Continuous slowing-down model

It is important to note that the concept of a slowing-down density is not limited to the continuous slowing-down model. This function has a much wider application, and it will be used later in connection with the analysis of the slowing-down process which allows for the step-function behavior illustrated in Fig. 4.10 (cf. Sec. 4.2c). 

The symbol roiu) denotes the age baaed on the Fermi continuous slowing-down model. 

In the analysis of our results we must note particularly that Eq. (3), like the equation of the continuous slowing-down model, is not applicable to a hydrogenous medium such as H2O and that Eq. (5) is for an infinite medium. With these assumptions in mind, we can then explain the deviations at the end of our plotted curves. Other possible sources of error to be considered are impurities in the water, inaccuracy in foil position, source thickness, and the transverse distribution of the fission neutrons. 

The picture has not been confirmed experimentally because time scales of less than 10 ps are not accessible at present and there are difficulties envisaged In reducing this limit below 1 ps. However, as a theoretical model It fits much of the experimental data and Is of much greater value than that which uses the continuous slowing down approximation whereby energy Is assumed to be deposited continuously along the track. 

S A point source in an infinite medium is emitting neutrons of zero lethargy isotropically at a constant rate in time. Assume that the slowing-down process may be described by means of the Fermi age model once the first collision has occurred. Thus at points of first collision, the neutrons enter a continuous slowing-down process. 

Apart from this limitation, the principal restriction in the use of the Fermi age model is due to the large number of conditions which must be satisfied by the physical system if the model is to be valid (see Sec. 7.3i). However, even with this shortcoming, the model is still very useful for preliminary studies and for gaining insight into the essential features of many reactor problems. The Fermi age or continuous-slowing-down diffusion theory, then, offers some generality without introducing excessive computational difficulties. 

The periodic recurrence of cell division suggests that globally the cell cycle functions like an autonomous oscillator. An extended model incorporating the sequential activation of the various cyclin-dependent kinases, followed by their inactivation, shows that even in the absence of control by cell mass, this sequence of biochemical events can operate as a limit cycle oscillator [145]. This supports the union of the two views of the cell cycle as dominoes and clock [146]. Because of the existence of checkpoints, however, the cell cycle stops at the end of certain phases before engaging in the next one. Thus the cell cycle looks more like an oscillator that slows down and makes occasional stops. A metaphor for such behavior is provided by the movement of the round plate on the table in a Chinese restaurant, which would rotate continuously under the movement imparted by the participants, were it not for frequent stops. 

One day, Mary, his top research assistant, reports to him that a problem has been detected in the tricuspid valve of the artificial heart model. With further testing, it is discovered that the rate at which this valve allows blood to pass tends to slow down after 8 months of continuous usage. The coroner s report states that the patient s... 

In order to account for these results Padalia et al. (1976) have proposed the following model of oxidation In Yb the oxide was assumed to be nucleated in islands and the linear kinetics was attributed to island growth. In the case of the other heavy rare earth metals the oxide was assumed to form a continuous film at the surface, which grows steadily deeper into the bulk thus accounting for the logarithmic relationship between exposure and O Is peak intensity. After an exposure of about 40 L O2 the oxide film was thought to form a protective layer which slows down the further oxidation as can be recognized in fig. 7. 

The difference between batch and continuous culture techniques with respect to the effect of product inhibition is that under the conditions of continuous cultures product is diluted, while in batch runs product is accumulated. Therefore, in batch cultures reaction rates eventually slow down. In chemostat cultures, however, oscillations of x and p appear due to periodic effect of, for example, pH control and/or permanent inflow and outflow of fresh medium. For the mathematical modeling and computer simulation of this problem, it is possible to formulate the following differential equations ... 

A similarity in k (from model I) and k (from model II) behavior indicates that under conditions of continuous initiation, all the termination processes slow down as the... 

Spin-lattice relaxation time increased continuously as a fimction of time, passing from 4000 ms to 8500 ms. It was possible to see two different evolutions. Ti increased rapidly during the two first days and slowed down after this time. Such a curve can be fitted with a power law model. The evolution was the same as for crystal size during Ostwald Ripening. The power law exponent determined for this system was 0.098, which is lower than the 0.2 to 0.3 which can be found for the evolution of crystal size followed by polarized microscopy. The actual deviation was due to the fact that we measured spin-lattiee relaxation times and not crystal size directly. However, the fact that we retained the power law model led us to expect a relationship between crystal size and spin-lattice relaxation time. 

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