Dynamical beats

Fig. 7.17 Time evolution of the nuclear forward scattering for metallic Ni foil. All measurements except for the upper curve were performed with external magnetic field B = 4 T. The solid lines show the fit. The arrows emphasize stretching of the dynamical beat structure by the applied magnetic field. The data at times below 14.6 ns had to be rescaled (from [34])...

Fig. 9.3 Mossbauer spectra (A q = 2 mm s ) in the energy domain and in the time domain. High effective thickness t ff appears in the energy domain as line broadening and in the time domain as dynamical beats which are superimposed over the quantum beats. (Taken from [7])...

In (9.2), AEy is the bandwidth of the incoming radiation and Cei is the electronic absorption cross section. The exponential decay is modulated by the square of a Bessel function of the first order (/j), giving rise to the aforementioned dynamical beats. The positions of their minima and maxima (i.e., the slope of the envelope of the time-dependent intensity) can be determined with high accuracy and thus give precise information about the effective thickness of the sample. 

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

NFS spectra of the molecular glass former ferrocene/dibutylphthalate (FC/DBP) recorded at 170 and 202 K are shown in Fig. 9.12a [31]. It is clear that the pattern of the dynamical beats changes drastically within this relatively narrow temperature range. The analysis of these and other NFS spectra between 100 and 200 K provides/factors, the temperature dependence of which is shown in Fig. 9.12b [31]. Up to about 150 K,/(T) follows the high-temperature approximation of the Debye model (straight line within the log scale in Fig. 9.12b), yielding a Debye tempera-ture 6x) = 41 K. For higher temperatures, a square-root term / v/(r, - T)/T,... 

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])... 

A series of NFS spectra of the spin-crossover complex [Fe(tpa)(NCS)2] were recorded over a wide temperature range [45]. A selection of spectra around the spin-crossover transition temperature is shown in Fig. 9.13. At 133 K, the regular quantum-beat structure reflects the quadrupole splitting from the pure high-spin (HS) phase, and the envelope of the spectrum represents the dynamical beating with a minimum around 200 ns. Below the transition, at 83 K, the QBs appear with lower frequency because of smaller AEq of the low-spin (LS) phase. Here the minima of... 

Fig. 9.13 Time evolution of the NFS intensity for various temperatures around the HS-LS transition of [Fe(tpa)(NCS)2]. The measurements were performed at 1D18, ESRF in hybrid-bunch mode. The left-hand side shows measurements in the transition region performed with decreasing temperature and the right-hand side with increasing temperature. (The spectral patterns at comparable temperatures do not match due to hysteresis in the spin-transition behavior). The points give the measured data and the curves are results from calculations performed with CONUSS [9, 10]. The dashed line drawn in the 133 K spectmm represents dynamical beating. (Taken from [41])...

Fossa, A.A.,Wisialowski,T, Magnano, A., Wolfgang, E., Winslow, R., Gorczyca, W, Crimin, K. and Raunig, D.L. (2005) Dynamic beat-to-beat modeling of... 

When experimental NFS spectra of samples with finite thickness are recorded, the time decay also shows modulations attributed to coherent multiple scattering occurring in solids (dynamical beats). These superimposed modulations have different (non-periodic) time modulation and are taken into account when the spectra are fitted. 

The NFS spectrum in energy domain exhibits a double-hump profile that results from a strong attenuation of the propagating wave through a thick absorber. At resonance, the incident wave and forward scattered wave exhibit about the same amplitudes and opposite phases leading to destructive interferences and minima in the transmitted intensity. As a result the double-hump profile around the resonance develops (Fig. l.lOe) [46]. The interferences between the corresponding propagating waves form the dynamical beat pattern in the NFS spectrum in time domain (Fig. I.9f). 

In general, the time dependence of the nuclear forward scattering comprises both quantum and dynamical beats, as depicted in Fig. l.lOf for the case of electric quadrupole interaction. If the resonances are well separated, the time development of the amplitude of nuclear forward scattering from a sample of thickness d can be expressed as [22]... 

Apart from the oscillations caused by nuclear hyperfine interactions, another oscillation due to multiple-scattering process of nuclear decay exists for the SR passing through a relative thick sample containing resonance nuclei. This oscillation is called dynamic beat (DB), it has been shown theoretically [22,23] and experimentally [24]. In the case of a single resonance (absence of nuclear hyperfine interactions), DB takes the form [22]... 

As already mentioned, electronically resonant, two-pulse impulsive Raman scattering (RISRS) has recently been perfonned on a number of dyes [124]. The main difference between resonant and nom-esonant ISRS is that the beats occur in the absorption of tlie probe rather than the spectral redistribution of the probe pulse energy [124]. These beats are out of phase with respect to the beats that occur in nonresonant ISRS (cosinelike rather tlian sinelike). RISRS has also been shown to have the phase of oscillation depend on the detuning from electronic resonance and it has been shown to be sensitive to the vibrational dynamics in both the ground and excited electronic states [122. 124]. 

Static friction decreases with an increase in load, and the static coefficient of friction is lower than the dynamic coefficient. The tendency to creep must be considered carefliUy in FEP products designed for service under continuous stresses. Creep can be minimized by suitable fillers. Fillets are also used to improve wear resistance and stiffness. Compositions such as 30% bronze-fiUed FEP, 20% graphite-filled FEP, and 10% glass-fiber-filled FEP offer high PV values ( 400(kPa-m)/s) and are suitable for beatings. 

In addition to the MD method, a wealth of Monte Carlo methods is used also at the atomistic level [6]. They use essentially the same models, force fields, for polymers. Their main advantage, however, is that by introduction of clever moves one can beat the slow physical dynamics of the systems and can run through phase space much faster than by MD. These methods are still in their infancy, but will certainly become more important. 

The events taking place in the RCs within the timescale of ps and sub-ps ranges usually involve vibrational relaxation, internal conversion, and photo-induced electron and energy transfers. It is important to note that in order to observe such ultrafast processes, ultrashort pulse laser spectroscopic techniques are often employed. In such cases, from the uncertainty principle AEAt Ti/2, one can see that a number of states can be coherently (or simultaneously) excited. In this case, the observed time-resolved spectra contain the information of the dynamics of both populations and coherences (or phases) of the system. Due to the dynamical contribution of coherences, the quantum beat is often observed in the fs time-resolved experiments. 

Recently, Scherer et al. have used the 10-fs laser pulse with A,excitation = 860 nm to study the dynamical behavior of Rb. Sphaeroides R26 at room temperatures. In this case, due to the use of the 10-fs pulse both P band and B band are coherently excited. Thus the quantum beat behaviors are much more complicated. We have used the data given in Table I and Fig. 19 to simulate the quantum beat behaviors (see also Fig. 22). Without including the electronic coherence, the agreement between experiment and theory can not be accomplished. 

The dynamic properties of the mucus fluid, serous fluid, and epithelial layers of the respiratory tract are important for the transport, absorption, and desorption of reactive gases. The cilia beat at a fairly constant frequency within the stationary serous layer and cause the outer mucus layer to move up the respiratory tract. Clearance of deposited particles and absorbed gases in the ciliated tracheobronchial tree depends partly on the movement of this mucus layer. 

The spectrum of scattered light contains dynamical information related to translational and internal motions of polymer chains. In the self-beating mode, the intensity-intensity time correlation function can be expressed (ID) as... 

Squier, J. A., Muller, M., Brakenhoff, G. J., and Wilson, K. R. 1998. Third harmonic generation microscopy. Review of dynamic imaging with THG in living organisms was first demonstrated. The point scanning source was used for THG imaging. Excitation at 1.2 (xm, 250 kHz. Interface orientation dependency in respect to the laser beam was shown in glass beats. Opt. Exp. 3 315-24. 

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