Dispersion formulas for real- and imaginary-frequency-dependent hyperpolarizabilities

1996 ◽  
Vol 74 (6) ◽  
pp. 781-785
Author(s):  
David M. Bishop
Keyword(s):  
Nonlinear Optics ◽  
Key Words ◽  
Electric Fields ◽  
Imaginary Frequency ◽  
Mots Clés ◽  
Frequency Dependent ◽  
Second Hyperpolarizability ◽  
Frequency Independent ◽  
De Formula ◽  
Static Quantity

The dynamic second hyperpolarizability for real frequencies, [Formula: see text] in the limit ωi → 0 can be expressed as [Formula: see text] where ωL2 = ωσ2 + ω12 + ω22 + ω32 and [Formula: see text] is the frequency-independent (static) quantity; the parallel sutsscript [Formula: see text] indicates that the polarization and electric fields all lie along the same axis. In this paper the coefficient [Formula: see text] is evaluated exactly for the H atom and very accurately for H−, He, and Li+. A similar analysis is carried out for [Formula: see text] in the limit ω → ∞. Key words: nonlinear optics, hyperpolarizabilities, dispersion formulas.On peut exprimer la deuxième hyperpolarisabilité dynamique de fréquences réelles, [Formula: see text] dans la limiteωi → 0, peut être exprimée sous la forme [Formula: see text], dans laquelle ωL2 = ωσ2 + ω12 + ω22 + ω32 et [Formula: see text] est la quantité (statique) indépendant de la fréquence; l'indice parallèle [Formula: see text] indique que la polarisation et les champs électriques sont situés dans le même axe. Dans ce travail, on a fait une évaluation exacte de [Formula: see text] pour l'atome d'hydrogène et d'une façon précise pour H−, He et Li+. On a effectué une analyse semble pour [Formula: see text]dans la limite ω → ∞. Mots clés : optique non linéaire, hyperpolarisabilités, formules de dispersion. [Traduit par la rédaction]

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

scholarly journals Diversité floristique du Parc National du Haut Atlas Oriental et des Massifs ayachi et Maâsker (Maroc).

2008 ◽  
Vol 33 ◽  
pp. 125-145 ◽  
Author(s):  
Mohammed Sghir Taleb ◽  
Mohamed Fennane
Keyword(s):  
Key Words ◽  
National Park ◽  
The Other ◽  
Mots Clés ◽  
High Atlas ◽  
Flora Diversity

RÉSUMÉ. Diversité floristique du Parc National du Haut Atlas Oriental et des massifs Ayachi etMaâsker (Maroc). Etant donné la rareté des études sur le Parc National du Haut Atlas Oriental et lesmassifs Ayachi et Maâsker, les connaissances sur la diversité floristique de ces régions, très accidentées,étaient très insuffisantes et fragmentaires. Actuellement la flore vasculaire du Parc, jbels Ayachi etMaâsker est estimée respectivement à 227, 140 et 96 espèces; la flore rare, menacée et/ou endémiqueconstitue une part importante. Le nombre d’endémiques dans le Parc (espèces et sous espèces)représente 6.8 % de l’ensemble des endémiques marocaines. Ce nombre est très important dans l’Ayachiavec 7.5 %. Dans le Maâsker, le nombre d’endémiques est évalué à 3.9 % de l’ensemble des endémiquesmarocaines. La flore rare (espèces et sous-espèces) est représentée par 3.6 % de la flore totale duParc, 4 % de la flore totale du jbel Ayachi et 4 % de la flore totale du jbel Maâsker. Par contre le tauxde la flore très rare est faible, respectivement de l’ordre de 1.9 %, 2 % et 2.4 %.Mots clés. Diversité floristique, Endémisme, Parc National du Haut Atlas Oriental, Maroc.SUMMARY. Flora diversity of the National Park of the Eastern High Atlas and the massifs Ayachiand Mâasker (Morocco). Considering the rare studies on the Eastern High Atlas National Park, Ayachiand Mâasker mountains, the knowledge on the flora diversity of these regions were very insufficient.Their flora is estimated currently 227, 140 and 96 species. The rare flora, threatened and/or endemicconstitutes an important part. The number of endemics in the Park (species and subspecies) represents6.8% of the endemics of Morocco. This number is very important in Ayachi (7.5%). In Maasker, thenumber of endemics is about 3.9% of the endemic of Morocco. The rare flora (species and subspecies)in the Park, Ayachi and Maasker is represented respectively by 3.6%, 4%, and 4%. On the other handthe very rare flora is poor respectively 1.9%, 2% and 2.4%.Key words. Flora diversity, Endemism, National Park of Eastern High Atlas, Morocco.

scholarly journals A Blind Calibration Model for I/Q Imbalances of Wideband Zero-IF Receivers

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1868
Author(s):  
Xiaoye Peng ◽  
Zhiyu Wang ◽  
Jiongjiong Mo ◽  
Chenge Wang ◽  
Jiarui Liu ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Finite Impulse Response ◽  
Low Cost ◽  
Classification Rule ◽  
Statistical Characteristics ◽  
High Signal ◽  
Calibration Model ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
Blind Calibration

Frequency-dependent I/Q imbalance and frequency-independent I/Q imbalance are the major impairments in wideband zero-IF receivers, and they both cannot be ignored. In this paper, a blind calibration model is designed for compensating these I/Q imbalances. In order to accurately estimate the imbalance parameters with low cost, a classification rule is proposed according to the frequency-domain statistical characteristics of the received signal. The calibration points in the frequency-domain are divided into two groups. Then, the amplitude imbalance and the frequency-dependent phase imbalance are derived from the group of signal points and, separately, the frequency-independent phase imbalance is calculated from the group of noise points. In the derivation of the frequency-dependent phase imbalance, a general fitting model suitable for all signal points is proposed, which does not require special calculations for either DC point or fs/2 point. Then, a finite impulse response (FIR) real-valued filter is designed to correct the impairments of received signal. The performances of the proposed calibration model are evaluated through both simulations and experiments. The simulation results show the image rejection ratio (IRR) improvement to around 35–45 dBc at high signal-to-noise ratio (SNR). Based on the mismatched data of the ADRV9009 evaluation board, the experimental results exhibit the IRR improvement of both multi-tone and wideband signals to about 30 dBc.

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Labyrinth Seal ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
The Impact

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 2: Model Uncertainty and Optimal Parameterization

2020 ◽  
Author(s):  
Maryam Safarshahi ◽  
Igor B. Morozov
Keyword(s):  
Measurement Errors ◽  
Nonparametric Model ◽  
Model Parameters ◽  
Geometrical Spreading ◽  
Model Quality ◽  
Frequency Dependent ◽  
Time Frequency ◽  
Trade Offs ◽  
Frequency Independent ◽  
Seismic Amplitudes

ABSTRACT In a companion article, Safarshahi and Morozov (2020) argued that construction of distance- and frequency-dependent models for seismic-wave amplitudes should include four general elements: (1) a sufficiently detailed (parametric or nonparametric) model of frequency-independent spreading, capturing all essential features of observations; (2) model parameters with well-defined and nonoverlapping physical meanings; (3) joint inversion for multiple parameters, including the geometrical spreading, Q, κ, and source and receiver couplings; and (4) the use of additional dataset-specific criteria of model quality, while fitting the logarithms of seismic amplitudes. Some of these elements are present in existing models, but, taken together, they are poorly understood and require an integrated approach. Such an approach was illustrated by detailed analysis of an S-wave amplitude dataset from southern Iran. The resulting model is based on a frequency-independent Q, and matches the data closer than conventional models and across the entire epicentral-distance range. Here, we complete the analysis of this model by evaluating the uncertainties and trade-offs of its parameters. Two types of trade-offs are differentiated: one caused by a (possibly) limited model parameterization and the second due to statistical data errors. Data bootstrapping shows that with adequate parameterization, attenuation properties Q, κ, and geometrical spreading parameters are resolved well and show moderate trade-offs due to measurement errors. Using the principal component analysis of these trade-offs, an optimal (trade-off free) parameterization of seismic amplitudes is obtained. By contrast, when assuming theoretical values for certain model parameters and using multistep inversion procedures (as commonly done), parameter trade-offs increase dramatically and become difficult to assess. In particular, the frequency-dependent Q correlates with the distribution of the source and receiver-site factors, and also with biases in the resulting median data residuals. In the new model, these trade-offs are removed using an improved parameterization of geometrical spreading, constant Q, and model quality constraints.

An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures

Geophysics ◽  
1987 ◽  
Vol 52 (1) ◽  
pp. 72-87 ◽  
Author(s):  
R. S. Jacobson
Keyword(s):  
Frequency Dependence ◽  
Seismic Waves ◽  
Velocity Dispersion ◽  
Seismic Refraction ◽  
Systematic Investigation ◽  
Data Sets ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
Apparent Attenuation ◽  
Seismic Refraction Data

Despite many attenuation measurements which indicate a linear functional frequency dependence of absorption or constant [Formula: see text] in sediments, several theories predict no such linear dependence. The primary justification for rejecting a first‐power frequency dependence of attenuation is that it implies that seismic waves cannot propagate causally. Seismic waves must also travel with some velocity dispersion to satisfy causality, yet there is a lack of velocity dispersion measurements in sediments. In‐situ attenuation is caused by two distinct mechanisms: anelastic heating, and scattering due to interbed multiples. Apparent, or scattering, attenuation can produce both frequency‐dependent and non‐frequency‐dependent effects. Accurate measurements of attenuation and velocity dispersion are difficult; it is not surprising that a systematic investigation into the frequency dependence of absorption and velocity has not been made. A reinvestigation into two seismic refraction data sets collected over thickly stratified deep‐sea fans indicates that [Formula: see text] should not be assumed to be independent of frequency. Further, significant frequency‐independent absorption is present, indicating a high degree of apparent attenuation. Phase, or velocity, dispersion was also measured, but the results are more ambiguous than those for attenuation, due to inherent limitations of digital signals. Nevertheless, the absorption and velocity dispersion results are largely compatible, suggesting that if apparent attenuation is observed, then the scattered waves propagate causally.

INVESTIGATING ELECTRIC FIELD CONTROL OF MAGNETISM WITH NEUTRON SCATTERING, NONLINEAR OPTICS AND SYNCHROTRON X-RAY SPECTROMICROSCOPY

2012 ◽  
Vol 26 (10) ◽  
pp. 1230004 ◽  
Author(s):  
M. B. HOLCOMB ◽  
S. POLISETTY ◽  
A. FRAILE RODRÍGUEZ ◽  
V. GOPALAN ◽  
R. RAMESH
Keyword(s):  
Nonlinear Optics ◽  
Electric Field ◽  
Neutron Scattering ◽  
Electric Fields ◽  
Single Phase ◽  
Future Directions ◽  
X Ray ◽  
Electrical Control ◽  
Essential Step ◽  
Field Control

This paper discusses recent efforts to control magnetism with electric fields in single and multilayer oxides, which has great potential to improve a variety of technological endeavors, such as magnetic sensing and magnetoelectric (ME) logic. The importance of electrical control of magnetism is followed by a discussion of multiferroics and MEs, which are the leading contenders for this task. The focus of this paper is on complementary methods in understanding the ME coupling, an essential step to electrical control of magnetism. Neutron scattering, nonlinear optics and X-ray spectromicroscopy are addressed in providing key parameters in the study of ME coupling. While primarily direct (single-phase multiferroics) ME materials are used as examples, the techniques discussed are also valuable to the study of indirect (e.g., multilayers and pillars) magnetoelectrics. We conclude with a summary of the field and future directions.

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