Half-width ratio

When pressure broadening dominates, the situation is more complicated because the resulting Lorentzian profile contributes significant area far from the line center. A further complication in this case is that the Lorentzian half-width cannot be accurately calculated and must be measured in other experiments. If both Doppler and pressure broadening are present, however, and if the Lorentzian to Doppler half-width ratio is small, the correction necessitated by pressure broadening is small. In this situation an accurate value of the Lorentzian half-width may not be needed. Line strength in the case of combined Doppler and pressure broadening may be obtained from the equivalent width by the use of tables (Jansson and Korb, 1968). 

TABLE IT. Intensity Ratio, Half-Width Ratio and Peak Shift for Peaks Studied in Uranium Tetrafluoride at Several Pressures... 

Figure 7. (a) Equipotentlal lines in the electrolyte for a sawtooth electrode surface in the high and low frequency limits, (b) complex impedance plots corresponding to (a) for different aspect ratios (height to half-width ratio) of the groove. ... 

Band Asymmetry. The peak asymmetry factor AF is often defined as the ratio of peak half-widths at 10% of peak height, that is, the ratio b/a, as shown in Fig. 11.2. When the asymmetry ratio lies outside the range 0.95-1.15 for a peak of k =2, the effective plate number should be calculated from the expression... 

Peak asymmetry or skewing is a well-documented (4,6,7) characteristic of chromatographic peaks and is measured easily by ratioing the peak half widths at 10% height as shown ... 

The analysis can be performed for several values of the relative peak height n, using the appropriate values of f(n) taken from Table I. Thus several estimates of Ed are obtained and either an average of them is calculated with its standard deviation, or provided a dependence of Ed on n is encountered, conclusions on the variability of Ed with coverage are drawn. As an alternative, only the half-widths of the peak are treated, as long as the experimental data are not distorted by some adjacent peak. Obviously, more information is obtained in such a case. The ratios of the half-widths taken at various values of n and compared with those given in Table I represent a criterion for the fit of the value of the desorption order. Since the estimates of Ed are free of contributions of fcd, the Tm relations can be used to estimate grossly the value of fcd, similarly as in Section V.C.2.b. 

The shapes of both /w and 7hv lines are assumed to be represented by simple Lorentzians. For a totally symmetric vibration with a low polarization ratio as in the present case, the vibrational and reorientational relaxation times Tv and can be determined from the half-widths of the isotropic and anisotropic spectra. Since the value of /hv is much smaller than that of /w for the 1050 cm" line, the contribution of /gv to the isotropic intensity can be neglected ... 

Peak asymmetry factor AF Ratio of peak half-widths at 10% peak height... 

Membranes and vesicles were labeled at a DPH/lipid ratio of 1/400 and measured using phase-modulation fluorometry at ten frequencies between 5 and 90 MHz at 37°C. y2 values were calculated assuming errors of 0.2 and 0.002 in the phase and modulation, respectively, except where otherwise noted. /, 2, Fraction of Exponential term or Lorentzian t, 2, lifetime (ns) cu, center of Lorentzians (ns) w12, half-width of Lorentzians (ns). 

The transmittance depends on the half-widths and 2 > only on the ratio tt2 / aj (Fig. 15). In the unidirectional approximation, the value of the linear transmittance is the same for light beams propagating in opposite directions through the discontinuity. 

Avd Avn Avp c A AW Doppler half-width in hertz natural half-width l/47cyN pressure-broadened half-width 1 /4nyP variable of integration wavelength of radiant flux triangle function of unit height and half-width % scaled ratio (AvN -1- Avc) /ln 2/AvD... 

In the present experiment, we took the aluminum Ka doublet components to be separated by 0.430 eV and to have a half-width of 0.35 eV each. The components were given a 2 1 intensity ratio and scaled to normalize the area under the combined peak. Figure 2 shows the resulting widened sx(x). 

We then investigated the formation of hybrid molecular assemblies in combinations of anionic peptide lipid 9 with cage-type hosts 7 and 8 after a previous method [44], Lamella-type aggregates are observed for a mixture of host 7 and lipid 9 at a 1 20 molar ratio in the dispersion state by negative staining electron microscopy. Phase transition parameters (temperature at peak maximum, T enthalpy change, AH entropy change, dS half-width of an endothermic peak, and hydrodynamic diameters (d,y) for the bilayer... 

The one exception in which phase contrast is not due to the dissipation arises when the tip jumps between attraction phases (>90°) and repulsion phases (<90°). Since sine is a symmetric function about 90°, the phase changes symmetric even if there are no losses in the tip-sample interaction. The relative contribution of the repulsive and attractive forces can be estimated experimentally from the frequency-sweep curves in Fig. lib by measuring the effective quality factor as Qe=co0/Ao)1/2, where Ago1/2 is the half-width of the amplitude curve. The relative contribution of the attractive forces was shown to increase with increasing the set-point ratio rsp=As/Af. Eventually, this may lead to the inversion of the phase contrast when the overall force becomes attractive [110,112]. The effect of the attractive forces becomes especially prominent for dull tips due to the larger contact area [147]. 

Let 0 be angular deflection of a dipole from the symmetry axis of the potential 1/(0), let p be a small angular half-width of the well (p Ci/2), and let (/0 be the well depth its reduced value u Uo/(kgT) is assumed to be 1. Since in any microscopically small volume a dipole moment of a fluid is assumed to be zero, we consider that two such wells with oppositely directed symmetry axes arise in the interval [0 < 0 < 2ji]. For brevity we consider now a quarter-arc of the circle. The bottom of the potential well is flat at 0 < 0 parabolic dependence U on 0. The form factor/is defined as the ratio of this flat-part width to the whole width of the well. Thus, the assumed potential profile is given by... 

Figure 7.4 Half-widths of the tetragonal (Ft) and rhombohedral (Fr) peaks for different Zr/Ti-ratios.

Recently, a novel method for determining the microstructure of crosslinked polybutadiene in latex using solution 13C-NMR technique was reported [133]. The surfactant and polymer concentrations in the latex were adjusted to give a good signal resolution of the latex sample, as indicated by half-width of the resonance peak at 32.7 ppm. Under these conditions, the S/N ratio was almost identical to that of sample in solution, as shown in Figure 11.31. The microstructure of sol and gel fractions in a radical initiated polybutadiene, determined by this technique, was similar to that of solution measurements. 

Gaussian Laser Profile-Voigt Atom Profile. This case turns out to be a better approximation of our experimental situation, i.e., the laser FWHM is fairly broad compared to the absorption line width and the absorption profile of atoms in an atmospheric combustion flame is described by a Voigt profile. Here the laser is assumed to have a Gaussian spectral profile as well as a Gaussian atomic absorption profile. In this case, convolution of two Gaussian functions is still a Gaussian function. Evaluation of the ratio n2/nT, and the fluorescence radiance. Bp, allows determination of the half width of the fluorescence excitation profile, 6X... 

Figure 7. Laser-induced absorbance changes at 561 nm as a function of time in detergent solubilised bovine rhodopsin (X) and isorhodopsin (9) at room temperature. Bathorhodopsin is the only intermediate during the bleaching of bovine rhodopsin known to absorb strongly at 561 nm. The energy of the 530-nm pump pulse was about 10 4J the energy of the 561-nm probe pulse was about 10 7J. The beam sizes were about 1 mm2 for the pump and 0.5 mm2 for the probe. The samples (about 1.5 mL) were held in 0.5-cm cuvettes. The concentrations were about 4 A cm I at the absorption peaks near 500 nm the ratios A Ajjj were about 0.3 and ratios ASsa. As<)o were about 0.7 for rhodopsin and 0.5 for isorhodopsin. Each data point shown is the average of six (rhodopsin) and nine (isorhodopsin) laser shots. Typical mean standard deviations are 0.03. The zero time is located using a 0.5 cm CS2 Kerr optical shutter at the sample site. The half width at half maximum for the CS2 shutter prompt response curve is about 6 ps.

In the zone of the MRC, the proportions of the contributions of the mean motion and of the synoptic and inertial variabilities to the total kinetic energy were 50 40 10, which is close to the estimates based on the data of moored buoy observations (see above). Thus, in the Black Sea, the relative contribution of the kinetic energy of synoptic fluctuations is sixfold lower than in the World Ocean. In the opinion of the authors of [25], this may be related to the small sizes of the sea and to the correspondingly high ratio R /L, where llL is the baroclinic Rossby radius and L is the half-width of the basin. In the Black Sea, R /L = 0.1, while in the World Ocean R /L = 0.01. At R /L > 1, no baroclinic mechanism for eddy formation cross section be implemented. 

This dimensionless parameter is used to describe impactor behavior. For impactors with rectangular openings, W is the slit width for circular openings W represents the diameter of the impactor opening. Thus the Stokes number is the ratio of the stop distance to the impactor opening half-width. 

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