Fourier Parameter Research Articles

Photometric and spectroscopic study of the Shakhbazian compact galaxy groups ShCG 254, ShCG 257, ShCG 351, and ShCG 371

Results of a detailed spectroscopic and photometric study of the four Shakhbazian compact galaxy groups ShCG 254, ShCG 257, ShCG 351, and ShCG 371 are reported. The redishifts of the member galaxies and radial velocity dispersions in these groups have been determined. The R surface brightness distributions of the member galaxies have been studied. The morphological types of the galaxies have been determined based on the profiles of the surface brightness, µ, as functions of the semimajor axis α1/4 or α. Some members of the groups are in the process of interacting. Curves of isophotal twisting and the Fourier parameter α4 have been plotted. The physical parameters of the groups (radial velocity dispersions, virial radii and masses, luminosities, mass-to-luminosity ratios, and crossing times) have also been derived.

A new method for the spectroscopic identification of stellar non-radial pulsation modes

We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. The mode identification is carried out by minimizing chi-square, using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 <= l <= 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of pm 1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating Delta Scuti and Beta Cephei stars.

Analysis of RR Lyrae Stars in the Northern Sky Variability Survey

We use data from the Northern Sky Variability Survey (NSVS), obtained from the first-generation Robotic Optical Transient Search Experiment (ROTSE-I), to identify and study RR Lyrae variable stars in the solar neighborhood. We initially identified 1197 RRab (RR0) candidate stars brighter than the ROTSE median magnitude V = 14. Periods, amplitudes, and mean V magnitudes are determined for a subset of 1188 RRab stars with well-defined light curves. Metallicities are determined for 589 stars by the Fourier parameter method and by the relationship between period, amplitude, and [Fe/H]. We comment on the difficulties of clearly classifying RRc (RR1) variables in the NSVS data set. Distances to the RRab stars are calculated using an adopted luminosity-metallicity relation with corrections for interstellar extinction. The 589 RRab stars in our final sample are used to study the properties of the RRab population within 5 kpc of the Sun. The Bailey diagram of period versus amplitude shows that the largest component of this sample belongs to Oosterhoff type I. Metal-rich ([Fe/H] > -1) RRab stars appear to be associated with the Galactic disk. Our metal-rich RRab sample may include a thin-disk, as well as a thick-disk population, although the uncertainties are too large to establish this. There is some evidence among the metal-rich RRab stars for a decline in scale height with increasing [Fe/H], as was found by Layden. The distribution of RRab stars with -1 < [Fe/H] < -1.25 indicates that within this metallicity range the RRab stars are a mixture of stars belonging to halo and disk populations.

Shakhbazian compact galaxy groups

We present the results of a detailed spectroscopic and photometric study of four Shakhbazian compact groups: ShCG 8, ShCG 14, ShCG 19, and ShCG 22. We determined the redshifts of member galaxies and radial velocity dispersions of groups. We also studied the distribution of the surface brightness of member galaxies in R and determined their morphological types. The profiles of the surface brightness versus semi-major axis, the curves of isophotal twisting, and Fourier parameter a4 are constructed. We found that some members of groups are in the process of interaction. We determined physical parameters of groups: virial masses, luminosities, mass-to-luminosity ratios, and the crossing times. On the basis of the results obtained in this and our previous works, the general properties of 22 ShCGs are discussed.

Spectroscopy and photometry of ShCG 191 - Abell 1097

In the course of investigation of Shakhbazian compact groups we studied the group ShCG 191 which has been identified also as the Abell cluster A1097. By its richness it may be classified as a rich compact group or a poor cluster. We determined redshifts of 14 objects in the area of the cluster and found that two of the supposed members of the group are stars. Redshifts of 12 galaxies show that the system is gravitationally bound. The V and R magnitudes of 23 member galaxies and their morphological types are determined. We present in this paper also the surface brightness contours of member galaxies in the central area of the cluster, the curves of isophotal twisting and the Fourier parameter a4. It is shown that some galaxies in the cluster are interacting with each other. Physical parameters of the group are close to those of ShCGs. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Dislocation Microstructures Identification by X-Ray Diffraction-Line Broadening Analysis

Our work placed within the framework analysis of the microstructure evolutions of the crystalline materials related to the linear defects (dislocations), in order to determine the associated stored (potential) elastic energy [1]. The aim is to identify the final dislocation configurations (density and arrangement) obtained after deformation. A new approach, based on micromechanical development introducing Green's function tensor and dislocation density tensor, was developed. Calculation of the elastic distortion tensor for an edge dislocation was deduced by analytical and numerical integration methods. By projection over the diffracting volumes, the variation of the Fourier coefficients versus the harmonic Fourier parameter is also determined for various diffracting planes. It is also shown that, as the dislocation crystallography is included in our approach, it is not necessary to use a contrast factor.

Interrelation of Modal Amplitudes of Double-Mode Pulsators

AbstractDuring the study of the factors governing the modal amplitudes of the double-mode radial pulsators, it has been found that the R21 Fourier parameter deduced from the light curves is in a relationship with the ratio of the modal amplitudes, for beat Cepheids and RR Lyrae variables, as well. The form of this relation gives a natural explanation for the fact that double-mode pulsators with slightly excited second modes do not exist.

The quantization of the chiral Schwinger model based on the BFT-BFV formalism II

We apply an improved version of Batalin-Fradkin-Tyutin Hamiltonian method to the a = 1 chiral Schwinger model, which is much more nontrivial than the a>1 one. Furthermore, through the path integral quantization, we newly resolve the problem of the nontrivial -function as well as that of the unwanted Fourier parameter in the measure. As a result, we explicitly obtain the fully gauge invariant partition function, which includes a new type of Wess-Zumino term irrelevant to the gauge symmetry as well as the usual WZ action.

Axisymmetric resonant disturbances in a homogeneous wave guide

Abstract The initial boundary-value linear stability problem for small localised axisymmetric disturbances in a homogeneous elastic wave guide, with the free upper surface and the lower surface being rigidly attached to a half-space, is formally solved by applying the Laplace transform in time and the Hankel transforms of zero and first orders in space. An asymptotic evaluation of the solution, expressed as a sum of inverse Laplace-Hankel integrals, is carried out by using the approach of the mathematical formalism of absolute and convective instabilities. It is shown that the dispersion-relation function of the problem D 0 ( κ , ω ), where the Hankel parameter κ is substituted by a wave number (and the Fourier parameter) κ, coincides with the dispersion-relation function D 0 ( k , ω ) for two-dimensional (2-D) disturbances in a homogeneous wave guide, where ω is the frequency (and the Laplace parameter) in both cases. An analysis for localised 2-D disturbances in a homogeneous wave guide is then applied. We obtain asymptotic expressions for wave packets, triggered by axisymmetric perturbations localised in space and finite in time, as well as for responses to axisymmetric sources localised in space, with the time dependence satisfying e − iω 0 t + O ( e − ϵt ) for t → ∞, where Im ω 0 = 0, ϵ > 0, and t denotes time, i.e. for signalling with frequency ω 0 . We demonstrate that, for certain combinations of physical parameters, axisymmetric wave packets with an algebraic temporal decay and axisymmetric signalling with an algebraic temporal growth, as √ t , i.e., axisymmetric temporal resonances, are present in a neutrally stable homogeneous wave guide. The set of physically relevant wave guides having axisymmetric resonances is shown to be fairly wide. Furthermore, since an axisymmetric part of any source is L 2 -orthogonal to its non-axisymmetric part, a 3-D signalling with a non-vanishing axisymmetric component at an axisymmetric resonant frequency will generally grow algebraically in time. These results support our hypothesis concerning a possible resonant triggering mechanism of certain earthquakes, see Brevdo, 1998 , J. Elasticity, 49, 201–237.

The characteristics of second-overtone-mode Cepheids predicted by non-linear pulsation models

Non-linear pulsation models of second-overtone-mode Cepheids have been constructed to study the theoretical characteristics of these hypothetical stars which could lead to observational criteria for their identification. The main results of this work are: (1) the light and velocity curves are similar in part to those of first-overtone Cepheid models; (2) the curves are modulated by the resonance between the second- and the sixth-overtone modes, P 2 /P 6 = 2; (3) observed stars should have smaller amplitudes than those of first-overtone s-Cepheids by a factor ∼1.6, and should have more symmetric light curves; (4) observed Fourier parameter-period diagrams should be similar to those of first-overtone Cepheids but with the observed resonance ‘centre’ at P ∼ 1 d; the true position, however, should be a function of the mass-luminosity relation. Since second-overtone-mode Cepheids may exist in Magellanic Clouds, they could be identified with a certain confidence level by considering their position both in the P – L diagram and in the Fourier parameter diagrams.

A modulation model for the vowel sound /i/ in human speech

An approach has been developed that models a nonstationary speech signal with very low error on a pitch period by pitch period basis using an AM–FM model. The speech signal is first separated into two independent signals, a low-frequency signal and a high-frequency signal. AM and FM signals are extracted from the high-frequency signal through the use of two nonlinear operators, the integral operator and the overmodulation detection algorithm. Model parameters are determined by a combination of direct Fourier series computation and parameter optimization using the correlation error measure and the Marquardt–Levenberg algorithm. This technique was applied to speech produced in various gas concentrations of air and helium in order to determine whether model parameters are directly related to the velocity of sound ratio. It was found that the amplitudes of the harmonics of the low-frequency signal were emphasized with the increase of the velocity of sound ratio. The standard deviation of the carrier frequency of the FM signal tended to increase with the velocity of sound ratio. The amplitudes of the AM signal had a modal structure, and the modes were independent of velocity of sound ratio.

Masses of c-type RR Lyrae Variables in Globular Clusters

The mass of RR Lyrae variables has been a controversial problem for about a decade: while the stellar evolution theory predicts masses ranging between 0.65 and 0.75 M⊙ for Oosterhoff type I and II clusters respectively, the stellar pulsation theory predicts smaller masses (0.55 and 0.65 respectively) using the double-mode pulsators. Simon (1990, M.N.R.A.S. 246, 70), comparing hydrodynamical models with observed stars by means of Fourier parameters, has found relations between the stellar mass and its luminosity, pulsation period, Helium content and Fourier parameter ϕ31. Combining his equations we obtain:(1)from which one can estimate the stellar mass by using the observable quantities P and ϕ31 and a luminosity scale, e.g. the one derived by Cacciari, Clementini and Fernley (1992, Astrophys. J. in press).

The Masses and Luminosities of Globular Cluster RRc Stars

AbstractA large number of hydrodynamic pulsation models are converged in the first overtone, and their mean properties compared with observations of RRc stars in six globular clusters. The two observed quantities, period and Fourier parameter ϕ31, lead, via the models, to inferred values for mean mass, luminosity and temperature of the RRc sample in each cluster. We find a narrow range in intracluster RRc luminosity and temperature, but a wider range in mass. At the same time, the intercluster spread is wide in all three parameters. A full discussion of our techniques and results will be given elsewhere (Simon and Clement, in preparation).

On the Design of a Linear Actuator for a Modular Robot System

As a part of the robot research and application programme FAIR, the Eindhoven University of Technology is developing a modular robot system. This paper deals with the first module of that system i.e. a linear actuator. The major specifications of the linear actuator are: positioning accuracy Letter than 0.01 mm, speed up to 1 m/s and a maximum acceleration of 5 m/s 2 for a mass of 50 kg. In view of these requirements the mechanical construction is designed fairly stiff, while at the same time the masses are kept minimal. The dc-motor is placed on the moving part of the actuator and is governed by an advanced microcomputer control system. The translation of the actuator is obtained by a spindle with a ballscrew nut. Stickslip and backlash are minimized through the application of a special ball- and roller bearing system. A dynamic analysis of the prototype of the actuator has been carried out in order to study the properties of the mechanical construction. Therefore, the driving system has been modeled as a three-degrees-of-freedom system which parameters are measured or estimated. Parameter adaptation techniques eliminate smoothly the differences between the prototype and the model. This adapted model supplies relevant information on the dynamic behaviour of the construction. It shows that the actuator can be considered as a one-degree-of-freedom system up to a frequency of 60 Hz. For higher frequencies the model supplies a formula for the transfer function which is essential for the control system. The results show very clearly the effectiveness of the use of discrete mass models in combination with Fourier analysis and parameter adaptation techniques.