Harmonic Power Spectrum Research Articles

Anomalies in Universal Intensity Scaling in Ultrarelativistic Laser-Plasma Interactions

Laser light incident on targets at intensities such that the electron dynamics is ultrarelativistic gives rise to a harmonic power spectrum extending to high orders and characterized by a relatively slow decay with the harmonic number m that follows a power law dependence, m(-p). Relativistic similarity theory predicts a universal value for p=8/3 up to some cutoff m=m*. The results presented in this Letter suggest that under conditions in which plasma effects contribute to the emission spectrum, the extent of this contribution may invalidate the concept of universal decay. We report a decay with the harmonic number in the ultrarelativistic range characterized by an index 5/3 < or approximately p < or approximately 7/3, significantly weaker than that predicted by the similarity model.

Method of Evaluation of Electron Transfer Kinetics of a Surface-Confined Redox System by Means of Fourier Transformed Square Wave Voltammetry

A new form of Fourier transformed square wave voltammetry (FT-SWV) is proposed to simplify and accelerate the electron transfer kinetics evaluation procedures for surface-confined redox systems. Even harmonic frequencies, which are derived from the nonlinear Faradaic response, will arise in the power spectrum after Fourier transformation of the current response of FT-SWV. The profile of the even harmonic power spectra is bell-shaped and shows a maximum at a certain frequency. The electrode kinetics-dependent maximum and the corresponding frequency are equivalent to the so-called "quasi-reversible maximum" and "critical frequency" (fmax) in traditional SWV, respectively. The critical frequency can be regarded as a frequency that is synchronized to the electron transfer rate constant (k(0)). As a result, it can serve as a probe of k(0) by means of a very simple equation, k(0) = kmax fmax. Compared with traditional cyclic voltammetry, square wave voltammetry, alternating current voltammetry, and several other voltammetric techniques, this method exhibits great advantages for its simplicity, rapidity, and sensitivity.

General Method for Reducing Adaptive Laser Pulse-Shaping Experiments to a Single Control Variable

Adaptive laser pulse shaping has proven to be expeditious for discovering laser pulse shapes capable of manipulating complex systems. However, if adaptive control is to be a valuable interrogative technique that informs physical and chemical research, methods that make it possible to infer mechanistic information from experimental results must be developed. Here, we demonstrate multivariate statistical analysis to extract a single control variable from results of a 137-parameter adaptive laser pulse-shaping optimization of multiphoton electronic excitation in a ruthenium(II) coordination complex in solution. We show that this single variable can be used to linearly manipulate the observed fitness, which is determined by the ratio of molecular emission to second harmonic generation of the laser pulse, over the range explored during the adaptive optimization. Further, manipulation of this variable reveals the latent control mechanism. For this system, that mechanism entails focusing the second harmonic power spectrum of the laser field in a spectral region where the probability of two-photon absorption by the molecule is also large. The statistical tools developed are general and will help elucidate control mechanisms in future adaptive pulse-shaping experiments.

Mirage: A new iterative map-making code for CMB experiments

A major goal of CMB experiments is to obtain highly sensitive CMB maps in order to extract Spherical Harmonic Power Spectrum (SHPS) and cosmological parameters with unprecedented accuracy. We present a new map-making code (Mirage), based on a two-phase iterative algorithm, involving low frequency drift treatment, Butterworth high-pass filtering and conjugate gradient method. This work was strongly motivated by Archeops CMB experiment data analysis. We believe that Archeops was a good test bench for the future Planck Surveyor data analysis, and Mirage was designed in order to be used for Planck data processing with minimal work. A strong feature of Mirage is that it handles experimental problems in data, such as holes in data stream, bright sources, and galaxy side effects, without jeopardising speed. The other advantage is its processing speed, allowing to run Monte Carlo simulations of Archeops data processing on a single processor workstation overnight. Algorithms are explained. Systematic effects on SHPS are investigated on various simulated data, including typical Archeops observational systematics. This code is available at adress http://www-dapnia.cea.fr/Telechargement/ Preprint with full resolution figures is available at http://www-dapnia.cea.fr/Doc/Publications/Archives/dapnia-03-378.pdf

Performance of a 1 MV A high temperature superconductors-enabled saturable magneticcore-type fault current limiter

A 1 MV A single-phase DC saturated iron core-type fault current limiter (FCL) employingDC coils manufactured from Bi-2223/Ag high temperature superconductor has beendesigned, constructed, and tested. The device, configured to respond to a fault occurring oneither the positive or negative wave cycle, exhibited instantaneous reaction and reset times.It could clip a continuous applied steady state fault current of 1200 A, and limited atransient peak fault current of 2200 A to the specified current of 100 A. The operation of thedevice did not produce any significant harmonic contribution from the clipping action, asunder fault conditions, 99.96% of the harmonic power spectrum of the clipped waveformcontributed to the fundamental, and the non-fault inductance of the FCL was<0.01 mH.

The harmonic power spectrum of the soft X-ray background

Fluctuations of the soft X-ray background are investigated using harmonic analysis. A section of the ROSAT All-Sky Survey around the north galactic pole is used. The flux distribution is expanded into a set of harmonic functions and the power spectrum is determined. Several subsamples of the RASS have been used and the spectra for different regions and energies are presented. The effects of the data binning in pixels are assessed and taken into account. The spectra of the analyzed samples reflect both small scale effects generated by strong discrete sources and the large scale gradients of the XRB distribution. Our results show that the power spectrum technique can be effectively used to investigate anisotropy of the XRB at various scales. This statistics will become a useful tool in the investigation of various XRB components.

Gravity and Nongravity Modes in the VIRMOS‐DESCART Weak‐Lensing Survey

We analyze the weak-lensing data of the VIRMOS imaging survey using projections (called E- and B-modes) of the two independent observable correlation functions. The E-mode contains all the lensing signal, while noise and systematics contribute equally to the E-and B-modes provided that intrinsic alignment is negligible. The mode separation allows a measurement of the signal with smaller error bars and a separate channel to test for systematic errors. We apply various transformations, including a spherical harmonic space power spectrum C and C, which provides a direct measurement of the projected dark matter distribution for 500 < l < 104.

Investigation of the Harmonic Generation in Conventional Radio Frequency Heating Systems

This paper investigates the generation of harmonics in conventional radio frequency (rf) heating systems. An extended circuit model encapsulating the harmonic characteristics of the system is derived using Foster’s theorem. This model is analyzed using both an analytic and a circuit simulation approach. The effect of varying the tuning conditions of the system on the harmonic power spectrum is investigated for a typical system. This has revealed some correlation between the resonant modes of the system and its harmonics, which has been postulated in mathematical form as dimensionless factors.

Reduced high harmonic power spectra in patients with old myocardial infarction.

Acceleration of blood flow ejected from the ventricle into the aorta and the hydraulic power state of blood flow in the aorta may be affected by asynchronous or locally depressed contraction of the left ventricle as well as by arterial impedance. In order to evaluate the effect of an infarcted heart on the hydraulic power state of blood flow, the aortic input impedance spectrum and the hydraulic power spectrum were calculated from simultaneous recordings of pulsatile aortic pressure and flow velocity at the aortic root in 6 normal controls (group 1), 6 patients with old myocardial infarction (OMI) without aneurysm (group 2), and 6 patients of OMI with aneurysm (group 3). The ratios (Rh) of power in high harmonics to that of fundamental harmonics, that is, Rh = (E2 + E3 + ...E10)/E1, where E represents hydraulic power and the numbers represent harmonic numbers, were 0.64 +/- 0.17, 0.23 +/- 0.09, and 0.22 +/- 0.10 in groups 1, 2, and respectively (p less than 0.001 between groups 1 and 2; p less than 0.001, between groups 1 and 3). As the acceleration of ejecting flow of blood by the left ventricle is inversely related with arterial impedance, Rh will be also inversely related with arterial impedance. Then, the product of Rh and the characteristic impedance (Zc) would be an indicator of the left ventricular contractility. In fact, the products were 64 +/- 15, 32 +/- 14, and 31 +/- 13 dyne.sec.cm-5 in groups 1, 2, and 3 respectively (p less than 0.005, between groups 1 and 2; p less than 0.005, between groups 1 and 3). These results suggest that asynchronous or locally depressed contractions of the left ventricular wall are closely related to depressed Rh and further to depressed values of the products of Rh and Zc. It is concluded that analysis of the power spectrum of blood flow in the root of the aorta provides information of the left ventricular contractility in connection with arterial impedance.

Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data

Analysis of global traveltime data has been formulated in terms of the stochastic properties of the Earth's heterogeneity pattern and random errors in the data. The formalism relates the coherency of traveltime residuals within bundles of rays (summary rays) of varying size to the spherical harmonic power spectrum of the slowness field of the medium. It has been applied to mantle P-wave data from the ISC catalogue. The measure of coherency is the variance within summary rays. It is estimated within bins in source depth, epicentral distance and the scale size of the area defining a summary ray. The variance at infinitesimal scale length represents the incoherent component of the data (random errors). The variation of the variance with scale length contains information about the autocorrelation function or power spectrum of slowness perturbations within the Earth. The variation with epicentral distance reflects the depth variation of the spectrum. The formalism accounts for the uneven distribution (clustering) of stations and events. We find that estimates of random errors correlate well with complexities on the traveltime curve of P-waves. The variance peaks at 1.0–2.0 s^2 at Δ ≈ 20°, where triplications occur on the traveltime curve, drops to 0.15–0.8s^2 at teleseismic distances, and rises to 0.4–1.3 s^2 approaching the core shadow, where the traveltime curves of P-waves and PcP-waves merge. These estimates should be considered upper bounds for the random error variance of the data. The signal to random noise ratio in the teleseismic ISC P-wave data is about S/N ≈ 2. Inversion of the scale-dependent structural signal in the data yields models that concentrate heterogeneity strongly in the upper mantle. The product of correlation length and power drops by about two orders of magnitude from the surface of the Earth to the lower mantle. About half of this quantity in the upper mantle is due to small-scale features (<300km). The lower mantle is devoid of small-scale structure. It contains 0.1 per cent velocity variations at a characteristic scale of about 1000km. This corresponds to a spectral band-width of l ≈ 7. The D″ layer at the bottom 100–200 km of the mantle shows up as a distinct layer in our results. It has 0.3 per cent velocity variations at a characteristic scale of 350km. The top of the lower mantle contains 0.3 per cent velocity variations on a scale of 500km and also contains some small-scale power. These results are compatible with previous deterministic lower mantle studies, although some details differ. The strength of heterogeneity in the upper mantle may obscure attempts to model the Earth's deep interior.

The Forcing of Gravitational Normal Modes by Condensational Heating

Abstract Time series of normal mode coefficients were determined by projection of data produced at every time step for 64 days of a long climate simulation with the NCAR Community Climate Model. Harmonic dials and power spectra for selected gravitational modes were examined. One result is that the greatest power for gravitational modes is typically at the longest periods examined, but noteworthy relative maxima also occur near a mode's resonant period and corresponding time-computational period. For most naturally fast modes, the power at long periods tends to be many times greater than the power near the resonant period, implying that the behavior of these modes may be characterized as approximately balanced. For naturally slow modes, such as Kelvin modes, however, the portion of power near the mode's resonant period is often nonnegligible, implying that these modes are characterized by quasi-linear, wavelike propagation, rather than by either diabatic or adiabatic balance behavior. For the same simulate...

ON SPHERICAL POWER SPECTRUM ANALYSIS

ABSTRACT The definition and interpretation of the spherical harmonic power spectrum of a set of positions on the sphere is reviewed, and the technique is then applied to samples of optical and radio bright quasars. The optical sample is shown to be affected by galactic obscuration, and, in addition, an inhomogeneity is found on the scale of the field centers. This is attributed to variations in sensitivity from field to field, as indicated by variations in the limiting magnitudes of the fields. The radio bright sample is found to be random.

The propagation characteristics of interannual low-frequency oscillations in the tropical air-sea system

The time series of sea surface temperature(SST), sea level pressure (SLP), zonal wind (U) and total cloudiness (CA), for the period of 1950-1979, over a 8°x8° grid-point latitudinal belt between 32° S and 32°N are made from COADS (Comprehensive Ocean-Atmosphere Data Set). The time harmonic analysis and power spectra analysis show that there exist quasi-biennial oscillation (QBO), three and half years oscillation (SO), five and half years oscillation (FYO) and eleven years oscillation (EYO) in these time series. The main propagation characteristics of these interannual low-frequency oscillations are as follows: (1) The variance analysis of SST shows that there is an active region of QBO and SO (with maximum variance), coming from the southwestern part of the subtropical Pacific, stretching eastward up to the west coast of South America, and then northward to the eastern equatorial Pacific. The QBO and SO disturbances of SST follow the same route and cause the anomaly of SST (El Nino and period of cold water) in the eastern equatorial Pacific. (2) Either the QBO or SO of SST can cause El Nino events, although it is easier when they are situated in the same phase of warm water at the eastern equatorial Pacific. The FYO of SST seems to be a standing oscillation. It plays an important role on the formation of strong El Nino events or strong cold water events. (3) The QBO and SO of U propagate eastward along the equator. The origin of QBO and SO may at least be traced as far as the western Indian Ocean. While they propagate along the equator, it strengthens two times at 90° E and the western Pacific, respectively. Like SST, the FYO of U is somehow a standing oscillation. (4) The Oscillations of U have a good coupling relationship with those of SST, while they propagate. When the QBO and SO of SST move to the east side of the eastern equatorial Pacific, it is the time for the QBO and SO of U to enter into the east part of the western Pacific.

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Lowes (1966, 1974) has introduced the function R n defined by R n =(n + 1) ∑ m=0 ∞ [(g m n) 2 + (h m n) 2] where g n m and h n m are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = −∇ V on a sphere of radius r > α is given by 〈 B ·〉 = ∑ n=1 ∞ R n( a/ r ) 2n=4 where a is the Earth's radius. We refer to R n as the spherical harmonic spatial power spectrum of the geomagnetic field. In this paper it is shown that R n = R M n = R C n where the components R n M due to the main (or core) field and R n C due to the crustal field are given approximately by R M n = [ (n =1)/ (n + 2) ](1.142 × 10 9)(0.288 n Λ 2 R C n = [ (n =1){[1 — exp(-n/290)]/ (n/290)} 0.52 Λ 2 where Iγ = 1 nT . The two components are approximately equal for n = 15. Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963). The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model. Equations relating average great circle power spectra of the geomagnetic field components to R n are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the R n for celestial bodies from average great circle power spectra of the magnetic field components.

Theory of statistical analysis of data distributed over a sphere

The problem of obtaining a representation of a variable on a sphere from irregularly distributed observations is divided into two topics (1) Spectral representation: the relationships between covariances, spherical harmonic coefficients, power spectra, etc.; and (2) statistical analysis: extrapolation, power spectrum, and coefficient determination, etc., under the assumption of stationarity. The relationships of various techniques are discussed.