Doppler contour

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

It ought to be stressed that the above description of relaxation does not account for the velocity of translational motion of a separate particle. That is justified in the case where the spectral intensity of the exciting laser light is constant within the range of the Doppler contour of the optical transition, and the molecules can thus absorb light irrespective... 

The data from Table 3.7 make it possible to make a few estimates. Let us consider a concrete example. If the length of the resonator is L = 2 m, the Doppler contour, say of a K2 molecule in the BlTlu state, contains about 11 axial modes, the distance between them being Au>i = ttc/L m 4 108 s-1. If we assume that the width of the Bennet dip is equal to the homogeneous line width, rBen T = 0.86 108s 1 (see... 

In these studies, not only rotational and vibrational states of products should be detected, but also the distribition of the velocity of the separation of products. Either time-of-flight mass spectroscopy, or the LIE method with a high spectral resolution is used for this purpose. When LIF is used, the Doppler contour of the line in the excitation spectrum is measured. Since atoms with different velocity vectors, according to the Doppler effect, absorb (emit) the light in different manners, this reflects the shape of the line in the excitation spectrum. Therefore, using the experimentally determined contour of the line in the excitation spectrum, one can obtain information about the values and direction of the velocity of the separation of products. 

It follows from this that the vector of separation velocity of products v is perpendicular to the rotational angular momentum of the CO molecule. This correlation between the vectors v and was experimentally confirmed from analysis of the Doppler contours of the excitation spectra of the CO molecule. The use of the law of energy conservation showed that the sulfur atom in the electronic state D is formed in this reaction. 

To analyze the data, first perform the vx- and ty-corrections and the time-to-speed transformation to make the velocity volume element the same for all data points, and then normalize each Doppler-selected TOF spectrum according to the averaged ID Doppler profile from several independent scans, I vz) = )T)(, vyS(vy vx 0,vz)dvy. Due to the large exothermicity of this reaction, the problematic density-to-flux transformation is not negligible (despite the large probe laser size used to minimize its effects) and needs to be accounted for (the wy-correction , see Sec. 3.3). By combining all the resulting TOF spectra, the product 3D velocity flux contour... 

Fig. 14. 3D representation of the H-atom velocity flux contour, d a/dvd(cos6). The contours are constructed directly from a total of 33 slices of the Doppler-selected TOF measurements. 

Fig. 21. The product D-atom velocity-flux contour map, d

UCAs were originally used with fundamental US imaging, providing inaeased image enhancement and contour detection. However, improvements from UCAs were minimal due to the low ratio of blood volume to tissue. Contrast-assisted US has proven far more useful with Doppler... 

US due to its ability to detect flow within vasculature on the micron level. Contrast-enhanced Doppler has proven successful in the detection and diagnosis of cancers, " detection of inflammation precursors, and brain imaging. Figure 3 shows an example of contrast-enhanced Doppler of a rabbit kidney using a poly(laaic-co-glycolic acid) (PLGA), air-filled UCA developed in our laboratory. After injection, UCAs within the kidney vasculature become apparent, providing substantial contour detection. 

Figwe 3 Power Doppler imaging of a rabbit kidney preinjection (a) and postinjection (b) of 0.15 ml kg" PLGA UCA. After injection, the vasculature and contours within the kidney (boxed) become enhanced. 

Fig. 19.9. a Sonography of the jejunal GIST. An oval-shaped tumor with a deep ulcer is demonstrated. The tumor is well demarcated and the contour of the tumor is smooth, b Color Doppler ultrasound of the tumor shows the rich vascularity, c Contrast-enhanced ultrasound reveals the rich perfusion with a focal perfusion defect inside the tumor (asterisk), d Endoscopic feature of the tumor. A submucosal tumor with a deep ulcer at the center is demonstrated... 

Ruptured cysts may have more lobulated contours and show perilesional Doppler signals. Calcified cysts appear as solid hypoechoic masses with multiple calcified foci associated with dense digital acoustic shadowing. 

An alternative spectroscopic approach would be to determine the rotational temperature from the intensities in a rotationally resolved vibrational or electronic spectrum. In this case, even if one cannot resolve individual rovihrational transitions, one can still estimate the temperature by simulating the rotational contour of an individual vibronic band [120]. For this, one needs to know the rotational constants of the molecule and the direction of the transition moment however, even rough estimates of these quantities can lead to a reasonable temperature estimate. In measuring either Doppler widths or rotational band contours, the linewidth one obtains may contain a contribution from the finite lifetime of the molecule, determined by its intramolecular vibrational energy redistribution and/or dissociation rate if some type of photofragment spectroscopy is used, and this can make the temperature appear to be higher than it really is. 

The translational anisotropy in the rotationally excited fragments retains the value p - -0.9, but the striking changes in their Doppler resolved LIF spectral contours with changes in the detection geometry and rotational branch (see Fig. 5) betray a maiked polarisation of the photofragment rotational vector distributions... 

FIGURE 6. Doppler resolved profiles of Pi(N ) and Qi(N ) features in 0H(X) generated by photodissociation of HONO2 at 280 ran. Note the change in spectral contours when the excitation-detection geometry changes from coaxial to perpendicular and the differences in contrast in the double peaked Pi(6) and Qi(6) lines. 

Laser methods make it possible to obtain particles with both a definite value and direction of the velocity vector and a definite orientation in the space. If a laser producing the radiation with the spectral width much shorter than the width of the absorption line is used for the excitation of a molecule, whose contour of the absorption line is due to the Doppler broadening, only molecules moving with a definite velocity in the direction of the laser beam will undergo excitation. For example, if the generation frequency of the laser corresponds to the frequency of the center of the absorption line of molecule, then only molecules at rest will be excited. 

The PDF model predicted velocity (Equation 28.5), and its overdamped equivalent, provides an excellent fit to all clinically recorded Doppler E-wave contours [21,32, Figure 28.1]. The PDF parameters... 

In a recent work, PRR has been vahdated as the invasive analog of the PDF parameter c [79]. The vahdation was performed in 40 NSR subjects from a database of simultaneous transmitral flow-micro-manometric LV pressure recordings. In each subject, for approximately 10 cardiac cycles, c was measured from the Doppler E-wave, and a PRR value was calculated from the simultaneously recorded LVP contour. As predicted by the derivation above, PRR and c were found to be strongly linearly correlated (R = 0.77) over all analyzed beats. When average values for each subject were compared, PRR and c maintained the expected strong linear correlation (R = 0.79). 

Hall AF, Aronovitz JA, Nudelman SP, and Kovics SJ. Automated method for characterization of diastohc transmitral Doppler velocity contours Late atrial filling. Ultrasound in Medicine and Biology 1994 20 859-69. 

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