Transverse profile

The theoretical approach is based on the solution to the mixed type linear/nonlinear generalized Schrodinger equation for spatiotemporal envelope of electrical field with account of transverse spatial derivatives and the transverse profile of refractive index. In the quasi-static approximation, this equation is reduced to the linear/nonlinear Schrodinger equation for spatiotemporal pulse envelope with temporal coordinate given as a parameter. Then the excitation problem can be formulated for a set of stationary light beams with initial amplitude distribution corresponding to temporal envelope of the initial pulse. 

Stationary (i.e. for dA/ dz = 0) localized solutions to Eq.(3.2) represent nonlinear modes in the planar waveguide and may be found in an analytical form via matching the partial solutions of Eq.(3.2) at the core/cladding boundary. The partial solutions are Jacobi elliptical function in the core and 2l rccosh — )E]/E in the cladding (the functional dependence similar to a fundamental soliton in a uniform nonlinear medium). Here is a parameter which depends on the boundary conditions. Contrary to the modes of a linear waveguide, the transverse profile of a nonlinear mode depends on the power in the mode. 

In this paper, we have used the next numerical scheme to evaluate transverse profiles of the nonlinear modes. First, continuity conditions for and dA / at the core-cladding boundary have been applied for a... 

Figures. Transverse profiles of a symmetric nonlinear mode with P=1 (1),5 (2), 10(3).

Concerning to the higher-order modes, a universal criterium of their stability is not yet available. In this paper, the stability of nonlinear modes was analysed numerically via solution of the Cauchy problem for Eq.(3.2) with 2l(, 0) = 2l( ) where 2l( ) is the transverse profile of a nonlinear... 

However, the difference between transverse profiles of linear and nonlinear modes can be significant for the considered range of powers (Fig.8). That is why numerical modeling of nonlinear mode propagation through the discontinuity is a reasonable way to study the spatial transformation of the mode field. 

In the structure A, the transverse profile of the initial pulse varies behind the junction due to the self-focusing effect. In the nonlinear waveguide of the structure, a fraction of an initial pulse power is emitted from the guiding region (Fig. 19). 

For a given pulse power, the SS effect depends on the transverse profile of the field and is less pronounced in waveguides with thinner cores (the dashed lines in Fig.26, 27 are plotted for a waveguide with <7= 2.4pm). 

These regional effects in the Rhone area (Valais with low precipitation and high evaporation) or in the Ticino area (high precipitation and low evaporation) are clearly expressed in the transversal profiles shown in Fig. 20. This diagram also... 

Figure 10.4 Transverse profiles of (a) mean and (6) RMS nondimensional temperature at five axial locations without (f) and with (2) radiation...

Bessel beams [39], because their transverse profile is a Bessel function. Because of their peculiar features, Bessel beams have a number of applications in the most disparate sectors, ranging from nondestructive evaluation of materials to medical imaging. 

Fig. 13.3. Transverse profile of the fluence (time-integrated intensity) measured at several propagation distances. The color scheme was chosen such that one can see the structure of the low-intensity background. On the other hand, it makes it difficult to compare filament intensities. The size of the depicted domain in all panels is 1 cm X 1 cm...

In tectonically active areas of the continental slope, structural topographic features dominate and, in the transverse profiles of the slope, relatively gentle (1-3°) accumulative surfaces are sharply replaced by steep almost vertical (10-30°) escarpments, often featuring a stepwise profile and cut by systems of faults. Over the steep slopes, landslide processes develop [9]. 

The morphologies of the different underwater canyons have much in common. They feature V-shaped or U-shaped transverse profiles. With depth, the width of the canyons increase from 150-200 m at the shelf edge to to... 

Davison, I. R., and Stewart, W. D. P. (1984). Studies on nitrate reductase activity in Laminaria digitata (Huds.) Lamour. I. Longitudnal and transverse profiles of nitrate reductase activity within the thaUus. J. Exp. Mar. Biol. Ecol. 74, 201—210. 

Martin (2000) proposes the following model to describe the transverse profile of a phytoplankton filament ... 

The idea of focussing on the transverse profile of filaments (see Sect. 2.7.1) has a long history, specially in the chemical engineering and combustion contexts (Carrier et al., 1975 Ranz, 1979 Ottino, 1994 Bish and Dahm, 1995), where it appears under the names of lamellar models or stretch models. More recently it has been explicitly used by Neufeld (2001), Neufeld et al. (2002b), McLeod et al. (2002), Neufeld et al. (2002c), Szalai et al. (2003), Hernandez-Garcfa et al. (2003), or Cox (2004) and is one of the ideas behind the approaches used in papers such as Jimenez and Martel (1991), Wonhas and Vassilicos (2002), or the ones reviewed in Tel et al. (2005). 

The sample is taken from running water, if possible, from the streamline. If the stream has several branches, the sample is taken from the branch with the highest flow rate. In shallow streams, the sample is taken approximately in the upper third or at a depth of about 20-30 cm from the surface in the case of deeper streams the depth for sampling depends on the purpose of the analysis. In some cases, zonal sampling is performed across the whole transversal profile with several vertical samplings. 

When the rolling inclinometer is used, the longitudinal and the transverse profiles of the travelled surface is determined, from which the roughness of the new pavement is quantified in terms of selective roughness index. The results are displayed by the on-board computer screen and also road roughness/smoothness and must grind areas can be reported in printed graphical and tabular report form. For more details, see ASTM E 2133 (2009). 

Almost all of the abovementioned high-speed profilometers are capable of determining the transverse profile as well some can also measure other surface characteristics such as texture, cracking, road geometry and so on. 

ASTM E 2133. 2009. Standard test method for using a rolling inclinometer to measure longitudinal and transverse profiles of a traveled surface. West Conshohocken, PA ASTM International. 

The laser devices are attached either at the front or at the rear of the vehicle and scan the pavement surface. These vehicles, apart from recording the pavement texture profile, also record other surface characteristics such as longitudinal profile, transverse profile (rut depth) (see Figure 16.30) or even surface cracking (Figure 16.36). 

Apart from the term unevenness, usually used by EN standards, the term roughness is also used, usually by US standards. According to ASTM E 867 (2012), travelled surface roughness is the deviations of a surface from a true planar surface with characteristic dimensions that affect vehicle dynamics, ride quality, dynamic loads and drainage, for example, longitudinal profile, transverse profile and cross slop. 

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