Article

1998 ◽  
Vol 76 (8) ◽  
pp. 609-620
Author(s):  
M RM Witwit ◽  
N A Gordon
Keyword(s):  
Large Class ◽  
Potential Function ◽  
Three Dimensional ◽  
Potential Functions ◽  
Numerical Calculations ◽  
Dimensional System ◽  
Perturbation Parameters ◽  
The Hill ◽  
Three Dimensional System

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential function V(x,y,z;Z2, λ,β)= –Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calculations using this expansion and the Hill-determinant approach are reported for a large class of potential functions and for various values of the perturbation parameters Z2, λ, and β. PACS No.:03.65

Inner-product theory calculations for some rational potentials in a three-dimensional system

1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Inner Product ◽  
Dimensional System ◽  
Product Technique ◽  
Special Cases ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Three Dimensional System ◽  
Range Of Values

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.

scholarly journals On the method of eigenvalues determination of the “truncated” matrix with morse hamiltonian as an example

2020 ◽  
pp. 172-177
Author(s):  
E.S. Bekhtereva ◽  
◽  
O.V. Gromova ◽  
P.A. Glushkov ◽  
A.S. Belova ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Potential Function ◽  
Prediction Accuracy ◽  
Polyatomic Molecules ◽  
High Order ◽  
Potential Functions ◽  
Numerical Calculations ◽  
Order Perturbation ◽  
Morse Oscillator

A method of precise eigenvalues determination is developed on the basis of high order perturbation theory and applied to di-atomic molecule, as an example. The proposed method makes it possible not only to obtain energy values, but also to estimate a prediction accuracy and limits of its applicability for a specific implemented model. Numerical calculations are performed with the use of the extended Morse oscillator functions. The sixth power of the Morse coordinate is included into the potential function expansion. Analysis of possibility to make calculation in the model of the "truncated" matrix of the Hamiltonian is performed. The comparative possibilities of the method are analyzed with respect to other approaches of the potential functions determination for polyatomic molecules.

scholarly journals A simple in situ visual and tristimulus colorimetric method for the determination of diphosgene in air

2007 ◽  
Vol 72 (10) ◽  
pp. 1031-1037 ◽  
Author(s):  
Vladimír Pitschmann ◽  
Zbyněk Kobliha ◽  
Emil Halámek ◽  
Ivana Tusarová
Keyword(s):  
Acetyl Chloride ◽  
Colorimetric Method ◽  
Three Dimensional ◽  
Field Analysis ◽  
Dimensional System ◽  
Optimal Composition ◽  
Fabric Filter ◽  
Three Dimensional System

A simple visual and tristimulus colorimetric method (three-dimensional system CIE-L*a*b*) for the determination of trace amounts of diphosgene in air has been developed. The method is based on the suction of diphosgene vapors through a modified cotton fabric filter fixed in a special adapter. Prior to analysis, the filter is saturated with a chromogenic reagent based on 4-(p- nitrobenzyl)pyridine. The optimal composition of the reagent is 2 g of 4-(p-nitrobenzyl)pyridine and 4 g of N-phenylbenzylamine in 100 ml of a 50:50 ethanol-glycerol mixture. The intensity of the formed red coloration of the filter is evaluated visually or by a tristimulus colorimeter (LMG 173, Lange, Germany). The detection limit is 0.01 mg m-3. Acetyl chloride and benzoyl chloride react in 150 and 50 times higher concentrations, respectively. The method is suitable for mobile field analysis. .

The influence of mean shear on Alfvén-internal wave propagation

1976 ◽  
Vol 15 (2) ◽  
pp. 197-222
Author(s):  
R. J. Hartman
Keyword(s):  
Three Dimensional ◽  
Dimensional System ◽  
Linear Wave ◽  
Mean Flow ◽  
Wave Processes ◽  
Initial Value ◽  
Initial Wave ◽  
Wave Phenomena ◽  
Three Dimensional System

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.

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