Pseudopotentials, the sizes of atoms and their s-p splittings.
Free-atomic pseudopotentials, sizes, s-p splittings and pseudowave functions
ENERGY LEVEL↗
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Serial segment method for measuring remnant
For tracking tasks where a sum of sine waves forcing function is used it is often difficult and/or expensive to obtain the pilot's remnant in the vicinity of the sine waves. For the case where each sine wave has at least four times an integer number of cycle per run length, this paper illustrates the serial segments method for measuring remnant power spectral density in a frequency band centered on each sine wave. This method can be implemented on digital, hybrid, or analog Fourier coefficient analyzers, and is particularly advantageous on the latter since properties of Fourier coefficients are exploited to yield both a remnant measure and an improved estimate of the correlated component.
Magdaleno, R. E.↗
Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions
The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.
Farassat, F.↗
Response functions of free mass gravitational wave antennas
The work of Gursel, Linsay, Spero, Saulson, Whitcomb and Weiss (1984) on the response of a free-mass interferometric antenna is extended. Starting from first principles, the earlier work derived the response of a 2-arm gravitational wave antenna to plane polarized gravitational waves. Equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) are obtained by a simple differencing of the '3-pulse' Doppler response functions of two 1-arm antennas. A '4-pulse' response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions ('3n+1 pulse') for antennas having multiple passes or more arms.
Estabrook, F. B.↗
Stochastic model of temporal changes of wind spectra in the free atmosphere
Data for wind profile spectra changes with respect to time from Cape Kennedy, Florida for the time period from 28 November 1964 to 11 May 1967 have been analyzed. A universal statistical distribution of the spectral change which encompasses all vertical wave numbers, wind speed categories, and elapsed time has been developed for the standard deviation of the time changes of detailed wind profile spectra as a function of wave number.
Huang, Y. H.↗
Influence of phase cancellation and pulse shape artifacts on ultrasonic spectrum analysis
Both continuous wave and Fourier transformed pulse ultrasonic spectroscopy are being applied to material and flow characterization. Ideal samples and flaws (flat, parallel, and homogeneous) and ideal ultrasonic apparatus (producing delta function stress waves) provide acoustic spectra which can be partially inverted. However, in the presence of material inhomogeneity, lack of sample flatness or parallelism, or finite risetime pulses, the spectra become quite complex and produce phase cancellations at the transducer as well as pulse shape spectral artifacts. In this paper, we examine the nature of these artifacts for both simple and practical samples. Sample spectra are contrasted for several different transducer/electronic systems. Spectra obtained with a phase insensitive acousto-electric transducer (AET) combined with a frequency tracked tone-burst spectroscopy (TBS) method are presented. Analysis of the test configuration is shown to produce spectra consistent with that obtained with the AET-TBS combination.
Heyman, J. S.↗
Dual frequency correlation radar measurements of the height statistics of ocean waves
A radar technique has been developed for measuring the statistical height properties of a random rough surface. This method is being applied to the problem of measuring the significant wave height and probability density function of ocean waves from an aircraft or spacecraft. Earlier theoretical and laboratory results have been extended to define the requirements and performance limitations of flight systems. Some details of the current airborne radar system are discussed and results obtained on several experimental missions are presented and interpreted.
Weissman, D. E.↗
Multi-wave interaction theory for wind-generated surface gravity waves
Consistently employing the assumption of localness of wave-wave interactions in the wavenumber space, the Kolmogorov treatment of the energy cascade is applied to the case of wind-generated surface gravity waves. The effective number v of resonantly interacting wave harmonics is not limited to four but is found as a solution of a coupled system of equations expressing: (i) the dependence of the spectrum shape on the degree of the wave nonlinearity, and (ii) the continuity of the wave action flux through the spectrum given a continuous positive input from wind. The latter is specified in a Miles-type fashion, and a simple scaling relationship based on the concept of the turnover time is derived in place of the kinetic equation. The mathematical problem is reduced to an ordinary differential equation of first order. The exponent in the 'power law' for the spectral density of the wave potential energy and the effective number of resonantly interacting wave harmonics are found as functions of the wave frequency and of external factors of wind-wave interaction. The solution is close to the Zakharov-Filonenko spectrum at low frequencies and low wind input while approaching the Phillips spectrum at high frequencies and sufficiently high wind.
Glazman, Roman E.↗
Equations, tables, and charts for compressible flow
This report, which is a revision and extension of NACA-TN-1428, presents a compilation of equations, tables, and charts useful in the analysis of high-speed flow of a compressible fluid. The equations provide relations for continuous one-dimensional flow, normal and oblique shock waves, and Prandtl-Meyer expansions for both perfect and imperfect gases. The tables present useful dimensionless ratios for continuous one-dimensional flow and for normal shock waves as functions of Mach number for air considered as a perfect gas. One series of charts presents the characteristics of the flow of air (considered a perfect gas) for oblique shock waves and for cones in a supersonic air stream. A second series shows the effects of caloric imperfections on continuous one-dimensional flow and on the flow through normal and oblique shock waves. (author)
Source record↗
Vertical tilts of tropospheric waves - Observations and theory
Two methods are used to investigate the vertical tilts of planetary waves as functions of zonal wavenumber and frequency. The vertical tilts are computed by cross-spectral analysis of the geopotential heights at different pressures. In the midlatitude troposphere, the eastward-moving waves had a westward tilt with height, as expected, but the westward-moving waves with frequencies higher than 0.2/d showed statistically significant eastward vertical tilts. For a free Rossby wave, this implies that the Eliassen-Palm flux is downward along with its energy propagation. A downward energy propagation suggests an upper-level source of these waves. It is proposed that the eastward-tilting waves were forced by the nonlinear interaction of stationary waves and baroclinically unstable cyclone-scale waves. The predicted vertical tilt and phase speed were consistent with the observations. In addition, simulations of a general circulation model were analyzed. In the control run, eastward-tilting waves disappeared when the sources of stationary waves were removed. This is consistent with the present theory.
Ebisuzaki, Wesley↗
On the generation of magnetohydrodynamic waves in a stratified and magnetized fluid. I - Vertical propagation
The generation of MHD waves by turbulent motions in a stratified medium with an embedded uniform magnetic field, a topic which is relevant to the study of the solar atmosphere, is considered. Both compressible and incompressible MHD waves are treated in a one-dimensional approach; however, the direction of the background magnetic field is permitted to vary in an arbitrary direction. Theoretical expressions for MHD energy fluxes are obtained as a function of wave frequency and multipole coefficients. It is shown that monopole, dipole, and quadrupole emissions are responsible for the generation of the compressible components of the fast and slow modes. However, the incompressible components and the Alfven modes can be generated by the dipole emission only. Specific results obtained for special magnetic field geometries are discussed for the fast and slow modes.
Musielak, Z. E.↗
A Comparison Between Gravity Wave Momentum Fluxes in Observations and Climate Models
For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations,MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.
mathematical models↗
D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems
In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.
D-wave↗
Jovian seismology
It is hypothesized that observations of the Doppler shifting of IR and UV absorption lines may furnish a powerful method for the detection of 4.5-9 min standing acoustic waves trapped in a wave duct beneath the Jupiter tropopause. Similarly, data could be obtained on Jupiter's thermal and density structure, and on the depth to which its zonal winds penetrate. The present model of standing oscillations in the molecular hydrogen envelope gives attention to theoretical eigenfrequencies and to such forcing functions for wave generation as coupling with turbulent and convective motions, thermal instability due to radiative transfer, wave propagation effects in a saturated atmosphere, and ortho-to-parahydrogen conversion. The small contribution that the forcing mechanisms make to velocity amplitudes implies that the Doppler shifting caused by the waves may only be resolvable through the superposition of oscillation records to enhance S/N ratios.
Bercovici, D.↗
Observations of collisionless drift waves.
Velocity distribution functions of both the electron and the proton component of the magnetospheric plasma are measured in 62 logarithmically spaced steps from 50 eV to 50 keV by an instrument carried upon the ATS-5 spacecraft in circular synchronous orbit (6.6 earth radii). Oscillations which appear to be collisionless drift waves having periods of several minutes or longer are found in this data. Linearized wave theory can be used to predict the theoretical perturbation distribution function in terms of the perturbing fields and the equilibrium distribution function. The functional dependence of the theoretical perturbation distribution function upon particle energy can then be compared with that of the measured perturbation.
Laquey, R. E.↗
Investigation of Site Amplifications Using Ambient-Noise-Derived Shallow Velocity Structures Under a Dense Array in Oklahoma
The shear-wave velocity (V S ) structure plays an important role in characterizing site amplification. The Large-n Seismic Survey in Oklahoma (LASSO; 1820 stations) revealed large vertical ground-motion variability in a 25 km × 32 km area in northern Oklahoma. The LASSO array has a relatively simple and flat topography, typical in a sedimentary basin environment in the central United States. In this study, we use the dense array to investigate the velocity structure under the LASSO array and how vertical ground motions relate to the shallow-to-deep structures. We extract the fundamental-mode Rayleigh wave by cross-correlating one month of ambient noise (0.7–5 Hz). We use double-beamforming to measure the group and phase velocities and anisotropy. By jointly inverting the group and phase velocities, we obtain the V S structure. Here, we observe correlations between V S at depths of 0.1–1.5 km and vertical ground motions using sites on the stiffer Permian formations. The shallow Quaternary alluvium and terrace deposits can amplify vertical ground motions by a factor of 2–4.5 between 2 and 25 Hz and attenuate signals above 25 Hz. We use 1D V S profiles to simulate the SV-wave transfer functions. An average V S of 250 m/s in the upper 20–40 m may cause the observed amplification between 2 and 40 Hz. V S estimated by topographic slopes cannot predict the relative amplification. Our results highlight the large variability of site-dependent ground motion in a small local region and the importance of characterizing shallow structures to estimate seismic hazards. Small thickness variations of the shallow formation can significantly change the resonance amplitude and frequency, which likely reduces the coherency of the Rayleigh waves extracted from ambient noise.
Chang, Hilary [Massachusetts Inst. of Technology (↗
Magnon-Magnon Interaction Induced by Dynamic Coupling in a Hybrid Magnonic Crystal
We report a combined experimental and numerical investigation of spin-wave dynamics in a hybrid magnonic crystal consisting of a CoFeB artificial spin ice (ASI) of stadium-shaped nanoelements patterned atop a continuous NiFe film separated by a 5 nm Al 2 O 3 spacer. Using Brillouin light scattering spectroscopy, we probe the frequency dependence of thermal spin waves as functions of applied magnetic field and wavevector, revealing the decisive role of interlayer dipolar coupling in the magnetization dynamics. Micromagnetic simulations complement the experiments, showing a strong interplay between ASI edge modes and backward volume modes in the NiFe film. The contrast in saturation magnetization between CoFeB and NiFe enhances this coupling, leading to a pronounced hybridization manifested as a triplet of peaks in the BLS spectra predicted by simulations and observed experimentally. This magnon−magnon coupling persists over a wide magnetic field range, shaping both the spin-wave dispersion at fixed fields and the full frequency-field response throughout the magnetic hysteresis loop. Our findings establish how ASI geometry can selectively enhance specific spin-wave wavelengths in the underlying film, thereby boosting their amplitude and identifying them as preferential channels for spin wave transmission and manipulation.
Brillouin light scattering spectroscopy↗
The correlation function in Kirchhoff's method of solution of scattering of waves from statistically rough surfaces.
Improved correlation function in Kirchhoff- Huygen method of solution of scattering of waves from statistically rough surfaces
ELECTROMAGNETIC SCATTERING↗