Crossover behavior temperature effects

Other crossover behavior can arise when one moves to a regime where the continuum picture is not valid. For examples, Giesen-Seibert et al. (1995) show that for PD, at very early times w behaves like t rather than t " because the dynamics are dominated by random walks of kinks. In their simulations the effective exponent decreases smoothly with increasing temperature, with no evident crossover in any of the fixed-Tlog-logplots of w vs. t. They also show how to take into account fast events, viz. rapid, inconsequential... 

Further, in continuation of the crossover studies, we investigated the comparative effect of hard and attractive slit pore surfaces on crossover behavior and also compared the effect of pore shape on this behavior. A typical comparison of crossover behavior is shown in Figure 8.14 with a typical model fluid. In Figure 8.14, the shift in critical temperature, (r b cpV cb is plotted as a function of effective pore width, or (i.e., H-t or D-t) on a log-log scale. This investigation indicates that, for a given model fluid confined in a hard slit-pore, the crossover behavior is significantly reduced... 

One of the (apparently) most complicated features of the kinetic behavior of glasses arises when the material is allowed to recover isothermally for a period of time t insufficient to reach equilibrium, and then heated to a higher temperature and allowed to recover. As shown in Figure 31, the volume departure from equilibrium can cross over the actual equilibrium and exhibits a maximum which depends upon the actual thermal history applied to the sample. These have been referred to as crossover or memory effects. As will be seen, they arise from the fact that the response function (e.g. for volume recovery) exhibits behavior equivalent to a multiplicity of retardation mechanisms. 

The observation of crossover has later been substantiated by several other studies. In particular, Jacob et al. [165] performed light scattering measurements on the system 3-MP + water + NaBr. The data indicate comparatively sharp crossover in the range 10-4 salt concentration. It is intriguing to characterize this crossover by a suitably defined crossover temperature Tx, defined here by the point of inflection in the T-dependence of the effective exponent yeff. Figure 8 shows fx as a function of the amount of added NaBr. Eventually, plain mean-field behavior is obtained in a solution containing about 16.8 mass% NaBr. 

The main effect of both types of electron localization, of course, is a crossover from metallic to nonmetalhc behavior (a M-NM transition). Nevertheless, it would be very beneficial to have a method of experimentally distinguishing between the effects of electron-electron Coulomb repulsion and disorder. In cases where only one or the other type of localization is present this task is relatively simpler. The Anderson transition, for example, is predicted to be continuous. That is, the zero-temperature electrical conductivity should drop to zero continuously as the impurity concentration is increased. By contrast, Mott predicted that electron-correlation effects lead to a first order, or discontinuous transition. The conductivity should show a discontinuous drop to zero with increasing impurity concentration. Unfortunately, experimental verification of a true first order Mott transition remains elusive. 

Above the crossover pressure, the opposite eifect occurs. This behavior can be understood by considering two opposing effects of temperature on solubility (Chimowitz 2005). The vapor pressure of the solid solute always increases with temperature, while the density (or solvent power) of supercritical carbon dioxide decreases. Below the crossover pressure where the compressibility is larger, the density effect dominates, and the solubility decreases with increasing temperature. At pressures above the crossover pressure, the vapor-pressure effect dominates hence solubility increases with temperature. 

As evident from the i-E response, the 1.0 M solution of methanol delivered better performance at low current densities compared with all concentrations of TMM studied at 90 C. However, at very high current densities (>750 mA/cm ) the 0.5 and 1.0 M solutions of TMM shows improved performance with respect to methanol. This type of behavior was observed at a number of different ceil operating temperatures. When the effect of TMM concentration upon cell performance was investigated, it was observed that at low current densities the solutions of low fuel concentration showed less polarization, whereas at higher current densities solutions of higher concentrations showed better performance. This trend in performance is due to fuel crossover effects which dominate at low... 

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