Analysis of auroral first negative bands

1987 ◽  
Vol 65 (9) ◽  
pp. 1119-1132 ◽  
Author(s):  
K. Henriksen ◽  
L. Veseth
Keyword(s):  
Electronic State ◽  
Least Squares Method ◽  
Rotational Temperature ◽  
Numerical Approach ◽  
Synthetic Spectrum ◽  
Particle Impact ◽  
Population Densities ◽  
Vibrational Levels ◽  
Rotational Part ◽  
E Region

An exact numerical approach is used to compute the rotational part of the line strengths (Hönl–London factors) for the [Formula: see text], [Formula: see text] transition (1NG bands). The computed Hönl–London factors enable a synthetic spectrum to be derived, which is then fitted as a final step to observed auroral [Formula: see text] 1NG bands by use of a least squares method. In this way we determine the population densities of the vibrational levels of the upper [Formula: see text] electronic state and, in addition, an average rotational temperature. Our results give clear evidence that the auroral [Formula: see text] 1NG bands are mainly generated by particle impact on neutral O2 molecules in their electronic and vibrational ground states, and that the bands are produced within the E region.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

The 3300 Å band system of cyclobutanone

1969 ◽  
Vol 47 (11) ◽  
pp. 1235-1236 ◽  
Author(s):  
D. C. Moule
Keyword(s):  
High Resolution ◽  
Electronic State ◽  
Potential Function ◽  
Band System ◽  
Ultraviolet Spectrum ◽  
Vibrational Levels ◽  
Minimum Potential

The ultraviolet spectrum of cyclobutanone vapor has been recorded under conditions of high resolution. The oxygen wagging vibrational levels have been found to be strongly anharmonic in the 1A2 electronic state and have been fitted to a double minimum potential function.

scholarly journals Sunlight-Initiated Photochemistry: Excited Vibrational States of Atmospheric Chromophores

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Veronica Vaida ◽  
Karl J. Feierabend ◽  
Nabilah Rontu ◽  
Kaito Takahashi
Keyword(s):  
Solar Radiation ◽  
Electronic State ◽  
Chemical Bond ◽  
Wavelength Range ◽  
Chemical Reactions ◽  
Energy Barrier ◽  
Bond Energies ◽  
Vibrational States ◽  
Vibrational Levels ◽  
Combination Bands

Atmospheric chemical reactions are often initiated by ultraviolet (UV) solar radiation since absorption in that wavelength range coincides to typical chemical bond energies. In this review, we present an alternative process by which chemical reactions occur with the excitation of vibrational levels in the ground electronic state by red solar photons. We focus on the O–H vibrational manifold which can be an atmospheric chromophore for driving vibrationally mediated overtone-induced chemical reactions. Experimental and theoretical O–H intensities of several carboxylic acids, alcohols, and peroxides are presented. The importance of combination bands in spectra at chemically relevant energies is examined in the context of atmospheric photochemistry. Candidate systems for overtone-initiated chemistry are provided, and their lowest energy barrier for reaction and the minimum quanta of O–H stretch required for reaction are calculated. We conclude with a discussion of the major pathways available for overtone-induced reactions in the atmosphere.

Straight Beams Rested on Nonlinear Elastic Foundations – Part 1 (Theory, Experiments, Numerical Approach)

2014 ◽  
Vol 684 ◽  
pp. 11-20 ◽  
Author(s):  
Karel Frydrýšek ◽  
Šárka Michenková ◽  
Marek Nikodým
Keyword(s):  
Difference Method ◽  
Least Squares Method ◽  
Reaction Force ◽  
Nonlinear Problems ◽  
Numerical Approach ◽  
Nonlinear Dependence ◽  
Central Difference ◽  
Central Difference Method ◽  
Nonlinear Elastic ◽  
Numerical Approaches

This paper presents theory, experiments and numerical approaches suitable for the solution of straight plane beams rested on an elastic (Winkler's) foundation, including nonlinearities. The nonlinear dependence of the reaction force on displacement in the foundation (i.e. the experimental data) can be described via bilateral linear or bilateral linear + cubic or bilateral linear + cubic + quintic approximations, or by unilateral approximation (i.e. by using the Least Squares Method). These applications lead to linear or nonlinear differential 4th-order equations. For solutions of nonlinear problems of mechanics, the Finite Difference Method (i.e. the Central Difference Method) and boundary conditions are applied. The solution and its evaluation is performed in second part of this article.

scholarly journals The spectrum of H 2 Part III―New bands and band systems ending on 2 s 3 Σ and an extension of the singlet system 1 Q → 2 p 1 Σ

1934 ◽  
Vol 147 (861) ◽  
pp. 272-292 ◽  
Keyword(s):  
Triplet State ◽  
Electronic State ◽  
Yellow Band ◽  
Vibrational Levels ◽  
System 1 ◽  
Diagonal Axis

In this paper we describe three new band systems ending on the lowest even triplet state 2 s 3 Σ of H 2 and coming from three hitherto undiscovered states which we call provisionally 3 D, 3 E, and 3 F. The main bands, which are all weak, lie in the yellow, blue, and violet respectively. We have found more of the system belonging to the isolated yellow band of Richardson and Das. This band ended on the v '' = 1 level of 2 s 3 Σ g . We now describe two other bands coming from the same electronic state at different vibrational levels and ending on 2 s 3 Σ at v '' = 0 and v '' = 2 respectively. All these band systems are of the type which consists practically of a sequence of bands along the diagonal axis. In addition, we describe the v ' = 0 progression of the singlet system 1 Q → 2 p 1 Σ of which Richardson and Davidson found only a single progression which now turns out to be the v ' = 1 progression.

THE 1600 Å BAND SYSTEM OF AMMONIA

1961 ◽  
Vol 39 (4) ◽  
pp. 479-501 ◽  
Author(s):  
A. E. Douglas ◽  
J. M. Hollas
Keyword(s):  
Excited State ◽  
High Resolution ◽  
Electronic State ◽  
Band System ◽  
Excited Electronic State ◽  
Degenerate State ◽  
Coriolis Interaction ◽  
Plane Vibration ◽  
Vibrational Levels ◽  
Out Of Plane

The progression of ammonia bands which extends from 1689 to 1400 Å has been photographed in absorption at high resolution. Six bands have been analyzed and found to be of the perpendicular type. The analysis shows that the molecule is planar in the excited state and that vibrational levels observed in the progression are those of the out-of-plane vibration. The excited electronic state is of the E′′ type. In addition to the normal Coriolis interaction of the degenerate levels, a second effect has been observed which behaves like the Coriolis interaction recently described as 'giant l-type doubling' by Garing, Nielsen, and Rao. No clear evidence has been found for any distortion of the degenerate state from D3h symmetry.

Vibrational populations of near-ultraviolet O2 band systems in the night airglow 1This article is part of a Special issue that honours the work of Dr. Donald M. Hunten FRSC who passed away in December 2010 after a very illustrious career.

2012 ◽  
Vol 90 (8) ◽  
pp. 741-751
Author(s):  
R.L. Gattinger ◽  
I.C. McDade ◽  
A.L. Broadfoot ◽  
W.F.J. Evans ◽  
J. Stegman ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Band System ◽  
Lower Thermosphere ◽  
Near Ultraviolet ◽  
Vibrational Levels ◽  
Mesosphere And Lower Thermosphere ◽  
The Individual ◽  
Franck Condon ◽  
Imaging Spectrograph ◽  
Night Airglow

Observations of the limb night airglow spectrum from 250 to 475 nm, emitted from the upper mesosphere and lower thermosphere, are compared with model spectra. Data from the Arizona GLO-1 imaging spectrograph and the OSIRIS spectrograph are combined to form the observed mean airglow spectrum; a tabulated version of this spectrum is included. Model spectra of the individual O2 Herzberg I, II, and III, Chamberlain, and Slanger band systems are combined to simulate the observed mean spectrum. Franck–Condon relative band intensities are used to form a series of basis functions for the upper vibrational levels in each band system. These functions are fitted to the observed airglow spectrum with a least-squares method, the relative vibrational populations are derived and discussed.

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