Model II

This mathematical model represents a four-state transit system in which a vehicle can be in any one of four states vehicle operating normally in the field, vehicle degraded in the field, vehicle failed in the field, and failed or degraded vehicle in the repair workshop. More specifically, in this case, the operating vehicle performance may degrade due to the failure of some of its parts. If the degradation of the vehicle is serious, then it is driven to the repair workshop otherwise it continues its operation in the field. 

The vehicle may fail either from its normal operating state or from its degraded state. The failed vehicle is taken to the repair workshop. The fully repaired vehicle is put back into its normal operation. Also, the partially repaired vehicle is put back into its degraded operating state. 

Xj = vehicle constant degradation rate from state 0 to state 1 = vehicle constant failure rate from state 1 to state 2 3 = vehicle constant failure rate from state 0 to state 2 4 = vehicle constant transition rate from state 1 to state 3 Xs = vehicle constant towing rate from state 2 to state 3 (includes the rate of taking the vehicle to the repair workshop by alternative means) 

and P3 = steady-state probabilities of the vehicle/transit system being in states 0,1,2, and 3, respectively. 

The following symbols are associated with this model  

As time t becomes large, the oil and gas industry system steady-state probability of failing safely using Equation 11.14 is 

Equation 11.17 gives the oil and gas industry system reliability at time t. In contrast Equations 11.18 and 11.19 give the probability of the oil and gas industry system failing unsafely and safely at time t, respectively. 

By integrating Equation 11.17 over the time interval [0,°°], we get the following equation for the oil and gas industry system mean time to failure [7,8]  

---

Model II Regenerator at higher elevation and lower pressure than reactor. Slide valves control catalyst circulation. 

In earlier Model II and Model III FCC units, spent catalyst was transported into the regenerator using 50% to 100% of combu.stion air. This spent cat riser was designed for a minimum air velocity of 30 ft/sec (9.1 m/sec). 

Weiss, J. M., Morgan, P. H., Lutz, M. W., and Kenakin, T. P. (1996b). The cubic ternary complex receptor-occupancy model. II. Understanding apparent affinity. J. Theroet. Biol. 178 169-182. 

Fig. 33. Unzippering of a staggered helical state according to model II,48)...

Figure 34 shows two equilibrium transition curves, one of them being computed with the help of the AON model (I), the other by means of the SZ model (II) for arbitrarily chosen parameters. 

At higher temperatures (T > Tm), model II predicts larger values of 0, because this increases the number of possibilities of forming a helix, in contrast to the AON model (I). On the other hand, at lower temperatures, model I gives more possibilities of the realization of the coiled state and thus the transition curve near = 1 is flat in comparison with the AON case. 

Model (II) Evaluate properties by Eqn. (24) after eliminating the first term, then... 

In this case, of course. A is not consistent with the stationary condition of Eqn. (1). Model (II) eliminates an apparent unlinked term, so is not completely size-extensive. On the other hand, the models (IT) and (III) do not contain any unlinked terms and are therefore exactly extensive. However, unlike EOM-CCSD itself, none of these models is exact for two-electron systems. 

Table 2 shows transition moments calculated by the different EOM-CCSD models. As has been discussed above, the right-hand transition moment 9 is size intensive but the left-hand transition moment 9 in model I and model II is not size intensive. Model II is much improved as far as size intensivity is concerned because of the elimination of the apparent unlinked terms. The apparent unlinked terms are a product of the size-intensive quantity ro and size-extensive quantities and therefore are size extensive. The difference between the values of model I and model II, as summarized in the fifth column, reveals strict size extensivity. Complete elimination of unlinked diagrams by using A amplitudes brings strict size intensivity for the transition moment and therefore the transition probabilities calculated by model III are strictly size intensive. 

S. Wold, Non-linear partial least squares modelling. II. Spline inner relation. Chemom. Intell. Lab. Syst., 14(1992)71-84. 

We present chemical evolution models for NGC 6822 computed with five fixed parameters, all constrained by observations, and only a free parameter, related with galactic winds. The fixed parameters are i) the infall history that has produced NGC 6822 is derived from its rotation curve and a cosmological model ii) the star formation history of the whole galaxy based on star formation histories for 8 zones inferred from H-R diagrams iii) the IMF, the stellar yields, and the percentage of Type la SNe progenitors are the same than those that reproduce the chemical history of the Solar Vicinity and the Galactic disk. 

The models (ii), (iii) and (iv) of course also involve a normal solvation by the solvent of the ions resulting from the processes (ii)-(iv) which have a much lower charge density. 

The model (ii) implies that in PhN02 solutions the species Pn+ and PnSv+ coexist and that both are propagators which are normally in equilibrium according to equation (9). The... 

Model 467), x-ray powder diffracton (Philips XRG-3000, x-ray diffractometer, CuK radiation Ni filter), and scanning electron microscopy, SEM (ISI scanning electron microscope, Model II). Infrared spectra and powder diffraction data were in agreement with the published values for apatite (19,20). Chemical analysis of the solid gave a molar ratio of Ca/P = 1.64 +0.01 the SSA was 21.5 m g"1. 

Toggweiler, J.R., K. Dixon, and K. Bryan. 1989b. Simulations of radiocarbon in a course resolution world ocean model II Distribution of bomb-produced C. Journal of Geophysical Research 94 8243-8264. 

Model II C B X Internal-Conversion Process in the Benzene Cation... 

Parameters of Model II, Which Represents a Three-State Eive-Mode Model of the Ultrafast C — B — X Internal-Conversion Process in the Benzene Cation [179, 180] ... 

Figure 2. Diabatic (left) and adiabatic (right) population probabiUties of the C (fuU line), B (dotted line), and X (dashed line) electronic states as obtained for Model II, which represents a three-state five-mode model of the benzene cation. Shown are (A) exact quantum calculations of Ref. 180, as well as mean-field-trajectory results [(B), (E)] and surface-hopping results [(C),(D),(F),(G)]. The latter are obtained either directly from the electronic coefficients [(C),(F)] or from binned coefficients [(D),(G)].

Let us next turn to Model II, representing the C —> B —> X internal-conversion process in the benzene cation. Figure 2 demonstrates that this (compared to the electronic two-state model, Model I) more complicated process is difficult to describe with a MFT ansatz. Although the method is seen to catch the initial fast C —> B decay quite accurately and can also qualitatively reproduce the oscillations of the diabatic populations of the C- and B-state, it essentially fails to reproduce the subsequent internal conversion to the electronic X-state. Jn particular, the MFT method predicts a too-slow population transfer from the C- and B-state to the electronic ground state. 

---