Calculation of fields

The calculation of field distribution in the whole waveguide structure using the immittance matrix starts from the output section. As there are no backward propagating modes in the output section, = 0, it follows from Eq. (14) that + p =, from which we get using Eq. (15)... 

Simplicity of this model allows us to investigate not only frequency responses of the magnetic field, measured by a receiver, but also a distribution of currents in a conducting medium. Such will help us to understand deeper physical principles of the induction logging as well as some approximate methods of calculation of fields which are widely used for interpretation. 

Table 10.6 contains data of calculations of field magnitude A = l/ij,] by exact and asymptotic formulas 10.33 and 10.70, illustrating the area of application of eq. 10.70. It is natural to distinguish three ranges of frequency responses of the amplitude spectrum (Figs. 10.5-10.8) the range of small parameters, the intermediate zone and the wave zone. 

In what follows, we propose a phenomenological model of the chemisorbed radical-anion standing in the electrochemical double-layer. We shall hence detail the reasons why this chemisorbed radical anion is intrinsically unstable but most probably has a finite lifetime on the polarized metallic surface. We outline the procedure through which we expect that an order of magnitude of the lifetime of the chemisorbed radical-anion may be evaluated numerically via this model. The model potential felt by the radical-anion as it is formed on the polarized electrode is described as the sum of three terms, for which a parametrisation is proposed. One of these terms is meant to include both the surrounding solvent and the repulsion by the polarized electrode, thanks to a mean, locally uniform, electric field. In the present paper, the intensity of this uniform electric field is calibrated on the basis of a conparison between experimental Stark-Tuning shifts for CO chemisorbed on palladium surfaces in solution and Density Functional Theory calculations of field-induced vibrational shifts for CO chemisorbed on palladium clusters. The shape of the resulting model potential is then discussed. 

The theory and computational methods for the analysis and calculation of field-free resonances in polyelecfronic afoms and molecules that are adumbrated here were initiated in 1972 [11a] as an alternative to the theoretical approaches mentioned above and in the review articles [12-16, 21], for the purpose of dealing efficiently with the MEP in arbitrary electronic structures. A complementary discussion based on the ideas in Ref. [11a] and on later publications dealing with various topics within energy-dependent and time-dependent frameworks was given a few years later [37b]. 

There are several theoretical studies on LaO and related lanthanide oxides. We have already mentioned the ligand-field theory model calculations of Field (1982) as well as Carette and Hocquet (1988). More recently, Kotzian et al. (1991a,b) have applied the INDO technique (Pople et al. (1967) extended to include spin-orbit coupling [see also Kotzian et al. (1989a, b)] to lanthanide oxides (LaO, CeO, GdO and LuO). The authors call it INDO/S-CI method. The INDO parameters were derived from atomic spectra, model Dirac Fock calculations on lanthanide atoms and ions to derive ionization potentials, Slater-Condon factors and basis sets. The spin-orbit parameter is derived from atomic spectra in this method. 

Cases of ground surface relief of the Earth were not considered in investigations. Or the cases were not brought to systematical numeral modeling. Currently available methods of relief form corrections have approximate pattern. In this study, for the calculation of fields in layered relief medium, we use the method of integral equations, well-established when performing modeling in resistivity method [7],[8],[9]. 

A system of integral equations for calculating the density of the secondary currents at the boundaries of contacting media in case of multiple layered relief media was established. The proposed method allows to calculate the field of the point source on the ground surface, which has a relief shape. Numerical examples of the calculation of fields of current densities of secondary sources were shown. 

Definition of fields of speeds of gas in shovels of an impeller by means of the mentioned theory of streams (Gurevich, 1979) represents labor-intensive process. For the simplified solution of a problem of calculation of separation of a dust, it is possible to be restricted to the approached model of a gas stream considering the basic regularity, installed at more exact calculation of fields of speeds (Stepans, 1986). Such computational model is represented on Figure 12.1. The gas stream between shovels at stream turn is modeled by a ring with internal radius / , and external radius A stream angle of rotation define a geometrical relationship. 

To proceed to the actual calculation of field-dependent effects, it is usual to expand the term jt i) in the Hamiltonian, obtaining... 

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