Comparison of infrared and Raman wave numbers of neat molecular liquids: Which is the correct infrared wave number to use?

1998 ◽  
Vol 109 (16) ◽  
pp. 6764-6771 ◽  
Author(s):  
John E. Bertie ◽  
Kirk H. Michaelian
Keyword(s):  
Wave Number ◽  
Molecular Liquids ◽  
Wave Numbers ◽  
Infrared Wave

Infrared spectra and substituent effects in 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones

1983 ◽  
Vol 48 (2) ◽  
pp. 586-595 ◽  
Author(s):  
Alexander Perjéssy ◽  
Pavol Hrnčiar ◽  
Ján Šraga
Keyword(s):  
Substituent Effects ◽  
Phenyl Group ◽  
Wave Number ◽  
Vibrational Coupling ◽  
Wave Numbers ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
The Relationship ◽  
Derivatives Of ◽  
Effect Of Structure

The wave numbers of the fundamental C=O and C=C stretching vibrations, as well as that of the first overtone of C=O stretching vibration of 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones and 1,3-cycloheptanedione were measured in tetrachloromethane and chloroform. The spectral data were correlated with σ+ constants of substituents attached to phenyl group and with wave number shifts of the C=O stretching vibration of substituted acetophenones. The slope of the linear dependence ν vs ν+ of the C=C stretching vibration of the ethylenic group was found to be more than two times higher than that of the analogous correlation of the C=O stretching vibration. Positive values of anharmonicity for asymmetric C=O stretching vibration can be considered as an evidence of the vibrational coupling in a cyclic 1,3-dicarbonyl system similarly, as with derivatives of 1,3-indanedione. The relationship between the wave numbers of the symmetric and asymmetric C=O stretching vibrations indicates that the effect of structure upon both vibrations is symmetric. The vibrational coupling in 1,3-cycloheptanediones and the application of Seth-Paul-Van-Duyse equation is discussed in relation to analogous results obtained for other cyclic 1,3-dicarbonyl compounds.

scholarly journals The band spectrum of hydrogen

1924 ◽  
Vol 106 (735) ◽  
pp. 69-82 ◽  
Keyword(s):  
Molecular Hydrogen ◽  
Hydrogen Molecule ◽  
Spectral Lines ◽  
Wave Number ◽  
Band Spectrum ◽  
Wave Numbers ◽  
Experimental Side ◽  
The Subject ◽  
The Moment ◽  
Theoretical Side

Many attempts have been made to detect regularities amongst the numerous lines which constitute the secondary or many-lined spectrum of hydrogen. The extreme complexity of the spectrum may be realised from the fact that in the Bakerian Lecture of 1922 Merton and Barratt record some 750 lines in the interval between Hα (wave-number v = 5233.216) and Hβ ( v = 20564.793). Three methods of investigation may be employed in the search for regularities. (1) The lines may be classified according to their physical characteristics, such as intensity or mode of excitation, as in the tables of Merton and Barrat ( loc. cit .). (2) Lines may be grouped together by the discovery of relations between their wave-lengths or wave-numbers, as in the important groups of lines which have been arranged in bands by Fulcher. (3) Lastly, the question may be attacked from the theoretical side, and a model of the hydrogen molecule may be imagined, which will give rise to the emission of certain characteristic spectral lines. Thus Sutherland, working on the foundation of the classical mechanical laws, more than twenty years ago, came to the conclusion that spectral series must arise from kinematical considera­tions, and explained them by considering the nodal sub-divisions of a circle. At the present time we may expect more successful results to follow from the application of the quantum theory, and in this paper an endeavour will be made to examine the secondary spectrum of hydrogen, and more particularly the Fulcher bands, from this standpoint. I may add that my interest in the subject was aroused when attempting to construct a model of the hydrogen molecule, for it seemed that the most likely method of obtaining reliable information from the experimental side as to the moment of inertia of the molecule would be from a study of the spectrum of molecular hydrogen.

scholarly journals Small-Scale Solar Magnetic Fields

1976 ◽  
Vol 71 ◽  
pp. 69-99 ◽  
Author(s):  
J. O. Stenflo
Keyword(s):  
Magnetic Fields ◽  
Magnetic Flux ◽  
Solar Surface ◽  
Life Time ◽  
Wave Number ◽  
Small Scale ◽  
Solar Magnetic Fields ◽  
Field Amplification ◽  
Wave Numbers ◽  
Diffuse Form

The observed properties of small-scale solar magnetic fields are reviewed. Most of the magnetic flux in the photosphere is in the form of strong fields of about 100–200 mT (1–2 kG), which have remarkably similar properties regardless of whether they occur in active or quiet regions. These fields are associated with strong atmospheric heating. Flux concentrations decay at a rate of about 107 Wb s-1, independent of the amount of flux in the decaying structure. The decay occurs by smaller flux fragments breaking loose from the larger ones, i.e. a transfer of magnetic flux from smaller to larger Fourier wave numbers, into the wave-number regime where ohmic diffusion becomes significant. This takes place in a time-scale much shorter than the length of the solar cycle.The field amplification occurs mainly below the solar surface, since very little magnetic flux appears in diffuse form in the photosphere, and the life-time of the smallest flux elements is very short. The observations further suggest that most of the magnetic flux in quiet regions is supplied directly from below the solar surface rather than being the result of turbulent diffusion of active-region magnetic fields.

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

1979 ◽  
Vol 46 (1) ◽  
pp. 113-119 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Body ◽  
Harmonic Wave ◽  
Wave Number ◽  
Periodic Medium ◽  
Frequency Wave ◽  
Wave Numbers ◽  
Band Characteristic

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear

1968 ◽  
Vol 32 (1) ◽  
pp. 145-171 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Internal Waves ◽  
Wind Shear ◽  
Wave Packets ◽  
Normal Modes ◽  
Wave Number ◽  
Spectral Energy ◽  
Air Turbulence ◽  
Wave Numbers ◽  
Horizontal Wave

The rate of generation of internal waves by a thin turbulent boundary layer was calculated in a previous paper for a stably-stratified atmosphere with no significant wind-shear outside the boundary layer by considering the excitation of normal modes of wave propagation. By using the concept of wave-packets propagating upwards from the boundary layer, the effects of wind-shear can be included. Conditions for the validity of the approximation are given. In general, the spectral distribution of wave-energy at a particular height takes large values in two bands of horizontal wave-number, one band deriving from wave-packets undergoing internal reflexion near that height and the other from wave-packets of very small local frequency that accumulate there. The ‘reflexion’ wave-numbers are dominant if the wind increases with height and the ‘accumulation’ wave-numbers if the wind initially decreases with height. The spectral energy distributions and intensities of the wave-motion are discussed in more detail for an atmosphere of uniform stability and unidirectional wind-shear. The accumulation process may lead to instability or overturning of the waves, and estimates are made of the probable scale and intensity of the ‘clear-air’ turbulence produced. An interesting point is that the rate of energy loss from the boundary layer by radiation of internal waves turns out to be comparable with the rate of production in the outer nine-tenths of the layer, both for atmospheric boundary layers and for the surface layer of the ocean. It seems likely that radiation limits the layer thickness to some extent.

scholarly journals The instability of an electron beam with a finite radius in a boundless plasma

1996 ◽  
Vol 14 (4) ◽  
pp. 367-374 ◽  
Author(s):  
G. V. Lizunov ◽  
A. S. Volokitin ◽  
D. B. Skidanov
Keyword(s):  
Growth Rate ◽  
Electron Beam ◽  
Electron Beams ◽  
Wave Number ◽  
Energy Losses ◽  
Finite Radius ◽  
Wave Numbers ◽  
Surrounding Space ◽  
The Waves ◽  
Beam Dimension

Abstract. Within the framework of a linear theory, the instability of an electron beam with a finite radius in a cold magnetised boundless plasma is considered. It is shown that a finite beam dimension influences the generation of quasi-potential waves in two aspects: the perpendicular wave number is quantised so that the frequencies of the waves are subjected to strong selection; a new kind of instability appears due to wave energy losses by emission into surrounding space. Growth rate dependence of wave numbers and frequencies is investigated for typical parameters of experiments with electron beams in space.

scholarly journals Spectral analysis of 10-m resolution temperature profiles from balloon soundings over Beijing

2006 ◽  
Vol 24 (7) ◽  
pp. 1801-1808 ◽  
Author(s):  
Y. Wu ◽  
J. Xu ◽  
W. Yuan ◽  
H. Chen ◽  
J. Bian
Keyword(s):  
Lower Stratosphere ◽  
Temperature Fluctuations ◽  
Wave Number ◽  
Temperature Profiles ◽  
Vertical Temperature ◽  
Spectral Character ◽  
Meteorological Observatory ◽  
Wave Numbers ◽  
Temperature Spectra ◽  
Spectrum Model

Abstract. Vertical temperature profiles with a height resolution of 10 m have been measured in the troposphere and lower stratosphere during March and April 2003 over the Beijing Meteorological Observatory. This resolution allows us to study temperature spectra up to higher wave numbers than many published papers. Our purposes in this study are to examine the spectral character of normalized temperature fluctuations in the 2.90–8.01 km (troposphere) and 14.65–19.76 km (lower stratosphere) altitude ranges and to compare them with model spectra. Vertical wave number spectra of six temperature profiles are presented. Results indicate that mean spectral slopes are about −1.9 in the troposphere and −2.2 in the lower stratosphere, which is believed to be the shallowest slopes ever measured by balloon-borne radiosonde soundings. Mean spectral amplitudes at m=1/(100 m) are about 17 times larger in the troposphere and 4 times larger in the lower stratosphere than the predicted saturated spectral amplitudes. These results show that the observed temperature spectra do not obey current gravity wave saturation models, the "universal" atmospheric spectrum model, or the wind-shifting model, in both slope and amplitude.

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

2012 ◽  
Vol 12 (4) ◽  
pp. 1275-1292 ◽  
Author(s):  
Qin Sheng ◽  
Hai-Wei Sun
Keyword(s):  
Helmholtz Equation ◽  
Numerical Stability ◽  
Splitting Method ◽  
Computational Procedure ◽  
Matrix Analysis ◽  
Wave Number ◽  
Large Wave ◽  
High Wave ◽  
Wave Numbers ◽  
Large Wave Number

AbstractThis paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.

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