A new method for calculating potential curves in the zero-order approximation of a generalized WKB method

1973 ◽  
Vol 16 (7) ◽  
pp. 996-998
Author(s):  
L. I. Vasilevskaya ◽  
A. S. Vasilevskii
Keyword(s):  
Order Approximation ◽  
Zero Order ◽  
New Method ◽  
Wkb Method ◽  
Zero Order Approximation ◽  
Potential Curves

Simultaneous Determination of Several Elements by Spectrochemical Addition Method … (II) (Tabulation of Analytical Value)

1968 ◽  
Vol 22 (6) ◽  
pp. 749-752 ◽  
Author(s):  
Isoo Masuda ◽  
Tamon Inouye
Keyword(s):  
Simultaneous Determination ◽  
Order Approximation ◽  
Analytical Data ◽  
Zero Order ◽  
Dilution Factor ◽  
Improved Method ◽  
Addition Method ◽  
Zero Order Approximation ◽  
First Approximation

An improved method for the tabulation of analytical data, obtained by addition and successive dilution procedures for spectrochemical analysis, is presented. The author's previous work shows that the solution of the first approximation diverges at some dilution factor smaller than unity when the slope of the working curve of added series is greater than that of unadded series. By obtaining the distance between this position and the origin, and taking it as a correction factor for zero-order approximation, tabulation of the analytical value, in the case of β>α, is carried out. One parameter of the calculation is deleted by normalizing the spectral intensity; therefore, the tabulation can be simplified.

scholarly journals On the Dynamics of Canyon–Flow Interactions

2018 ◽  
Vol 6 (4) ◽  
pp. 129 ◽  
Author(s):  
Jochen Kämpf
Keyword(s):  
Rossby Waves ◽  
Order Approximation ◽  
Zero Order ◽  
Submarine Canyons ◽  
Zero Order Approximation ◽  
Flow Disturbances ◽  
Flow Interactions ◽  
Direction Dependence ◽  
Topographic Rossby Waves ◽  
Fundamental Physical

This paper explores the dynamical origin and physical characteristics of flow disturbances induced by ocean currents in interaction with shelf-incised submarine canyons. To this end, a process-oriented hydrodynamic model is applied in a series of case studies. The focus of studies is the canyon-upwelling process in which seawater is moved from the upper continental slope onto the shelf within a shelf-break canyon. Results reveal that the generation of canyon upwelling, to zero-order approximation, is a barotropic and friction-independent quasi-geostrophic process. Hence, the principle of conservation of potential vorticity for such flows is sufficient to explain the fundamental physical properties of the canyon-upwelling process. For instance, this principle explains the direction-dependence of the canyon-upwelling process. This principle also explains the formation of stationary topographic Rossby waves downstream from the canyon that can lead to far-field effects. Density effects, being of secondary influence to the canyon-upwelling process, result in the intensification of canyon-upwelling flows via the formation of narrow near-bottom density fronts and associated baroclinic geostrophic frontal flows. Findings of this work reveal that the apparently complex canyon-upwelling process is much more basic than previously thought.

A perturbation method for Dirac’s new electrodynamics

1952 ◽  
Vol 213 (1115) ◽  
pp. 520-529 ◽  
Keyword(s):  
General Solution ◽  
Perturbation Method ◽  
Order Approximation ◽  
Zero Order ◽  
Classical Electrodynamics ◽  
Coupling Constant ◽  
Irrotational Flow ◽  
Zero Order Approximation ◽  
Fundamental Equations

The fundamental equations of Dirac’s new classical electrodynamics cannot be solved with the conventional perturbation method because there is no possibility of setting the coupling constant e equal to zero to start with. A perturbation method is worked out under the assumption that the charge is small, which means that the field created by the charge is neglected in the zero-order approximation. A general solution for the case of irrotational flow and another one for small vorticity are given. The equations derived are not easily soluble for large vorticity.

VACUUM-ULTRAVIOLET EMISSION AND ABSORPTION SPECTRUM OF THE NO MOLECULE: THE 2Δ STATES AND THEIR INTERACTIONS

1966 ◽  
Vol 44 (12) ◽  
pp. 3197-3216 ◽  
Author(s):  
Ch. Jungen
Keyword(s):  
Absorption Spectrum ◽  
Excited States ◽  
Vacuum Ultraviolet ◽  
Order Approximation ◽  
Electronic Configuration ◽  
Zero Order ◽  
Matrix Elements ◽  
Ultraviolet Emission ◽  
Zero Order Approximation ◽  
The Matrix

The emission spectrum of NO between 1 600 and 1 400 Å has been studied with a 1-m vacuum spectrograph. It consists of the two types of mutually perturbing 2Δ–X2Π bands already known from the much more complex absorption spectrum: the Rydberg systems F2Δ–X2Π, N2Δ–X2Π and the non-Rydberg system B′ 2Δ–X2Π. The interactions between the excited states of different electron configurations are of special interest. The matrix elements H = Hvib ∙ He have been obtained from detailed rotational analyses, a "deperturbation" in two steps has been carried out, and constants for the deperturbed 2Δ states are given. With calculated overlap integrals Hvib, the electronic configuration interaction energy He is derived. "Crossing" potential energy curves have been shown to be the appropriate zero-order approximation when [Formula: see text]. The phase of the interaction, i.e. the sign of He, has been deduced from the perturbed intensities of the observed bands.

scholarly journals LOW-TEMPERATURE EQUATION OF STATE OF SOLID METHANE

2016 ◽  
Vol 52 (1) ◽  
Author(s):  
L. N. Yakub ◽  
O. S. Bodiul
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Low Temperature ◽  
Thermodynamic Properties ◽  
Triple Point ◽  
Order Approximation ◽  
Zero Order ◽  
Zero Order Approximation ◽  
Temperature Equation ◽  
Solid Methane

The theoretical equation of state for solid methane, developed within the framework of perturbation theory, with the crystal consisting of spherical molecules as zero-order approximation, and octupole – octupole interaction of methane molecules as a perturbation, is proposed. Thermodynamic functions are computed on the sublimation line up to the triple point. The contribution of the octupole – octupole interaction to the thermodynamic properties of solid methane is estimated.

scholarly journals Explicit Multipole Formula for the Local Thermal Resistance in an Energy Pile—The Line-Source Approximation

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5445
Author(s):  
Johan Claesson ◽  
Saqib Javed
Keyword(s):  
Thermal Resistance ◽  
Order Approximation ◽  
Input Parameter ◽  
Zero Order ◽  
Mean Value Theorem ◽  
Carrier Fluid ◽  
Energy Pile ◽  
Zero Order Approximation ◽  
Wide Range ◽  
Multipole Method

This paper presents a closed-form quite handy formula for the local thermal resistance Rb between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy’s mean value theorem of analytical functions is used. The formula for thermal resistance Rb0 for the zero-order approximation (J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation (J = 0) are shown to be quite small by comparisons with eight-order approximation (J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance Rb0 for the zero-order approximation (J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance Rbmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.

Perturbation theory with model zero-order approximation for Li2 molecules

1988 ◽  
Vol 29 (1) ◽  
pp. 147-149
Author(s):  
A. V. Glushkov ◽  
N. N. Dudnik ◽  
S. V. Malinovskaya
Keyword(s):  
Perturbation Theory ◽  
Order Approximation ◽  
Zero Order ◽  
Zero Order Approximation

A simple geminal approach to bonding. I. Helium–helium interaction

1967 ◽  
Vol 45 (8) ◽  
pp. 847-849 ◽  
Author(s):  
F. David Peat
Keyword(s):  
Wave Function ◽  
Electron Energy ◽  
Reasonable Agreement ◽  
Order Approximation ◽  
Energy Levels ◽  
Zero Order ◽  
Experimental Results ◽  
Zero Order Approximation ◽  
Weight Factors ◽  
Variation Parameter

The energy of a molecule may be expressed as the sum of two-electron energy levels; the weight factors involved in this sum may be determined in the zero-order approximation. This method is applied to the He–He interaction, the two-electron energy levels being calculated using a wave function containing a single-variation parameter. Reasonable agreement is obtained with experimental results.

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