Trapped motion time distribution

Figure 5.1.7 shows the propagator of the motion measured for a clean and a biofilm impacted capillary [14,15] and the residence time distributions calculated for each from these velocity distributions. The clean capillary gives an experimental propagator equal to the theoretical velocity distribution convolved with a Gaussian diffusion curve [14], as shown in Figure 5.1.2. For the flow around the biofilm structure note the appearance of a high velocity tail indicating higher probability of large displacements relative to the clean capillary. The slow flow peak near zero displacement results from the protons trapped within the EPS gel matrix where the...

The effect of random noise on nonstationary motions has been recently studied to examine the stability of the long-time tails in Hamiltonian dynamics [15], where the survival time distribution for a particle trapped in a potential well is studied under random perturbations. The results were very clear the Weibull distribution describes the intermediate long-time regime in the same manner shown in the case of cluster formation, but the contribution of the log-Weibull distribution completely disappears in the intrinsic long-time regime and the Gumbel distribution takes the phase of it. The details will be reported in a... 

The main ingredients of the model are as follows. Inside a dendrite with a uniform surface spine density, particles perform Brownian motion with a constant drift V along the dendrite and a diffusion coefficient D. This describes, e.g., the motion of an overdamped ion under the action of an electric field E such that v = jxE, where /u. is the ion mobility. After a random time distributed according to the PDF the particle hits the neck of a spine on the surface of the dendrite. It is then trapped inside the spine for a random time The PDF for the sojourn time... 

Fig. 9. Incidence energy dependence of the vibrational state population distribution resulting when NO(u = 12) is scattered from LiF(OOl) at a surface temperature of (a) 480 K, and (b) 290 K. Relaxation of large amplitude vibrational motion to phonons is weak compared to what is possible on metals. Increased relaxation at the lowest incidence energies and surface temperatures are indicators of a trapping/desorption mechanism for vibrational energy transfer. Angular and rotational population distributions support this conclusion. Estimations of the residence times suggest that coupling to phonons is significant when residence times are only as long as ps. (See Ref. 58.)...

The main experimental elfects are accounted for with this model. Some approximations have been made a higher-level calculation is needed which takes into account the fact that the charge distribution of the trapped electron may extend outside the cavity into the liquid. A significant unknown is the value of the quasi-free mobility in low mobility liquids. In principle, Hall mobility measurements (see Sec. 6.3) could provide an answer but so far have not. Berlin et al. [144] estimated a value of = 27 cm /Vs for hexane. Recently, terahertz (THz) time-domain spectroscopy has been utilized which is sensitive to the transport of quasi-free electrons [161]. For hexane, this technique gave a value of qf = 470 cm /Vs. Mozumder [162] introduced the modification that motion of the electron in the quasi-free state may be in part ballistic that is, there is very little scattering of the electron while in the quasi-free state. 

The problem of vacancy-mediated tracer diffusion in two dimensions has been investigated for a long time [40-44] and several different methods (simulation, analytical models, enumeration of trajectories, etc.) can be used to address it. The mathematics of this type of diffusion was solved first for the simplest case [41], when the diffusion of the vacancy is unbiased (all diffusion barriers are equal the tracer atom is identical to the other atoms), the lattice is two-dimensional and infinite. There is a single vacancy present that makes a nearest-neighbor move in a random direction at regular time intervals and has an infinite lifetime, as there are no traps. The solution is constructed by separating the motion of the tracer and that of the vacancy. The correlation between the moves of the tracer atom is calculated from the probability that the vacancy returns to the tracer from a direction, which is equal, perpendicular or opposite to its previous departure. The probability density distribution of the tracer atom spreads with... 

The hydrogen diffusion coefficient is not constant, but decreases with time (Street et al. 1987b). The data in Fig. 2.22 show a power law decrease in p-type a-Si H of the form r , with a 0.2 at the measurement temperature of 2(X) C. The time dependence is associated with a distribution of traps originating from the disorder. A similar effect is found in the trap-limited motion of electrons and holes and is analyzed in Section 3.2.1. The time dependence of is reflected in the kinetics of structural relaxation discussed in Section 6.3.1. 

There are several techniques for measuring the mobility in a-Si H, most notably the time-of-flight method. All the techniques measure the average motion of the carriers over a time longer than that taken to trap a carrier in the band tail states, so that the drift mobility is always measured, rather than the free carrier mobility. The drift mobility depends on the distribution of traps and the free mobility can only be extracted if the density of states distribution is known. Chapter 3 describes how the time-of-flight experiment is used to determine the shape of the band tail through the analysis of the dispersive transport process. 

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