scholarly journals Quasi-Exactly Soluble Potentials and Deformed Oscillators

2020 ◽  
Vol 6 ◽  
pp. 199
Author(s):  
Dennis Bonatsos ◽  
C. Daskaloyannis ◽  
H. A. Mavrommatis
Keyword(s):  
Vibrational Spectra ◽  
Diatomic Molecules ◽  
Approximate Determination ◽  
Anharmonic Oscillators ◽  
Opposite Parity ◽  
Poten Tials ◽  
Deformed Oscillator

It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n+1 lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent poten- tials corresponding to deformed anharmonic oscillators of SUq(1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. This connection allows for the immediate approximate determination of the levels of the same parity lying above the fewest n+1 known levels, as well as of all levels of the opposite parity. Such connections are not possible in the cases of the q-deformed oscillator, the Q-deformed oscillator, and the modified Pöschl-Teller potential with SU(1,1) symmetry.

scholarly journals Vibrational molecular and nuclear spectra in terms of quantum algebras

2020 ◽  
Vol 4 ◽  
pp. 121
Author(s):  
Dennis Bonatsos ◽  
C. Daskaloyannis
Keyword(s):  
Vibrational Spectra ◽  
Coupled Oscillators ◽  
Its Region ◽  
Computational Effort ◽  
Molecular Spectra ◽  
Anharmonic Oscillators ◽  
Deformed Oscillator ◽  
Nuclear Models ◽  
Present Formalism ◽  
Exactly Soluble Models

A generalized deformed oscillator giving the same spectrum as the Morse potential is con­ structed through the use of quantum algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss, suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscilla­tors. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown. Nuclear models giving good descriptions of vibrational spectra are reviewed and the need of modifying the SUq(2) model in order to extend its region of applicability towards the vibrational limit is discussed.

Generalized deformed oscillators for vibrational spectra of diatomic molecules

1992 ◽  
Vol 46 (1) ◽  
pp. 75-80 ◽  
Author(s):  
Dennis Bonatsos ◽  
C. Daskaloyannis
Keyword(s):  
Vibrational Spectra ◽  
Diatomic Molecules

The harmonic and transient electromagnetic response of a thin dipping dike

Geophysics ◽  
1983 ◽  
Vol 48 (7) ◽  
pp. 934-952 ◽  
Author(s):  
P. Weidelt
Keyword(s):  
Formal Solution ◽  
Harmonic Excitation ◽  
Electromagnetic Response ◽  
Approximate Determination ◽  
Finite Conductivity ◽  
Circular Loop ◽  
Decay Modes ◽  
Transient Electromagnetic ◽  
Free Decay

An exact solution is given for the electromagnetic induction in a dipping dike of finite conductivity, represented as a thin half‐sheet in a nonconducting surrounding. The problem is formulated for arbitrary dipole or circular loop [Formula: see text] configurations. The formal solution obtained by the Wiener‐Hopf technique is cast into a rapidly convergent triple integral suitable for an effective numerical treatment. A good agreement is found between numerical results and analog measurements available for harmonic excitation. The transient response is obtained as a superposition of the half‐sheet free‐decay modes and is illustrated by some numerical examples for coincident loops, including a diagram for the approximate determination of conductance and depth of a vertical dike.

Caracterización de la roca mediante propiedades físicas y su relación con la resistencia a la compresión simple

2021 ◽  
Vol 2 (4) ◽  
pp. 5081-5093
Author(s):  
Patricio Feijoo Calle ◽  
Elizabeth Brito Verdezoto
Keyword(s):  
Compressive Strength ◽  
Physical Properties ◽  
Unconfined Compressive Strength ◽  
Approximate Determination ◽  
Practical Application ◽  
Calculation Methodology

En este trabajo se propone una metodología sencilla y de aplicación práctica en campo para la determinación aproximada de la Resistencia a la Compresión Simple (RCS) en rocas, propiedad o característica que es importante en minería, ya que mediante la misma, se ejecutan análisis para la valoración de factores de seguridad y estabilidad y/o posibles sistemas de fortificación en las obras o estructuras mineras, a más de que la caracterización de la RCS es también influyente en el uso de explosivos para la explotación o extracción de materiales de una cantera o mina. Esta estimación se la propone en base a la determinación de las siguientes tres propiedades de la roca, que en esta investigación las denominamos densidad, porosidad y absorción “en mina”. Estas propiedades físicas se las puede obtener de una forma simple, pero metódica y en este trabajo se han ejecutado ensayos sobre un mismo material o roca proveniente de la zona de Cojitambo, provincia del Cañar (Ecuador) y sobre una base de 60 muestras o probetas. Los resultados obtenidos permiten una correlación entre las propiedades antes descritas y la RCS, a más que se ha estructurado una metodología de cálculo para el objetivo planteado.   This work proposes a simple methodology and practical application in the field for the approximate determination of the Unconfined Compressive Strength (UCS) in rocks, property or characteristic that is important in mining, since through it analyzes are carried out to the assessment of security and stability factors and/or possible fortification systems in the works or mining structures, in addition to the characterization of the UCS is also influential in the use of explosives for the exploitation or extraction of materials from a quarry or mine. This estimate is proposed based on the determination of the following three properties of the rock, which in this investigation we call density, porosity and absorption “in mine”. These physical properties can be obtained in a simple, but methodical way and in this work, tests have been carried out on the same material or rock from the Cojitambo area, Cañar province (Ecuador) and on the basis of 60 samples or test tubes. The results obtained allow a correlation between the properties described above and the UCS, in addition to a calculation methodology for the proposed objective.

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