Beat patterns

Nonciliated cells separate fields of ciliated epithelial cells from each other. Synchronized ciliary movement, with a beat frequency in human proximal airways under normal conditions of 8-15 EIz, propels mucus along the mucociliary escalator at a rate of up to 25 mm/min. Beat frequencies appear to slow to roughly 7 Hz in more distal airways. Cilia move in the same direction and in phase within each field but cilia in adjacent fields move in slightly different directions and are phase shifted. These beat patterns result in metachronal waves that steadily move mucus at higher velocities ( -12-18 mm/min) than would be achievable by summing the motion of individual cilia. 

Free induction decay A decay time-domain beat pattern obtained when the nuclear spin system is subjected to a radiofrequency pulse and then allowed to precess in the absence of Rf fields. 

Fluctuations of the EFG cause a dephasing of the originally coherent waves which affects the quantum-beat pattern (as described for Mb02 in Sect. 9.4.3) and... 

Variations of the msd of the resonant nuclei affect the dynamical beat pattern... 

Fig. 9.12 (a) NFS spectra of FC/DBP with quantum beat and dynamical beat pattern, (b) Temperature-dependent /-factor. The solid line is a fit using the Debye model with 0D = 41 K below 150 K. Above, a square-root term / - V(Tc - T)/Tc was added to account for the drastic decrease of /. At Tc = 202 K the glass-to-liquid transition occurs. (Taken Ifom [31])... 

Fig. 9.16 Time-dependent NFS of [Fe(tpa)(NCS)2] recorded at 108 K. The two curves represent comparison of a coherent vs incoherent superposition of the scattering from 50 % LS and 50 % HS iron(II) characterized by their corresponding quantum beat pattern. The effective thickness of the sample was =18. (Taken from [42])...

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

Chilvers, M. A. and O Callaghan, C., Analysis of ciliary beat pattern and beat frequency using digital high speed imaging comparison with the photomultiplier and photodiode methods, Thorax, 55, 314-317, 2000. 

Geller, A. and Muller, D. G., Analysis of the flagellar beat pattern of male Ectocarpus siliculosus gametes (Phaeophyta) in relation to chemotactic stimulation by female cells, J. Exp. Biol., 92,53, 1981. 

Figure 4.2b is a presentation of the FID of the decoupled 13C NMR spectrum of cholesterol. Figure 4.2c is an expanded, small section of the FID from Figure 4.2b. The complex FID is the result of a number of overlapping sine-waves and interfering (beat) patterns. A series of repetitive pulses, signal acquisitions, and relaxation delays builds the signal. Fourier transform by the computer converts the accumulated FID (a time domain spectrum) to the decoupled, frequency-domain spectrum of cholesterol (at 150.9 MHz in CDC13). See Figure 4.1b.

Figure 12.1. Beat pattern resulting from interference between two similar frequencies.

Since the pulse time is so short (see Sec. 3.6.2.2.3) one can coherently excite many vibrational modes at a time and monitor relaxation processes in real time. The first reported femtosecond time-resolved CARS experiments (Leonhardt et al., 1987 Zinth et al., 1988) showed beautiful beating patterns and fast decays of the coherent signal for several molecular liquids. The existence of an intermolecular coherence transfer effect was suggested from the analysis of the beating patterns (Rosker et al., 1986). Subsequent studies by Okamoto and Yoshihara (1990) include the vibrational dephasing of the 992 cm benzene mode. A fast dephasing process was found that is possibly related to... 

Quantum beats have been observed in a variety of experiments, particularly in beam—foil measurements. Teubner et al. (1981) were the first to observe quantum beats in electron—photon coincidence measurements, using sodium as a target. The zero-field quantum beats observed by them are due to the hyperfine structure associated with the 3 Pii2 excited state (see fig. 2.20). The coincidence decay curve showed a beat pattern... 

Figure 6. ISRS data from a-perylene crystal at two temperatures, recorded with transient grating experimental arrangement. Oscillations in each sweep due to 80- and 104-cm optic phonons. Data contain sum and difference frequencies that produce beating pattern.

This expression describes the important case of an inhomogeneously broadened band with homogeneously broadened components. If the number of components is small or they are regularly spaced in frequency, a beat pattern for C(t) is obtained. Exjjerimentally, a time-resolved CARS experiment (which gives C(t) for t > tp) displays directly this oscillatory behavior, as was observed in an early study of (Fig. 5). The corresponding Raman... 

Next, we consider the case of two narrow lines at wave numbers i>i and i>2-The interferogram obtained in this case (see Fig. 2) is the superposition (sum) of the two interferograms of the lines. It exhibits the typical beat pattern usually encountered in connection with acoustical or electrotechnical problems. Mathematically, the interferogram is... 

The second cos factor describes the oscillation at the average wave number r=—(j>i+i>2) and the first cos factor is responsible for the beat pattern with... 

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