Slow-decay constant

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. 

We observe threshold effects at different temperatures both for the slow decay constants r2 and in the fraction of surviving carbynes after the thermal treatment Rq. This has a value of roughly 29% after the metastable decay at RT, it drops at 15% at lOO C remaining constant up to 150°C. We observe another drop to 8% at 200°C. This suggests the presence of two activated processes with energy barriers situated between 25 and 40meV. 

Kinetic Equations 3-143 and 3-153 are obeyed by nucleides undergoing radioactive decay, where the rate constant kj is large and kj is small. The reactant A is converted rapidly into the intermediate B, which slowly forms C. Figure 3-13b shows plots of the exponentials g-kit and and of tlieu difference. Since kj is small, tlie exponential g-kit shows a slow decay while e d shows a rapid decline. The... 

Where Ao is the activity at the sediment surface, w is the sedimentation rate (cm yr ), D is the mixing rate (cm yr ), is the decay constant for the nuclide of interest (yr ) and z is the depth in the sediment (cm). In some near-shore environments both sedimentation and bioturbation must be considered. But in most open marine environments the sedimentation rate is sufficiently slow that it can be ignored and the equation simplifies to ... 

The reason for this divergence can be understood as follows. The integral (124) represents the cumulative intra-positronium annihilation as positro-nium leaves away from the proton until the channel wavefunction decays as exp( KimR)/R. The extremely slow decay of this wavefunction near e = 0, together with the nearly constant F(e) as e ->-0, causes the S-wave divergence. 

Kinetic Equations 3-143 and 3-153 are obeyed by nucleides undergoing radioactive decay, where the rate constant k, is large and k2 is small. The reactant A is converted rapidly into the intermediate B, which slowly forms C. Figure 3-13b shows plots of the exponentials C-M and e-M and of their difference. Since k2 is small, the exponential e-k2t shows a slow decay while e klt shows a rapid decline. The difference of e-k2t-e-kl is shown by the dashed line in Figure 3-13b. The concentration of B is (Equation 3-143) equal to this difference multiplied by CAO (since kt k2). Therefore, the concentration of B rapidly rises to the value of CAO and then slowly declines. The rise in concentration C then approximately follows the simple first-order law. Conversely, when k, is small and k2 is large (k2 kj), the concentration of B is given by Equation 3-143 ... 

A preliminary value for the rate of water vapor removal in the closed tomb was calculated from these peaks by fitting the first five or six points of the slow decays to a pseudo-first-order rate law. The rate constant was approximately 5 X 10 3 min1. From these data, it is possible to estimate quantitatively the effects of human entry on the atmospheric water vapor... 

Of these absorptions the latter two produce most of the emission intensity so that we are concerned mainly with the v = 32 excited vibrational level. Detailed studies of single vibrational-rotational states show only slow variation of the relaxation constants with upper state J. Thus in this experiment it will be assumed that a single decay constant is sufficient to describe the average relaxation. This assumption has been validated by using a Nd YAG laser that had a single-frequency output, which was tunable to any of the three transitions the decay times vary by less than 10 percent among these three upper states. ... 

The Sm-Nd isotopic method depends upon the decay of " Sm, comprising —15% of natural samarium, to " Nd by a-decay. With a reasonably well-known decay constant of 6.54 X 10 yr i (Lugmair and Marti, 1978 Begemann et al., 2001), production of " Nd is slow. The ratio which is measured by isotope geologists, changed from —0.50687 at the birth... 

Rate constant for fast decay population, cm / j,W s Rate constant for slow decay population, cm /mW s UV inactivation rate coefficient, cm /mW s Disinfection rate constant, s ... 

FIGURE 7.11. EL decay time constants (fast decay-open squares, slow decay-open circles) are independent on temperature. This is in contrast with the temperature dependence of the polymer matrix polarization time (closed triangles). 

The real-time single-turnover trajectories also enabled Xie and coworkers to analyze the time-dependent activity of each enzyme molecule. They found that individual COx molecules show temporal activity fluctuations (i.e., dynamic disorder in activity), attributable to the slow conformational dynamics of the enzyme. The timescale of the activity fluctuation is the timescale of the conformational dynamics that are longer than the catalytic turnovers and can be obtained from the autocorrelation function of the waiting times (Figure 1(d)), which shows an exponential decay behavior versus the index of turnovers (m) and whose decay constant is the fluctuation timescale. This conformational dynamics-coupled enzyme catalysis is fundamental to enzyme catalysis and extremely challenging to study with traditional methods measuring the average behaviors of a population of molecules. 

One detail of the experimental procedure should be considered in more detail. Regardless of the procedure used, the catalysts always exhibit some slow decay in the activity and sometimes an extended selfpoisoning can cause changes in selectivities. We observed that the decay is small and has no influence on the selectivities when the following procedure is adopted. It is measured from low to high temperatures and after each temperature jump, the temperature is kept constant for 30 minutes. 

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