VIBRATIONAL RELAXATION IN DISSOCIATING DIATOMIC GASES

1963 ◽  
Vol 41 (5) ◽  
pp. 717-723 ◽  
Author(s):  
M. McChesney
Keyword(s):  
Vibrational Relaxation ◽  
Vibrational Excitation ◽  
Thermal Dissociation ◽  
Boltzmann Distribution ◽  
Anharmonic Oscillators ◽  
Distribution Law ◽  
Relaxation Equation ◽  
Vibrational Levels ◽  
Equilibrium Level ◽  
Theoretical Analyses

This article questions the available theoretical analyses relating to the vibrational excitation of a dissociating gas which assume that the gas dissociates from vibrational level populations given by the Maxwell–Boltzmann distribution law. The two theories of thermal dissociation are briefly outlined and it is shown that either theory gives non-equilibrium-level populations. Furthermore, the use of a simple relaxation equation to describe the vibrational excitation of anharmonic oscillators in high vibrational levels is questioned.

Altitude dependence of the vibrational distribution of in the nightglow and the possible effects of vibrational excitation in the formation of O(1S)

1984 ◽  
Vol 62 (8) ◽  
pp. 780-788 ◽  
Author(s):  
I. C. McDade ◽  
E. J. Llewellyn ◽  
R. G. H. Greer ◽  
G. Witt
Keyword(s):  
Vibrational Relaxation ◽  
Vibrational Excitation ◽  
Relaxation Model ◽  
Terrestrial Atmosphere ◽  
Transfer Step ◽  
Vibrational Distribution ◽  
Altitude Dependence ◽  
Vibrational Levels ◽  
The Individual

A simple vibrational relaxation model that reproduces the observed vibrational distribution of the [Formula: see text] Herzberg II bands in the terrestrial nightglow is used to derive the altitude profiles of the fractional populations in the individual vibrational levels. Through consideration of these profiles it is shown that if [Formula: see text] is the Barth precursor of O(1S) in the nightglow then, at least in the terrestrial atmosphere, the higher vibrational levels appear to be more effective in the Barth transfer step than the lower vibrational levels.

scholarly journals New insights for mesospheric OH: multi-quantum vibrational relaxation as a driver for non-local thermodynamic equilibrium

2018 ◽  
Vol 36 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Konstantinos S. Kalogerakis ◽  
Daniel Matsiev ◽  
Philip C. Cosby ◽  
James A. Dodd ◽  
Stefano Falcinelli ◽  
...  
Keyword(s):  
Thermodynamic Equilibrium ◽  
Vibrational Relaxation ◽  
Local Thermodynamic Equilibrium ◽  
Vibrational Excitation ◽  
Kinetic Temperature ◽  
Population Distributions ◽  
Vibrational Levels ◽  
Non Local ◽  
Relationship Of ◽  
The Relationship

Abstract. The question of whether mesospheric OH(v) rotational population distributions are in equilibrium with the local kinetic temperature has been debated over several decades. Despite several indications for the existence of non-equilibrium effects, the general consensus has been that emissions originating from low rotational levels are thermalized. Sky spectra simultaneously observing several vibrational levels demonstrated reproducible trends in the extracted OH(v) rotational temperatures as a function of vibrational excitation. Laboratory experiments provided information on rotational energy transfer and direct evidence for fast multi-quantum OH(high-v) vibrational relaxation by O atoms. We examine the relationship of the new relaxation pathways with the behavior exhibited by OH(v) rotational population distributions. Rapid OH(high-v) + O multi-quantum vibrational relaxation connects high and low vibrational levels and enhances the hot tail of the OH(low-v) rotational distributions. The effective rotational temperatures of mesospheric OH(v) are found to deviate from local thermodynamic equilibrium for all observed vibrational levels. Dedicated to Tom G. Slanger in celebration of his 5 decades of research in aeronomy.

Weak spherical shock-wave transitions of N-waves in air with vibrational excitation

1984 ◽  
Vol 391 (1800) ◽  
pp. 55-83 ◽  
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation ◽  
Stokes Equations ◽  
Vibrational Excitation ◽  
Finite Difference Schemes ◽  
Relaxation Equation ◽  
Splitting Technique ◽  
Spherical Waves ◽  
Attenuation Rate ◽  
N Wave

In order to clarify the effects of vibrational excitation on shock-wave transitions of weak, spherical N-waves, which were generated by using sparks and exploding wires as sources, the compressible Navier-Stokes equations were solved numerically, with a vibrational-relaxation equation for oxygen. An explosion from a small pressurized sphere filled with air was used to simulate the N-waves generated from the actual sources. By employing the random-choice method (r. c. m.) with an operator-splitting technique, the effects of artificial viscosity appearing in finite-difference schemes were eliminated and accurate profiles of the shock transitions were obtained. However, a slight randomness in the variation of the shock thickness remains. It is shown that a computer simulation is possible by using a proper choice of initial parameters to obtain the variations of N-wave overpressure and half-duration with distance from the source. The calculated rise times are also shown to simulate both spark and exploding-wire data. It was found that, in addition to the vibrational-relaxation time of oxygen, both the duration (N-wave effect) and the attenuation rate (non-stationary effect) of a spherical N-wave are important factors controlling its rise time. These effects are discussed in more detail in relation to Lighthill’s analytical solutions and the r. c. m. solutions for non-stationary plane waves and spherical N-waves. It is also shown that the duration and the attenuation rate of a spherical N-wave are affected by viscosity, and vibrational non-equilibrium, so that they can deviate from the results of classical, linear acoustic theory for very weak spherical waves.

Vibrational relaxation of anharmonic oscillators in expanding flows

1992 ◽  
Author(s):  
STEPHEN RUFFIN ◽  
CHUL PARK
Keyword(s):  
Vibrational Relaxation ◽  
Anharmonic Oscillators

scholarly journals Safe and Efficient Coal Mining Below the Goaf: A Case Study

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 864 ◽  
Author(s):  
Weidong Pan ◽  
Shaopeng Zhang ◽  
Yi Liu
Keyword(s):  
Abutment Pressure ◽  
Theoretical Calculations ◽  
Distribution Law ◽  
Working Face ◽  
Strata Behavior ◽  
Working Resistance ◽  
Behavior Characteristics ◽  
Theoretical Analyses ◽  
Important Significance

Mining at the fully mechanized working face below the goaf of the short-distance coal seam is influenced by the upper goaf. To address this problem, methods such as theoretical analyses, numerical simulation, and on-site measurement are used to study the strata behavior characteristics of the Ningxia Lingxin Coal Mine 051508 working face in this study. The roof weighting intervals of the working faces below the goaf and the non-goaf are obtained via theoretical calculations. The stoping processes of the working faces below the goaf and the non-goaf are simulated with FLAC3D to obtain the distribution law of the bearing pressure and plastic zones before the working face. Based on the statistical analysis of the measured working resistance of the supports and its distribution, the roof weighting interval of the working face mining below the goaf is obtained. The results show that the roof weighting interval and the advanced abutment pressure during mining at the working face below the goaf are smaller than those below the non-goaf, providing a reasonable theoretical basis for mining below the goaf, and having important significance for safe and efficient mining.

Experimental Study of Low Energy e-O2 Collision Processes

1971 ◽  
Vol 26 (10) ◽  
pp. 1617-1625 ◽  
Author(s):  
F. Linder ◽  
H. Schmidt
Keyword(s):  
Angular Dependence ◽  
Cross Sections ◽  
Vibrational Excitation ◽  
Resonance Scattering ◽  
Spectroscopic Constants ◽  
Extended Model ◽  
Vibrational Levels ◽  
Electronically Excited ◽  
The Cross ◽  
Electronic Ground

Abstract Elastic scattering, vibrational excitation to v=1, 2, 3, 4 of the electronic ground state, and electronic excitation to the states a1Δ g and b1Σg+ of O2 have been measured in a crossed beam apparatus for collision energies from nearly 0 eV to 4 eV. Differential and integral cross sections have been determined and calibrated on an absolute scale. From 15 vibrational levels of O2-, which could be observed as resonances in the cross sections, the spectroscopic constants for the vibrational structure of O2- have been derived: ωe = 135 meV and ωeχe = 1 meV. The cross sections for vibrational excitation have the order of 10-18 cm2. eV for the larger resonance peaks. Detailed cross sections have been listed in Table 1. The half width of the resonance can be estimated to Γ ≈ 0.5 meV, which corresponds to a lifetime tof 10-12 sec for the O2- states. The angular dependence of pure resonance scattering is rather flat and not in accordance with the simplest theoretical model. An analysis of the angular dependence and of the rotational structure of the resonance in a somewhat extended model have been performed. - No electronically excited O2-states could be detected in the energy range up to 3 eV.

Comparison of exact and approximate methods for analysing vibrational relaxation regions

1961 ◽  
Vol 10 (1) ◽  
pp. 33-47 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Exact Solution ◽  
Shock Waves ◽  
Numerical Integration ◽  
Vibrational Relaxation ◽  
Relaxation Frequency ◽  
Rayleigh Line ◽  
Relaxation Equation ◽  
Approximate Methods ◽  
Exact And Approximate Methods

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.

On the First Moment Relaxation Equation of Anharmonic Oscillators

1970 ◽  
Vol 53 (10) ◽  
pp. 4107-4108 ◽  
Author(s):  
C. T. Hsu ◽  
L. D. McMillen
Keyword(s):  
Anharmonic Oscillators ◽  
Relaxation Equation ◽  
First Moment

Simultaneous vibrational relaxation and thermal dissociation of diatomic molecules

1971 ◽  
Vol 4 (3) ◽  
pp. 200-202 ◽  
Author(s):  
N. A. Generalov ◽  
B. V. Kuksenko ◽  
S. A. Losev ◽  
A. I. Osipov
Keyword(s):  
Vibrational Relaxation ◽  
Diatomic Molecules ◽  
Thermal Dissociation
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