Current Generator Model

We shall now consider the problem of impulse speed in a homogeneous fiber within the scope of this model. 

By definition at point = 0 we have = 1. It is easy to see that at this point, in addition, dijf/8 = W [the second condition from Eq. (44)]. Substituting Eq. (56) into Eq. (59) and making the Laplace transformations identical to those made in the last section, we come up with the following equation for speed 

From the definition of t, it is seen that the value is almost equal to the maximum/threshold potential ratio, i.e., to the safety factor. Normally, the maximum potential is several times higher than the threshold potential (it may be 4 to 5 times as great). Therefore, if W is not too small the exponentially small terms may be neglected to give  

the solution of Eq. (60) is = 1 which corresponds to the dimensional speed [Eq. (55)]. Thus the fact that the impulse propagation speed is independent of events sufficiently remote in time, which we mentioned in the preceding subsection when we calculated the speed, is actually due to the large enough safety factor (tj 1) or, which is the same, to the sufiiciently long duration of the inward current. To make sure that there is a second solution to Eq. (60) it is sufficient to consider the behavior of FaJ W) at W 1, where the first two terms of the expansion of F iW) have the form  

Considerations of a general nature suggest that the solution [Eq. (65)] is unstable. From the form of Eq. (65) it follows that the ratio of the stable speed to the unstable speed is close to the safety factor. It must be noted that the existence of unstable solutions has been demonstrated earlier by computer treatment of the H-H equations.It may be added that the second unstable solution appears when the second current step is taken into account. 

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Theoretically this problem has been studied with the FitzHugh-Nagumo and current generator models. It has been shown experimentally that the shorter the ring, the smaller the propagation speed of excitation, and in a ring of a small diameter repetitive excitation becomes impossible, i.e., there exists a critical ring size. 

C. N. Montreiul, S. D. WiUiams, and A. A. Adanc2yk, Modeling Current Generation Catalytic Converters Eaboratoy Experiments and Kinetic Parameter Optimisation—Steady State Kinetics, SAE 920096, Society of Automotive Engineers, Warrendale, Pa., 1992. 

The simplest and most widely used model to explain the response of organic photovoltaic devices under illumination is a metal-insulaior-metal (MIM) tunnel diode [55] with asymmetrical work-function metal electrodes (see Fig. 15-10). In forward bias, holes from the high work-function metal and electrons from the low work-function metal are injected into the organic semiconductor thin film. Because of the asymmetry of the work-functions for the two different metals, forward bias currents are orders of magnitude larger than reverse bias currents at low voltages. The expansion of the current transport model described above to a carrier generation term was not taken into account until now. 

For example, the investigations of the current-generating mechanism for the polyaniline (PANI) electrode have shown that at least within the main range of potential AEn the "capacitor" model of ion electrosorption/ desorption in well conducting emeraldine salt phase is more preferable. Nevertheless, the possibilities of redox processes at the limits and beyond this range of potentials AEn should be taken into account. At the same time, these processes can lead to the fast formation of thin insulation passive layers of new poorly conducting phases (leucoemeraldine salt, leucoemeraldine base, etc.) near the current collector (Figure 7). The formation of such phases even in small amounts rapidly inhibits and discontinues the electrochemical process. 

Studied in both an experimental and theoretical manner. The link between glycolytic oscillations and the pulsatile secretion of insulin in pancreatic p cells [53] is another topic of current concern. Models for the latter phenomenon rely on the coupling between intracellular metabolic oscillations and an ionic mechanism generating action potentials. Such coupling results in bursting oscillations of the membrane potential, which are known to accompany insulin secretion in these cells [54, 55]. 

Arbel, A., Huang, Z., Rinard, I.H., Shinnar, R., and Sapre, A.V. (1995) Dynamics and control of fluid catalytic crackers 1. Modelling of the current generation of FCC s. Industrial Engineering Chemistry Research, 34, 1228. 

This model can be easily applied to the new generation of computer systems by incorporating the requirements contained in Part 11 at the beginning the development process. For the current generation of systems, an assessment will have to performed to evaluate the level of conformity with the regulation. 

We label the factors such that all factors have the same meaning in the three simulation models. To achieve this, we introduce dummy factors for the Current and the Next Generation models that represent those factors that are removed as the supply chain is changed. Such dummy factors have zero effects but simplify the calculations and interpretations of the sequential bifurcation results. 

The aggregated effects of the Old supply chain exceed those of the Next Generation supply chain, because the former aggregates more (positive) individual effects. For example, the Current simulation model has 14 dummy factors (which have zero effects), so the first sequential bifurcation step gives a smaller main (group) effect for the Current model this effect is 7,101,983, whereas it is 15,016,102 for the Old model. 

Furthermore, the shortlists are slightly shorter for the Current and the Next Generation models. The individual factors on the three shortlists are the same, except that the Next Generation model includes on its shortlist the extra factors 91 (product demand), 44, and 46 (where the latter two factors represent transportation between operations). The most important factor (92) is the demand for one of Ericsson s fast-selling products. The other factors represent transportation and yield. 

Chemical models can be further characterized by their application. The intended utilization of a model usually directs the developmental stages of choosing the type of model and the mathematical method. We have grouped current computerized models into "major schools" according to their point of origin and their application. Since the second generation models frequently used the same basic numerical approach as their predecessors, the classification into schools also tends to separate different mathematical formulations. 

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