Time phenomena

As discussed above the errors in the trajectory are correlated with the missing rapid motions. In contrast to the friction approach of estimating the variance, which may affect long time phenomena, we identify our errors as the missing ( filtered ) high frequency modes. We therefore attempt to account approximately for the fast motions by choosing the trajectory variance accordingly. 

These "time phenomena, contrary to everyday consciousness, seemed totally convincing—not hallucinations but another part of reality. Mayhew is definite on this ... 

At the same time, phenomena of contrary natures are well known—for example, an increase in the concentration of high active catalyst centers during the reaction due to transforming the state of the catalyst precursor under the action of the reaction medium (reduction of inactive ionic species of the active metal to the active metal state, etc.). 

To understand why this is so, let us consider briefly systems containing a large number of atoms, typically a number greater than the Avogadro number (ca. 6.02 x 10 ). With such a large number, we may be reasonably sure that the probability of events occurring will be described by Eq. (1). Having said this, however, it is necessary to point out that Eq. (1) applies only to random occurrences, which is to say that all the events under consideration should be random ones and all the entities (particles) involved should exhibit only random behavior. Whether any of the phenomena of nature are strictly random is still a matter of some dispute at the present time. Phenomena may appear to be random only because... 

For real fluids the hard-sphere model gives a reasonable approximation to long-time phenomena, such as particle diffusion, but it is not realistic for short-time phenomena, such as collisional excitation of the internal motions of molecules, because of the impulsive nature of hard-sphere impacts. In the next two sections the more realistic case will be studied in which the test particle-bath particle interaction occurs through a continuous central potential. 

While the distinction between discrete time and continuous time is mathematically clear-cut, we may in applied work use discrete time approximation to a continuous time phenomena and vice versa. However, discrete time models are usually easier for numerical analysis, whereas simple analytical solutions are more likely to emerge in continuous time. 

The sensitivity of these results to the choice of boundary conditions is examined in Figure 4.3.3. We note that the use of reaction field boundary conditions as implemented here is strictly valid only for equilibrium simulations, since the dynamic response of the dielectric continuum at R > R, is not taken into account. One could argue that for the short-time phenomena considered here, should have been taken smaller than the static dielectric constant of the system. Figure 4.3.3 shows that on the relevant time scale our dynamical results do not change if we take e = 1 instead of e = e = 17. (The absolute solvation energy does depend on e, and replacing e = 17 by e = 1 changes it by = 5%.)... 

This incubation time phenomena, which has not been reported for other nitriding processes, such as plasma nitiiding, may be related to the nature of the fluidized bed process, where the disruption of the native oxide film on the specimen surface, which is required to effect the nitriding reactions, has to rely on thermal dissociation. The higher the temperature, the faster is the dissociation of the oxide film and thus the shorter the incubation time. 

For a similar treatment duration, the Plasma process is reported by Tsujiwaka on 2005 which is produce about 18 pm thick layer which is much higher compared to that of the present conventional nitriding treatment in fluidized bed furnace. In plasma ptrocess the native oxide layer is removed mostly by bombardment of the plasma gas which is completely absent in conventional fluidized process. This is one of the reasons why convention fluidized bed treatment produced small layer thickness compared to the corresponding plasma nitriding. Previous investigation revealed that nitriding at 450°C became effective after treatment for 6 h where a continuous nitrided layer was produced (Sun, 2006). This is due to the fact that the incubation time phenomena which may be related to the nature of... 

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