Localization Depths

three levels of localization are established for each state variable. 

The first level is the line, or, more rigorously speaking, a curve. Variables at this level are named lineic densities, or fields in certain energy varieties (viz., electrodynamics, gravitation). In case of homogeneous distribution of the state variable in space, the lineic density is the state variable divided by a length. 

Understanding Physics and Physical Chemistry Using Formal Graphs 

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Practicable isotopic enrichment has the following prerequisites adequately short time for the enrichment process, acceptable asymptotic enrichment factor, and adequate accuracy for the estimation of the enrichment factor. (When total activity, rather than specific activity, is limiting, one must also pay attention to losses during enrichment.) For the argon and carbon enrichments referred to above, enrichment factors of about 100 and 500 were obtained within a week and a few hours, respectively and enrichment factors were deduced from direct observations of adjacent, stable isotopes. The 14C enrichment process provided extra dividends for AMS measurement the sample was implanted in an ideal form for the accelerator ion source, and it was spatially localized (depth) which gave added signal-to-noise enhancement. 

Mayer (M7), 1961 Experimental and theoretical study of wavy flow of water in open channel (slopes up to 5°). Data on growth of turbulent spots, local depths, surface velocity, length of entry zone, wave velocities, heights, frequencies, effect of surface-active materials. 

This equation gives the local volumetric solid flow rate (Qv) according to the kiln radius (R), the different operating variables (6, n), the angle of repose of materials (fi) and the local depth of the solid bed (II). The spatial variable (z) is defined from the kiln end for example, H(z = 0) corresponds to the depth of the solid bed at the exit of the kiln. Two views of the kiln are presented in Fig. 2 with the main variables used in the equations. 

Good correlation with local depth, as seen in Blumau, the Bunter sandstone aquifer of eastern England, the Stripa granite in Sweden (Fig. 14.1), and in other examples included in Table 14.1, or good correlation with temperature, as seen at the Molasse Basin in Austria and the Great Artesian Basin in Australia (Fig. 14.1). 

Locality Depth of faulting (m) Matrix cement prior to faulting Fault throws (m) Deformation characteristics Fault cement Later, burial modification of faults Max. burial (m) Late uplift Late extensional fracture fill... 

Fig. 8.31. Image processing in 3D SIMS generation of a local depth profile and a transaxial layer image (a) and of a coaxial layer image, a spatial diagonal image, and a point analytical information (b) the representation is inspired from Rudenauer [1989]...

There are of course numerous other analysis methods, including grain size, localized depth analyses, etc. The reader is referred to the manuals of the AFM software and to the Appendix for independent analysis software packages. 

The local depths represent irregularly distributed point data. 

The effect of the interaction of the cladding with steam is normally evaluated by the local depth of cladding oxidation, which implies an equivalent thickness of the oxidized layer. This is calculated as the conditional thickness of the metal layer converted to Zr02 provided that all the oxygen absorbed by the cladding metal has formed the oxide (in terms of the stoichiometric ratio). The... 

A second example is worth discussing because it illustrates links between other localization depths In translational mechanics, the inductance is the inertial mass M, defined in the general case as an operator in Equation 3.8. In one-dimensional systems, such as a string or a thin chain, modeling... 

A reduced constitutive property is specific to the material of the system when the sum of the localization depths of the related variables is equal to the number of spatial dimensions of the system. 

Wave records were analyzed by the zero-downcrossing method, and calculated results of characteristic wave heights and periods are presented in tabular forms. Prom these results, the ratios of and H ms to the local depth (inclusive of mean water level change) are calculated and plotted against the relative water depth h/Lo, as shown in Fig. 4.2. 

The time step At is chosen as 3 s, and the actual grid size Aa slowly varies in the range of 1312-1556 m. The dispersion-correction parameters 7 calculated by given conditions such as time step At, actual spatial grid Aa , and local depth h, give the values between —2.93 and 0.08 in the whole computational domain. As mentioned above, the minimum value of 7 is restricted to —0.125 to maintain the stabihty for the deep areas of the East Sea. Due to this limitation, the dispersion effects are underestimated in the numerical solutions. However, the present scheme gives more accurate solutions than the conventional models which use a uniform 7 value, i.e., 7 = 0.0, everywhere. 

Mean wind and current velocities are considered negligible during the passage. Their possible effects on the maneuvering conditions and ship response have been included as model uncertainties. The nominal value of the local depth along the channel was obtained from bathymetric data in LWL. The relative error in the depth measurements is 5%. The morphologic state during the storm event is considered stationary (i.e., Tc). The presence of small-scale bedforms and... 

Local depth of fuel cladding oxidation, % of the initial cladding thickness 18... 

The shear rate is approximated as constant, that is, the velocity profile in the x-direction is approximated as linearly dependent on the local depth of the flowing layer... 

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