Time constant exponential decay processes

The effect of slippage at a substrate-film interface can also be described in terms of sbp time [39]. To understand the physical meaning of the slip time, one can consider an adsorbate film on a substrate, moving at constant velocity. If the substrate stops, the velocity and momentum of the film decay exponentially, and the time constant of this process is the slip time. If this process is very rapid, i.e., we have a rigidly adsorbed film, the time constant will be close to zero, and there will be no noticeable shp. The shp time is related to the interfacial friction coefficient through the equation [39] ... 

A solution NMR peak commonly has a Lorentzian shape. A Lorentzian line in the frequency domain results from a first-order exponential decay process with a time constant, Tz It is specified by the line-shape function, f v), where... 

The electron-spin time-correlation functions of Eq. (56) were evaluated numerically by constructing an ensemble of trajectories containing the time dependence of the spin operators and spatial functions, in a manner independent of the validity of the Redfield limit for the rotational modulation of the static ZFS. Before inserting thus obtained electron-spin time-correlation functions into an equation closely related to Eq. (38), Abernathy and Sharp also discussed the effect of distortional/vibrational processes on the electron spin relaxation. They suggested that the electron spin relaxation could be described in terms of simple exponential decay rate constant Ts, expressed as a sum of a rotational and a distortional contribution ... 

Figure 15. Amplitude -time plots obtained from AFM measurements for the decay of sinusoidal 1-D gratings with the periods indieated on the surface of a silicate glass(Corning 1737) annealed in air at827C.[42], The exponential decay constant scales approximately as q as expected for a viscous flow controlled process[l].

An attempt is often made to relate T] and T2 to the molecular dynamics of a system. For this purpose a relationship is sought between T1 or T2 and the correlation time tc of the nuclei under investigation. The correlation time is the time constant for exponential decay of the fluctuations in the medium that are responsible for relaxation of the magnetism of the nuclei. In general, l/xc can be thought of as a rate constant made up of the sum of all the rate constants for various independent processes that lead to relaxation. One of the most important of these (1 /t2) is for molecular tumbling. 

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