Gauss profile

This is a Gauss profile with a lorentzian hole, the width of which is determined by the homogeneous linewidth parameters 7ab> T with 7ab " rb depending on the lifetimes 7a, Tb of... 

Figure 9 The emission spectrum of a tetracene film evaporated onto a glass substrate kept at 89 K and the emission monitored at 180 K (full circles). Its decomposition into Gauss profiles (II, III, IV, V) is shown by solid lines. The dashed curve is the sum of the gaussians. The lacking band I (=540 nm) is characteristic of the monomer emission from crystalline films formed at T > 140 K. Adapted from Ref. 72.

ELIAS II (LTB Lasertechnik Berlin GmbH, Berlin, Germany), having an instrument profile width of 0.13 pm (FWHM), which is negligible compared to the line width. The measured profiles were used to determine the line positions and intensities of the Cu doublet. For these values Gauss profiles with 1.4 pm FWHM were calculated, representing the Doppler broadening for Cu at 2600 K. 

Figure 2.8 Convolution of the synthetic Voigt profile from Figure 2.7 with a Gauss profile representing the instrument function of SuperDEMON A Voigt profile B convoluting Gauss profile with 0.9 pm FWHM C convolution result D measured absorbance profile in an air/ acetylene flame...

Application of the Gauss error-function equation for velocity profile in the form proposed by Shepelev (Table 7.12) in Eq. (7.39) results in the following formula for the centerline velocity in Zone 3 of the compact jet ... 

Air velocity in each jet cross-section, described using the Reichardt Gauss error-function profile... 

The equation for the centerline temperature differential in Zone 3 of the compact jet derived" from Eq. (7.61) using the Gauss error-function temperature profile (Table 7.14) is... 

Another typical problem met in this kind of analysis is known as the hook effect . It is due to an overestimation of the background line to the detriment of the peak tails. As a consequence, the low order Fourier coefficients of the profile are underestimated. In the fitting procedure by pseudo-Voigt functions, this problem occurs if the Gauss content is so high that the second derivative of the Fourier coefficients is negative this is obviously physically impossible because it represents a probability density. 

We use the function gauss.m in several examples, not only for the generation of chromatographic concentration profiles, but also for the generation of absorption spectra since these can often be approximated by a combination of Gaussian profiles. For example ... 

The Newton-Gauss algorithm requires initial estimates for the parameters in T. These can be computed from the same estimated concentration profiles Cguess as before (Figure 5-44). It is determined by... 

Determine the velocity profile and traction profiles in a pressure driven slit flow of a Newtonian fluid. Use Ap =1000 Pa, //, =1000 Pa-s, h 1 mm and a distance from entrance to exit of 1000 mm. Solve the problem using isoparametric 2D quadratic elements and different gauss points, compare your solutions with the analytical solution for slit flow. 

Figure 6.1 Comparison of 26 — 6 scan profiles obtained by a monochromatized (pure Cu kal) parallel beam configuration (hybrid x-ray mirror) and a conventional parallel beam configuration achieved by divergence slit (ds) module measured at 001/100 (a), 002/200 (b), 003/300 (c), 004/400 (d) of 500nm-thick Pb(Zro.B4Tio.46)03 thin film. Dotted lines represent the second derivative of the profiles, indicating the peak positions. Note that the profiles are simulated fitted profiles for obtained spectrum using pseudo-Voight function (mixed Lorentz and Gauss function).

Gaussian profile "Bell-shaped" profile following the Gauss equation (Eq. 6.5). 

The Gauss-Laplace equation describing liquid menisci in general was discussed in detail by Padday Russel (1960) and Padday et al. (1975). The profile of an axisymmetric drop can be calculated in dimensionless co-ordinates from the following equation (Rotenberg et al. 1983),... 

Beside the fitting of drop profile co-ordinates to the Gauss-Laplace equation, based on least square algorithms, a relation exists which allows the surface tension to be calculated from the characteristic diameters and Dj (Andreas et al. 1938, Girault et al. 1984, Hansen Rodsrud 1991). 

Eqs(5.19), (5.20). The accuracy of measurements with the pendent drop depends on the algorithm used for the drop shape analysis. While the accuracy is of the order of 1 mN/m when using characteristic drop diameters only, the analysis of the full drop profile by fitting the data to the Gauss-Laplace equation gives values with an accuracy of 0.1 mN/m. 

Where, y - width of Lorentz profile, w - width of Gauss pa-ofile and Wo - central position of absorption band. To take into account the individual rate of thermal decomposition of absorbing Lorentz profiles of aggregates, we need to include in the Voight function the equation describing the thermal decay curve, depending on the energy activation distribution. The equation for thermal decomposition as follows from (4) shown in the above curve is... 

The detail points on profiles were read by tracing the profiles drawn on a map of scale 1 1000. The model coordinates and heights were determined for detail points on the profiles. The model coordinates were first transformed into the Gauss-Kruger coordinate system as a geodetic network system and then to a system of classical determined profiles. 

By periodic measurements of the profile detail points we can use the same photo-theodolite base stations and also the same orientation points. All this can simplify the field measurements and so the photogrammetrical measurements were also more economical. The cost also depends on automatic registration of the stereo-model coordinates and further on-line transformation to Gauss-Kriiger and profile coordinates. 

ESR lines in solution can almost always be approximated by a Lorentz function. In the solid state the line-shape can in general be reproduced by a Gauss curve. In some instances a so-called Voigt profile can give a better approximation to the experimental line-shape. A Voigt line is a convolution of a Lorentz and a Gauss line. The shape is determined by the ratio ABi/ABg of the respective line-widths. The shapes of the 1st derivative lines of these types are given in Fig. 9.1. 

The line-shape of an experimental spectrum can in principle be determined by the procedure illustrated in Fig, 9.2. The 2nd derivative of the resonance line is then recorded. For a Gauss line the ratio hi/h2 between the minimum and maximum amplitudes of the 2nd derivative (Fig. 9.2(a)) equals 2.24 [18], while for a Lorentz shape it approaches the value 4. The hi/h2 ratio for a Voigt profile varies... 

In brief, via the CCD camera (1) with objective (2) and the frame grabber (3), an image of the shape of a drop (9) is transferred to a computer, where by using the ADSA software the coordinates of this drop are determined and compared to profiles calculated from the Gauss-Laplace equation of capillarity. The only free parameter in this equation, die interfaeial tension Y, is obtained at optimum fitting of the drop-shape coordinates. The dosing system (7) allows one to change the drop volume and hence the drop surface area. This possibility is used in dilational relaxation experiments as outlined in Sec. VI. 

To describe a liquid meniscus and hence to obtain the interfacial tension from the profile coordinates the Gauss - Laplace equation is used. This equation represents the mechanical equilibrium for two homogeneous fluids separated by an interface (Neumann and Spelt 1996). It relates the pressure difference across a curved interface to the surface tension and the curvature of the interface... 

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