scholarly journals Overtone Frequencies of NO2 using Lie algebraic model

2021 ◽  
Vol 37 (6) ◽  
pp. 1493-1495
Author(s):  
J. Vijayasekhar J. Vijayasekhar ◽  
K. Anil Kumar ◽  
N. Srinivas
Keyword(s):  
Nitrogen Dioxide ◽  
Gas Phase ◽  
Reference Values ◽  
Hamiltonian Operator ◽  
Algebraic Model ◽  
Vibrational Frequencies ◽  
Bending Vibrations ◽  
One Dimensional ◽  
Experimental Values ◽  
The One

In this paper, we used the one dimensional unitatry Lie algebraic model to compute the vibrational frequencies of nitrogen dioxide (NO2) molecule in the gas phase up to the sixth overtone. In this model, the Hamiltonian operator describes the stretching and bending vibrations with algebraic parameters. The calculated fundamental vibrational frequencies are compared with experimental values and results consistent with the reference values.

The spread of flame across a liquid surface II. Steady-state conditions

1968 ◽  
Vol 308 (1492) ◽  
pp. 55-68 ◽  
Keyword(s):  
Steady State ◽  
Gas Phase ◽  
Flame Spread ◽  
Initial Temperature ◽  
Liquid Surface ◽  
Flash Point ◽  
One Dimensional ◽  
Flammable Liquids ◽  
The One ◽  
Qualitative Picture

The one-dimensional spread of flame along the surface of flammable liquids confined in a parallel-sided channel has been studied and the effects of physical dimensions and initial temperature upon its rate established. When the initial temperature of the liquid is below the closed flash point, flame spread depends upon the transfer of heat to the liquid sufficient to raise its surface temperature to the flash-point value and a qualitative picture of the mechanism by which this takes place is developed. When the initial temperature is above the flash point, flame spread is dependent upon conditions in the gas phase above the liquid and these are defined.

Predictable Model for Characteristics of One-Dimensional Solid-Gas-Liquid Three-Phase Mixtures Flow Along a Vertical Pipeline With an Abrupt Enlargement in Diameter

1999 ◽  
Vol 121 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Natsuo Hatta ◽  
Masaaki Omodaka ◽  
Fumitaka Nakajima ◽  
Takahiro Takatsu ◽  
Hitoshi Fujimoto ◽  
...  
Keyword(s):  
Gas Flow ◽  
Sudden Change ◽  
Flow Characteristics ◽  
Point Of View ◽  
Solid Particles ◽  
Governing Equations ◽  
One Dimensional ◽  
Three Phase ◽  
Experimental Values ◽  
The One

This paper treats the numerical analysis of the rising process of a solid-gas-liquid three-phase mixture along a vertical pipeline with an abrupt enlargement in diameter. The system of governing equations used is based upon the one-dimensional multifluid model and the transitions of gas flow pattern are taken into account in the system of governing equations. For the case of a sudden enlargement in diameter in a coaxial pipeline, the procedure of the numerical calculation to obtain the flow characteristics in the pipeline section after a sudden change in diameter has been established here. Furthermore, in order to confirm the validity of the present theoretical model by the comparison between the calculated and experimental values, the experiments have been made using four kinds of lifting pipes, including the straight one. Thereby, it has been found that the numerical model proposed here gives good fit to the prediction of the flow rates of lifted water and solid particles against that of air supplied for the case of a sudden change in diameter. In addition, the flowing process for each phase has been investigated from a photographic point of view. As a result, we found that the moving process of the solid particles depends strongly upon the volumetric flux of gas-phase as well as the submergence ratio.

QUANTUM HALL EDGE PHYSICS AND ITS ONE-DIMENSIONAL LUTTINGER LIQUID DESCRIPTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1244001 ◽  
Author(s):  
ORION CIFTJA
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Quantum Hall ◽  
Luttinger Liquid ◽  
Edge States ◽  
One Dimensional ◽  
Liquid Model ◽  
Experimental Values ◽  
The One ◽  
The Relationship

We describe the relationship between quantum Hall edge states and the one-dimensional Luttinger liquid model. The Luttinger liquid model originated from studies of one-dimensional Fermi systems, however, it results that many ideas inspired by such a model can find applications to phenomena occurring even in higher dimensions. Quantum Hall systems which essentially are correlated two-dimensional electronic systems in a strong perpendicular magnetic field have an edge. It turns out that the quantum Hall edge states can be described by a one-dimensional Luttinger model. In this work, we give a general background of the quantum Hall and Luttinger liquid physics and then point out the relationship between the quantum Hall edge states and its one-dimensional Luttinger liquid representation. Such a description is very useful given that the Luttinger liquid model has the property that it can be bosonized and solved. The fact that we can introduce a simpler model of noninteracting bosons, even if the quantum Hall edge states of electrons are interacting, allows one to calculate exactly various quantities of interest. One such quantity is the correlation function which, in the asymptotic limit, is predicted to have a power law form. The Luttinger liquid model also suggests that such a power law exponent should have a universal value. A large number of experiments have found the quantum Hall edge states to show behavior consistent with a Luttinger liquid description. However, while a power law dependence of the correlation function has been observed, the experimental values of the exponent appear not to be universal. This discrepancy might be due to various correlation effects between electrons that sometimes are not easy to incorporate within a standard Luttinger liquid model.

scholarly journals Vibrational Frequencies of Dichlorine Monoxide: A Mathematical Model

2021 ◽  
Vol 37 (1) ◽  
pp. 240-242
Author(s):  
N. Srinivas ◽  
J. Vijayasekhar
Keyword(s):  
Mathematical Model ◽  
Algebraic Model ◽  
Vibrational Frequencies ◽  
Triatomic Molecule ◽  
Experimental Values ◽  
Dichlorine Monoxide ◽  
Vibrational Wavenumbers

Determinedstretching vibrational frequencies of a triatomic molecule, i.e..Dichlorine Monoxide (Cl2O) upto third overtone by Lie algebraic method.Fundamental vibrational wavenumbers calculated by Lie algebraic model are compared with available experimental values.

scholarly journals SUPERSYMMETRIC APPROACH TO EXACTLY SOLVABLE SYSTEMS WITH POSITION-DEPENDENT EFFECTIVE MASSES

2002 ◽  
Vol 17 (31) ◽  
pp. 2057-2066 ◽  
Author(s):  
BEŞİ GÖNÜL ◽  
BÜLENT GÖNÜL ◽  
DİLEK TUTCU ◽  
OKAN ÖZER
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Hamiltonian Operator ◽  
One Dimensional ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
The One ◽  
Dependent Mass ◽  
The Relationship

We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the framework of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

The occurrence of chemical reactions in supersonic expansions of a gas into a vacuum and its relation to mass spectrometric sampling

1971 ◽  
Vol 322 (1551) ◽  
pp. 483-507 ◽  
Keyword(s):  
Gas Phase ◽  
Chemical Reactions ◽  
Chemical Change ◽  
Small Sample ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Specific Heats ◽  
Phase Systems ◽  
The One

Chemical reactions in gas phase systems such as flames are often studied by pumping a small sample of the gas through an orifice, after which the sample expands down a conical duct into one or more vacuum chambers, where finally it is analysed mass spectrometrically. One purpose of the expansion is to reduce suddenly the temperature and pressure of the gas to prevent chemical change in it. The extent to which chemical reactions in fact proceed during such an expansion is computed here using, as an example, the hydration of H 3 O + (the most commonly occurring ion in flames) in H 3 O + + H 2 O + M ⇌H 5 O 2 + + M. (I) Here M represents any molecule acting as a chaperon. For this purpose it is necessary to calculate the temperature, pressure and density of the gas in a conical expansion duct. This has been done in two ways, namely, with a simple one-dimensional model and also with a more realistic two-dimensional treatment employing the method of characteristics. This information on the flow field has been used together with thermodynamic and kinetic data on reaction (I) to compute the extent to which H 3 O + hydrates everywhere in the expansion and also the final levels of hydration attained when (I) finally freezes. Considerable hydration is predicted with final compositions corresponding to conditions roughly three or four orifice diameters inside the duct. Differences between the results of the one- and two-dimensional models are obtained, but it is established that both approaches give the same final extent of hydration, when averaged over all mass, for conical nozzles with total angles as large as 90°. The one-dimensional model, having been shown to be adequate, is used to determine the effect of the following parameters on the extent of reaction in the nozzle: initial temperature and composition, throat diameter, angle of the nozzle, mean molecular weight and ratio of the principal specific heats of the gas, and velocity constants for reaction (I). The results are compared with experimental determinations of [H 5 O 2 + ]/[H 3 O + ] in a hydrogen flame at 2000 K. Such a comparison indicates first that the majority of the H 5 O 2 + ion observed in practice is produced during the sampling process, rather than in a flame, and secondly that the velocity constant for the three-body hydration process in (I) is 7 x 10 -28 molecule -2 ml 2 s -1 at 300 K. Criteria are given for ascertaining whether any particular chemical reaction is likely to proceed in these expansions and thereby falsify measurements of chemical composition. The implications of this work for sampling gas phase systems in general are illustrated by computations on the hydration of alkali metal ions.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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