The theoretical model

We propose a physical model, being based on the variation of the magnetic flow, allowing to determine defects characteristics. Some is the material and some is the geometry of the product, the presence of a defect allocates the flow in the straight section of the solenoid. The theoretical model proposed allows to find defects characteristics from the analysis of the impedance variation. 

The experimental tests have validated the theoretical model for eylindrical products in non ferromagnetic material, therefore with a long solenoid ... 

Projection radiography is widely used for pipe inspection and corrosion monitoring. Film digitisation allows a direct access to the local density variations by computer software. Following to a calibration step an interactive estimation of local wall thickness change based on the obtained density variation is possible. The theoretical model is discussed, the limitations of the application range are shown and examples of the practical use are given. The accuracy of this method is compared to results from wall thickness measurements with ultrasonic devices. 

Furtak T E and Reyes J 1980 A critical analysis of the theoretical models for the giant Raman effect from adsorbed molecules Surf. Sc/. 93 351-82... 

The theoretical models caimot predict flux rates. Plant-design parameters must be obtained from laboratory testing, pilot-plant data, or in the case of estabhshed apphcations, performance of operating plants. 

Once these first estimates for the geometric dimensions of the cyclone have been obtained, a full theoretical analysis of the fluid and particle motions in the cyclone may be performed using the theoretical models given in Section 13.2.1.2. A substantial use of the expression (13.26) for the collection efficiency should be employed so that an updated design of the geometry of the cyclone can be obtained. 

The total energy of a vessel s contents is a measure of the strength of the explosion following rupture. For both the statistical and the theoretical models, a value for this energy must be calculated. The first equation for a vessel filled with an ideal gas was derived by Brode (1959) ... 

Gaussian includes many different model chemistries. The theoretical model chemistries in Gaussian have been subjected to the testing procedure described previously and so may be recommended for general use with any system for which they are computationally feasible. 

Tadaki and Maeda (Tl) examined the desorption of carbon dioxide from water in a bubble-column and analyzed the experimental results under the assumption that while the gas phase moves in piston flow, the liquid undergoes axial mixing that can be characterized by the diffusion model. (Shulman and Molstad, in contrast, assumed piston flow for both phases.) Only poor agreement was obtained between the theoretical model and the experimental... 

Kolbel et al. (K16) examined the conversion of carbon monoxide and hydrogen to methane catalyzed by a nickel-magnesium oxide catalyst suspended in a paraffinic hydrocarbon, as well as the oxidation of carbon monoxide catalyzed by a manganese-cupric oxide catalyst suspended in a silicone oil. The results are interpreted in terms of the theoretical model referred to in Section IV,B, in which gas-liquid mass transfer and chemical reaction are assumed to be rate-determining process steps. Conversion data for technical and pilot-scale reactors are also presented. 

It should be emphasized that whereas the theoretical modelling of An3+ spectra in the condensed phase has reached a high degree of sophistication, the type of modelling of electronic structure of the (IV) and higher-valent actinides discussed here is restricted to very basic interactions and is in an initial state of development. The use of independent experimental methods for establishing the symmetry character of observed transitions is essential to further theoretical interpretation just as it was in the trivalent ion case. 

It is noteworthy that several studies exhibit contradictory results for both the mechanical and thermal characteristics of the flow. This is generally due to differences in the many parameters that characterize these studies such as the geometry, shape and surface roughness of the channels, the fluid, the boundary conditions and the measuring methodology itself. These discrepancies indicate the need for extension of the experimental base to provide the necessary background to the theoretical model. 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

Kumar et al. have studied the miUing behavior of brominated isobutylene-co-p-methyl styrene (BIMS) and its blends with EPDM [40]. Using the theoretical model of Tokita, they have tried to optimize the rmU parameters. They measured the critical nip-gap at which a front-to-back roll transition takes place. They concluded that addition of different fillers reduced the critical nip-gap for BIMS as compared to the gum polymer. The critical nip-gap is lower for systems containing... 

Since no experimental work is available to confront the theoretical model designed to describe C3H2 excited states correctly, test calculations had to be done in a preliminary step. For that purpose, we have chosen ethylene, for which extensive calculations of the vertical spectrum as well as experimental measures are available. It is well known indeed that a correct quantitative and even qualitative description of small rr-electronsystems, is still a challenge for theoretical chemistry. The difficulties are found at each step of the computational approach ... 

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