Characteristic decay time

For the special case of a uniform wind, where and are constants, an isolated source located at (0,0,H) continuously emits a mass per unit time of species i at a constant rate Q, and the removal rate from internal sinks is governed by linear processes, C, = -C /tj. with t. being a characteristic decay time. 

This expression describes the decay of the stress with time when a rapid strain is applied to a Maxwell model. The characteristic decay time im is given by the ratio of the viscosity to the shear modulus ... 

The fluorescence characteristics (decay time and/or fluorescence quantum yield) of M are affected by the presence of Q as a result of competition between the intrinsic de-excitation and these intermolecular processes ... 

Different properties have different characteristic decay times, and these decay times can be quite helpful in deciding how long to run a particular MD simulation. Since the point of a simulation is usually to obtain a statistically meaningful sample, one does not want to compute an average over a time shorter than several multiples of the characteristic decay time. 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

Sensors based on fluorescence are quite robust because the wavelength and the orthogonal detection geometry of the incident and emitted radiation results in a high signal-to-noise ratio. The sensors described here utilize quenching of fluorescence. Thus, the analyte is the quencher Q and the indicator is a fluorescing dye F, which when excited to F, emits fluorescence with a characteristic decay time. 

Before results from MD simulation were available, it was assumed that ML (k, t) would both be predominantly diffusive and that the characteristic decay time tl for 4>ml (k, t) would be related to the Debye relaxation time rD characterizing the Lorentzian width of e(m) by [1,62]... 

T2 relaxation of oil-extended EPDM revealed two distinct relaxation components whose characteristic decay times are comparable with those of initial rubber and paraffinic oil (Figure 10.7) [74]. This suggests that the components with a short and long decay time mainly originate from the relaxation of rubbery chains and oil molecules, respectively. 

T2 experiments are used to determine the concentration of (inter)phases/components in polymer materials if polymer chains in these (inter)phases/components reveal a significant difference in molecular mobility [17, 34]. In such cases, the T2 relaxation function is the weighted sum of the T2 decays of different components/phases. The relative fraction of these components is proportional to the concentration of hydrogen in these (inter)phases/ components (see Sections 10.4 and 10.7). The characteristic decay time, T2, is related to molecular mobility in different phases. 

Lin et al. [17] studied the dynamics of copolymers adsorbed on an air-water interface. These measurements complemented the static measurements described above and in Fig. 4. The extent of the polymer films perpendicular to the surface is small compared to penetration distance and wavelength so that EWDLS is most sensitive to variation of composition in the plane of the interface. Figure 7 shows the measured normalized autocorrelation I (/) for different surface pressures. Frames a-d were taken during the first compression of the monolayer, and frames e-h were taken during the second compression. The difference between the two sets of measurements is an indication of structural changes induced by compression cycling. The frames e-g can be compared to the data in Fig. 4. The solid lines in the three frames are fits to a sum of two exponential functions, each with a characteristic decay time. The fast decay constant has a characteristic associated with diffusive motion of the disks. The slow decay constant ( several seconds) was ascribed to the dynamics of the associations of disks. 

FIG. 1 Normalized intensity-intensity time correlation function of poly (urethane-urea) microcapsule suspension at c = 5 x 10-5 g/cm measured at 60 and at 30 C. r(l/l ) is the characteristic decay time. (Reprinted with permission from the paper entitled An experimental investigation on the structure of microcapsules, by T. Dobashi. F. Yeh, Q. Ying, K. Ichikawa, and B. Chu. Langmuir // 4278. Copyright 1995 American Chemical Society.)... 

In order to avoid bias due to number fluctuations, it is necessary that there is at least 1000 particles present in the measuring volume and, for a typical value of the scattering volume of 10 cm, effects of number fluctuations are to be expected for particle diameters greater than around 0.5 pm. Number fluctuations lead to an additional time decaying term in the autocorrelation function. Since the characteristic decay time of this additional term is usually much slower than the decay attributed to Brownian motion, the average particle size, which is proportional to the average decay time, will be overestimated if the effect of number fluctuations is neglected [277]. 

A whose k() is 10 s this represents a characteristic decay time (r) of over 10 s, 18 orders of magnitude less than the values implied by the experimental data [105],... 

And fourth, the autocorrelation time, t, in Eq. 8, must be determined to solve the equations given above. For each inverse temperature, /9,-, r,- is the characteristic decay time of the energy autocorrelation function... 

The limit in front of the ratio means that the time t has to be much longer than the longest relaxation time of the chain. The resulting diffusion coefficients obtained by Monte Carlo simulation of the Evans-Edwards model of entangled polymers are presented in Fig. 9.33(a). The diffusion coefficient decreases with the number of monomers in the chain. Another quantity that can be extracted from the Monte Carlo simulations of the Evans-Edwards model is the relaxation time of the chain. It can be defined as the characteristic decay time of the time correlation function of the end-to-end vector R[t)R 0)) exp( t/Trep). Figure 9.33(b) presents the results of such simulations. 

This expression states that the maximum correlation between the velocities at two times occurs when those times are equal, and is equal to cr2. As the time separation between u(t) and w(x) increases, the correlation decays exponentially with a characteristic decay time of 1 jb. Stationarity implies that the statistical properties of u at two different times t and t depend only on t — x and not on t and t individually. 

The sampling efficiency is also related to the autocorrelation or relaxation time of the system, t, For each temperature, r is the characteristic decay time of the energy autocorrelation function for the system once equilibrium has been reached. The autocorrelation function, a t), can be estimated from Eq. (4.3) as the annealing sweep progresses ... 

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