Doppler speed

For very large Doppler speeds, there is no resonance absorption at all (note that the exponential part of the integrand is 1 at the limit l l — oo), and therefore, the baseline b can be expressed as... 

As it has turned out, the peak shape - in this thin-source, thin-absorber approximation - is indeed Lorentzian, and the FWHM of the peak (Wo), apart from the conversion factor between Doppler speed and energy, is twice the natural line width F. 

E energy of the level, Tt/2- half-life, a internal conversion coefficient, a natural abundance, / nuclear spin, Q nuclear quadrupole moment, b barn, /i nuclear magnetic moment, fin nuclear magneton, Co - nuclear absorption cross section. Wo- natural line width expressed as Doppler-speed interval. Absence of sign in the Q and n values means that the sign is undetermined (Cohen and Taylor 1987 Raghavan 1989 Pyykko 2001, 2008 NuDat 2009). 

Durand, M. (1984), Use of Optical Fibers for Velocity Measurement by Laser Doppler Interferometry with a Fabry-Perot Interferometer. In High Speed Photography and Photonics, Proc. SPIE, 491 (edited by M. Andre and M. Hugenschmidt), pp. 650-656. 

There are many nonintrusive experimental tools available that can help scientists to develop a good picture of fluid dynamics and transport in chemical reactors. Laser Doppler velocimetry (LDV), particle image velocimetry (PIV) and sonar Doppler for velocity measurement, planar laser induced fluorescence (PLIF) for mixing studies, and high-speed cameras and tomography are very useful for multiphase studies. These experimental methods combined with computational fluid dynamics (CFDs) provide very good tools to understand what is happening in chemical reactors. 

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... 

The linear speed of the limb of Jupiter (from the text) is 43000 kmh-1 and so the Doppler shift is given by ... 

Doppler spectroscopy spect A technique for measuring the speed with which an object is moving toward or away from the observer by measuring the amount that light from the object is shifted to a higher or lower frequency by the Doppler effect. dap-l3r spek tras-ko-pe)... 

In an earlier phase of this work [9] the intensities of axial and circumferential components of velocity fluctuation were measured in the TC annulus, using Laser Doppler Velocimetry (LDV), for a wide range of cylinder rotation speeds. On average, the intensities of axial velocity fluctuations were found to be within 25% of the intensities of circumferential velocity fluctuations [9]. As in Ronney et al. [5], turbulence intensities were found to be nearly homogeneous along the axial direction and over most of the annulus width, and to be linearly proportional... 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

It is of interest to compare the half-widths at half-intensity of the spectral functions of the three systems shown in Fig. 3.2. These amount to roughly 140, 80 and 50 cm-1 for He-Ar, Ne-Ar and Ar-Kr, respectively, which are enormous widths if compared to the widths of common Doppler profiles, etc. The observed widths reflect the short lifetimes of collisional complexes. From the theory of Fourier transforms we know that the product of lifetime, At, and bandwidth, A/, is of the order of unity, Eq. 1.5. The duration of the fly-by interaction is given roughly by the range of the induced dipole function, Eq. 4.30 (1/a = 0.73 a.u. for He-Ar), divided by the mean relative speed, Eq. 2.12. We obtain readily ... 

Figure 1.1a shows the Gaussian function. The Lorentzian shape is similar to the Gaussian, but falls off more slowly. The Doppler shift of radiation from an emitting molecule is proportional to its velocity component in the direction of observation. The one-dimensional distribution of speeds in a gas is a Gaussian function. (See any physical-chemistry text.) Hence when Doppler broadening is dominant, we get a Gaussian-shaped line. 

We might imagine that we could prepare a system that physically moves the source of the radiation toward the absorbing nuclei with sufficient speed that the Doppler shift compensates for the energy difference. Restricting the motion... 

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