather unusual among transition metal lasers. Their potential usefulness, however, has been demonstrated by the recent development of near infrared laser materials such as Cr:forsterite and Cr:YAG, which are based on tetrahedrally coordinated Cr(4+) ions. According to the Laporte selection rule, electric-dipole transition within the optically active 3d-electron shells are parity forbidden. However, a static acentric electric crystal field or the coupling of asymmetric phonons can force electric-dipole transitions by the admixture of wave functions with opposite parity. Tetrahedral sites lack inversion symmetry which provides the odd-parity field necessary to relax the parity selection rule. Therefore, high absorption and emission cross sections are observed. An enhanced radiative emission rate is also expected to reduce the detrimental effect of non-radiative decay. Motivated by the initial results on Cr doped ZnS and ZnSe, we have started a comprehensive effort to study Cr(2+) doped II-VI semiconductors for solid-state laser applications. In this paper we present the optical properties and the demonstration of mid-infrared lasing from Cr doped Cd(0.85)Mn(0.15)Te.

Davis, V. R.↗

Line Coupling and Line Mixing Effects on Calculated Widths of Symmetric-Top Molecules With the k-Degeneracy: A Theoretical Study of N 2 -, O 2 -, and Air-Broadened Lines of CH 3 I

Calculations of the N 2 -, O 2 - and air-broadened widths, together with their temperature dependence exponents have been made for transitions of CH 3 I in the v 5 and v 6 bands. The calculations are based on a semi-classical line shape formalism developed by the current authors through modifying and refining the Robert-Bonamy formalism. In recent years, we have applied this formalism for linear molecules, symmetric-top molecules with inversion symmetry, and asymmetric-top molecules. For symmetric-top molecules with the k degeneracy such as CH 3 I, the formalism has a new feature. In this case, one should consider each of the CH 3 I transitions labeled by k i or ƒ ≠ 0 as a doublet. Then, one needs to consider the effects of the line mixing process between these two components. Comparisons of our theoretical predictions with some data available demonstrate a very reasonable agreement. Finally we propose new experiments at higher perturber pressures that would enable one to check the theoretically calculated relaxation matrices and to extend the analysis to the interdoublet mixing effects.

Line coupling↗

Suppression of Speckles at High Adaptive Correction Using Speckle Symmetry

Focal-plane speckles set important sensitivity limits on ground- or space-based imagers and coronagraphs that may be used to search for faint companions, perhaps ultimately including exoplanets, around stars. As speckles vary with atmospheric fluctuations or with drifting beamtrain aberrations, they contribute speckle noise proportional to their full amplitude. Schemes to suppress speckles are thus of great interest. At high adaptive correction, speckles organize into species, represented by algebraic terms in the expansion of the phase exponential, that have distinct spatial symmetry, even or odd, under spatial inversion. Filtering speckle patterns by symmetry may eliminate a disproportionate fraction of the speckle noise while blocking (only) half of the image signal from the off-axis companion being sought. The fraction of speckle power and hence of speckle noise in each term will vary with degree of correction, and so also will the net symmetry in the speckle pattern.

atmospheric turbulence↗

Analysis of lightning field changes produced by Florida thunderstorms

A new method is introduced for inferring the charges deposited in a lightning flash. Lightning-caused field changes (delta E's) are described by a more general volume charge distribution than is defined on a large cartesian grid system centered above the measuring networks. It is shown that a linear system of equations can be used to relate delta E's at the ground to the values of charge on this grid. It is possible to apply more general physical constraints to the charge solutions, and it is possible to access the information content of the delta E data. Computer-simulated delta E inversions show that the location and symmetry of the charge retrievals are usually consistent with the known test sources.

Koshak, William John↗

Spectroscopic line parameters of NH3 and PH3 in the far infrared

NH3 and PH3 rotation and rotation-inversion line parameters in the far to medium IR are calculated for remote sounding purposes of planetary atmospheres; 1607 lines of (N-14)H3, 362 lines of (N-15)H3 and 325 lines of PH3 are compiled. The absolute intensity formulation has been reviewed in the case of rotation and rotation-inversion lines of molecules with C(3v) symmetry. The justification for the general agreement between the authors, and comparisons with other published expressions are given.

Husson, N.↗

Use of switched capacitor filters to implement the discrete wavelet transform

This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.

Kaiser, Kraig E.↗

Collisional broadening, line shifting, and line mixing in the stimulated Raman 2nu2 Q branch of CH4

Self-, argon-, and helium-broadening coefficients have been measured for 13 lines in the 2nu2 Raman Q branch of CH4 using stimulated inverse Raman spectroscopy. The linewidths clearly show the symmetry-state dependence characteristic of pressure broadening, and inelastic processes in general, involving spherical-top molecules. Pressure-induced line shifts have also been measured for these features in pure methane. The pressure-shift coefficients do not display the symmetry-state dependence found for the linewidths. By applying the Rosenkranz perturbation treatment to a pair of collisionally mixed lines, an estimate of individual state-to-state contributions to the overall linewidth has been obtained.

Millot, G.↗

Electromagnetic inverse scattering

A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.

Bojarski, N. N.↗

Excited State Chemistry in the Free Stream of the NASA IHF Arc Jet Facility Observed by Emission Spectroscopy

Spectroscopic measurements of non-equilibrium emission were made in the free stream of the 60 megawatts Interaction Heating Facility at NASA Ames Research Center. In the visible near infrared wavelength region, the most prominent emission was from molecular N2, and in the ultra violet region, the spectra were dominated by emission from molecular NO. The only atomic lines observed were those of copper (an erosion product of the electrodes). The bands of the 1st Positive system of N2 (if B is true then A is true) differed significantly from spectra computed spectra assuming only thermal excitation, suggesting overpopulation of the high vibrational states of the B state of N2. Populations of these high vibrational levels (peaking at v (sub upper) equals 13) of the N2 B state were determined by scaling simulated spectra; calculations were performed for each upper vibrational state separately. The experimental-theoretical procedure was repeated for several radial positions away from the nozzle axis to obtain spatial distributions of the upper state populations; rotational symmetry of the flow was assumed in simulations. The overpopulation of the high vibrational levels has been interpreted as the effect of inverse pre-dissociation of neutral atoms in the N2 A state, which populates the N2 B state through a level crossing process at v (sub upper) is greater than 10.

arc-jet testing↗

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Thurston, G. A.↗

Unoccupied electronic resonances of Sc adsorbed on W(001) by k-resolved inverse photoemission

Scandium adsorbed on the (001) face of tungsten has been studied using Auger-electron spectroscopy, low-energy electron diffraction, k-resolved inverse photoelectron spectroscopy, work-function measurements, and relativistic-electronic-structure calculations. We find that the work function of W(001) does not decrease monotonically as a function of scandium adsorption but reaches a minimum value of Phi = 3.25 eV at 50% coverage. For a complete monolayer, an order 1 X 1 Sc overlayer is formed. Inverse photoemission in the isochromat mode was used to map the unoccupied energy levels of this overlayer along the bar-Gamma(bar-Mu) symmetry direction of the surface Brillouin zone. Local-density-functional calculations using the muffin-tin orbital method were performed for a 1 X 1 Sc overlayer on W and are compared with the experimental two-dimensional band structure.

Lamouri, A.↗

Singular Isothermal Disks: Nonaxiymmetric Bifurcations and Equilibria - Paper 2

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Danielle↗