Time-averaged period

Odors may be detected for a very short exposure period, perhaps less than one second. It is thus necessary to determine the likely one-second peaks knowing the concentrations derived from the Gaussian equation. This is based on 10-minute average period. The equation to convert the time-averaging period is ... 

It is emphasized that ilJk)T is by definition the time average of the quantity V fc over the entire time averaging period T. 

Exposure time Average corrosion rate for period (mm/y) ... 

One of the few attempts to examine a polymerization reactor in periodic operation experimentally is the work of Spitz, Laurence and Chappelear (X6)who reported the influence of periodicity in the initiator feed to the bulk polymerization of styrene in a CSTR. To induce periodicity the initiator feed was pulsed on-and-off and the reactor output compared with steady-state operation with the same time-averaged initiator input. 

The system could be energy conservative if the atoms moved smoothly over the potential field. In that case, an atom, when traveling over one period of the potential, would experience a symmetrically distributed lateral force so that its time average and the net work done by the force would be zero. In reality, however, this is not going to happen that way. The author will demonstrate in the following how the system becomes unstable which inevitably leads to energy dissipation and friction. 

Performance of a simulated countercurrent moving bed reactor, SCMCR is experimentally investigated for oxidation of CO at low concentration in the absence of hydrogen over Pt/AljOs catelyst/adsorhent. The time-average conversion of CO obtained in the SCMBR was higher than the conversion of CO obtained from a conventional PBR for all over the tested range (period = 2-15 min). For the next step, the effects of operating variables on its performance are planed for both CO oxidation in the absence of H2 and Hz-rich gas system. 

Diffusion is transient in each of the haff-periods, but the effects produced in one half-period (e.g., an increase in concentration) are compensated by the effects produced in the foiiowing haff-period (in this exampie, a decrease in concentration). Therefore, the time-average thickness of the diffusion iayer remains unchanged and the state of the system as a whole is quasisteady. 

In most systems the substrate electrodes are larger than the powered electrodes. This asymmetric configuration results in a negative dc self-bias voltage Vdc on the powered electrode. Without that, the difference in electrode areas would result in a net electron current per RF period [134, 169]. It has been shown that the ratio of the time-averaged potential drops for the sheaths at the grounded (V g) and the powered electrode (Vsp) are inversely proportional to a power of the ratio of the areas of the two electrodes (Ag, Ap) [134, 170-172] ... 

The energy position e, of the peak and the corresponding number p of periods of time T are used by Hamers et al. [163. 332] to reconstruct the time-averaged potential profile V(x) in the sheath. An ion that arrives with energy at the electrode has a velocity that follows from mv- = , — eV x). With v — dx/dt one derives... 

The energy position Cp of peak p in the lED of an ion with mass m is seen to be dependent on the plasma potential Vpi, the RE period T, and the ion plasma frequency cd, = yje n j m(o). Equation (48) can be used to determine the (net) charge carrier density in the sheath and the time-averaged potential Vpi from measured lEDs. The mean position Xp follows from combining Eq. (47) and Eq. (48) ... 

The Bragg scattering of X-rays by a periodic lattice in contrast to a Mossbauer transition is a collective event which is short in time as compared to the typical lattice vibration frequencies. Therefore, the mean-square displacement (x ) in the Debye-Waller factor is obtained from the average over the ensemble, whereas (r4) in the Lamb-Mossbauer factor describes a time average. The results are equivalent. 

Fig. 1. Rate enhancement for S02 oxidation over a commercial promoted vanadia catalyst as a function of forcing period, time average feed composition as S02 02 ratio, and forcing manipulation (1 bar and 405°C, s = 0.5). (Figure adapted from Unni et at., 1973, with permission of the authors.)...

The calculated conversions presented in Table VIII used Eq. (57). They are quite remarkable. They reproduce experimental trends of lower conversion and higher peak bed temperature as the S02 content in the feed increases. Bunimovich et al. (1995) compared simulated and experimental conversion and peak bed temperature data for full-scale commercial plants and large-scale pilot plants using the model given in Table IX and the steady-state kinetic model [Eq. (57)]. Although the time-average plant performance was predicted closely, limiting cycle period predicted by the... 

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