Time required

Execution times for the higher level subroutines FLASH and ELIPS will be highly dependent on the problems involved. The times required per iteration can be estimated from times for lower level subroutines and the descriptions given for FLASH and ELIPS. Computation times for two specific cases calculated with FLASH and one case claculated with ELIPS are included in Table J-1 to show approximate magnitudes required. 

TABLE J-1 Computer Storage and Execution Time Requirements for Thermodynamic Subroutines ... 

Key = 1 represents an initial calculation for a new system Key 2-5 are subsequent calculations not differing significantly in time requirements Key = 6,7 require temperature derivatives of virial coefficients. 

For batch reactors, account has to be taken of the time required to achieve a given conversion. Batch cycle time is addressed later. 

Increasing the pressure of irreversible vapor-phase reactions increases the rate of reaction and hence decreases reactor volume both by decreasing the residence time required for a given reactor conversion and increasing the vapor density. In general, pressure has little effect on the rate of liquid-phase reactions. 

Decreasing the size of equipment for those steps which are not limiting to increase the time required for those steps which are not limiting and hence reduce the dead time for the nonlimiting steps. 

Franck-Condon principle According to this principle the time required for an electronic transition in a molecule is very much less than the period of vibration of the constituent nuclei of the molecule. Consequently, it may be assumed that during the electronic transition the nuclei do not change their positions or momenta. This principle is of great importance in discussing the energy changes and spectra of molecules. 

Kinematic viscosity NFT 60-100 ISO 3104 and 3105 ASTM D 445 and D 446 Measurement of time required to flow between 2 marks in a tube... 

The point at which the cumulative cash flow turns positive indicates the payout time (or payback time). This is the length of time required to receive accumulated net revenues equal to the investment. This indicator says nothing about the cash flow after the payback time and does not consider the total profitability of the investment opportunity. 

In maintenance practice, we base our decisions on NDT that is performed during shutdowns. A significant amount of money could be saved if we would have NDT methods that minimise the time required for that shutdown, or, a step further, avoid it by performing inspections onstream. 

However, it is expected that this situation will change, since a number of novel "non-invasive NDT techniques are now becoming available. With some of these techniques, the time required for a shutdown can be reduced. Other techniques make it possible to perform inspections whilst the installation is in full service. It is obvious that the availability of such techniques could support the knowledge already available on operational parameters and degradation mechanisms, in order to base shutdown intervals on actual plant condition. 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

The bromate-ferroin reaction has a quadratic autocatalytic sequence, but in this case the induction period is detennined primarily by the time required for the concentration of the hiliibitor bromide ion to fall to a critical low value tlirough the reactions... 

One of the major limiting factors for the time resolution of flow-hibe experiments is the time required for mixing reactants and—to a lesser extent—the resolution of distance. With typical fast flow rates of more than 25 ms [42, 43] the time resolution lies between milliseconds and microseconds. 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

A. Since tire applied field is red detuned, all A have negative values. Now in order for tire cooling mechanism to be effective tire optical pumping time tp should be comparable to tire time required for tire atom with velocity v to travel from tire bottom to tire top of a potential hill,... 

The examples discussed in tliis chapter show a strong synergy between fundamental physical chemistry and device processing metliods. This is expected only to become richer as shrinking dimensions place ever more stringent demands on process reliability. Selecting key aspects of processes for fundamental study in simpler environments will not only enable finer control over processes, but also enable more sophisticated simulations tliat will reduce tire cost and time required for process optimization. 

The time that the trajectory must spend at / max to ensure that the equilibrium distribution is sampled is at least Tmin, the time required to surmount the largest barrier separating the global energy minimum from other thermodynamically important states. Using Eq. (39) we find... 

Nevertheless, the technique suffers from a severe time scale problem -the trajectories are computed for (at most) a few nanoseconds. This is far too short compared to times required for many processes in biophysics. For example, the ii to T conformational transition in hemoglobin lasts tens of microseconds [1], and the typical time for ion migration through the gramicidin channel is hundreds of nanoseconds. This limits (of course) our ability to make a meaningful comparison to experiments, using MD. 

One of the most expensive parts of a MD or MC simulations is the computation of long range interactions. Since the CPU time required for the... 

In Table 1 the CPU time required by the two methods (LFV and SISM) for 1000 MD integration steps computed on an HP 735 workstation are compared for the same model system, a box of 50 water molecules, respectively. The computation cost per integration step is approximately the same for both methods so that th< syieed up of the SISM over the LFV algorithm is deter-... 

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