Rebound model

This model is useful, first, because we can calculate in mathematical detail just how much push a billiard ball exerts on a cushion at each rebound, and, second, because exactly the same mathematics describes the pressure behavior of gas in a balloon. The success of the model leads to new directions of thought. For example, we might now wonder whether the pressure-volume behavior of oxygen, as shown in Table l-II (p. 14), can be explained in terms of the particle model of a gas. 

Ogliaro F, Harris N, Cohen S, et al. A model rebound mechanism of hydroxylation by cytochrome P450 stepwise and effectively concerted pathways, and their reactivity patterns. J Am Chem Soc 2000 122(37) 8977-8989. 

F. Ogliaro, N. Harris, S. Cohen, M. Filatov, S. R de Visser, and S. Shaik, A Model Rebound Mechanism of Hydroxylation by Cytochrome P450. Stepwise and Effectively Concerted Pathways, and Their Reactivity Patterns, J. Am. Chem. Soc. 2000,122, 8977. Calculations explain puzzling aspects of cytochrome P450 hydroxylation reactions in terms of two, different, reactive spin states of the enzyme. 

Adams, R. Younger, P. L. 2001. A strategy for modeling ground water rebound in abandoned deep mine systems. Ground Water, 39, 249-261. 

Raw data gathered from seismic surveys must be processed to compensate for and to remove a variety of distortions unwanted noises created by weathered near-surface rocks, normal time delays, and echoing by rebounding acoustic waves—to provide the clearest possible image of the strata below. Computers can restore these distortions in a fraction of the time that was formerly required to adjust the data painstakingly by hand. Advanced techniques not only permit presentations in three dimensions, but also in color, and to create contour maps and models of subterranean features. However, even with the use of sophisticated tools, there remains a large measure of uncertainty. History has shown repeatedly that a prospective area rejected by one petroleum firm has been accepted by another and proved to be successful. 

In one study (2), plasma and RBC ChE activities were followed from May to September in two mixer-loaders (ML) who used a Swampmate closed-transfer system (Cherlor Manufacturing Co., Salinas, California), and in three mixer-loader applicators (MLA) who used a Model SS 12-4 closed-transfer system (Soil Serv, Salinas, California). The results shown in Fig. 1 indicate that the activities of plasma and RBC ChE were depressed during the application season, but returned to normal by the middle of September. The MLA showed less plasma and RBC ChE depression. It is interesting to note that the plasma ChE showed the "rebound effect," recording levels way above baseline. 

Drug administration is a common method to study neonatal RSD. Both subcutaneous injection and oral administration are applicable. The consequence of neonatal RSD by drug depends on the dose and the way that the drug was administered, such as the treatment duration (38,49). In contrast to an adult response, RSD in the rat at age 2 weeks or younger does not produce a REM rebound to REM suppression (50). Therefore, a dose-response relationship between drug and REM suppression is not as easy to differentiate as in adult models. For uniformity, an injection of a full dose once a day may not produce the same result as an injection of this dose split into a twice-daily dose (51). One to two weeks of total treatment duration with appropriate doses has been proven to be effective in producing long-term developmental abnormalities (38). 

Prediction of the restitution coefficient has been a challenging research topic for decades. Unfortunately, no reliable and accurate prediction method has been found so far. However, some useful simplified models with certain limits have been developed. One of them is the elastic-plastic impact model in which the compression process is assumed to be plastic with part of the kinetic energy stored for later elastic rebounding, with the rebound process considered to be completely elastic [Johnson, 1985]. In this model, it is postulated that (1) during the plastic compression process, a — r3/2a (2) during the compression process, the averaged contact pressure pm is constant and is equal to 3 Y and (3) the elastic rebound process starts when maximum deformation is reached. Therefore, the compressional force is... 

Example 2.4 A copper ball of 1 cm diameter normally collides with a stainless steel wall with an impact velocity of 0.5 m/s. Estimate the restitution coefficient using the elastic-plastic model. What is the rebound velocity of the ball The yield strength of copper is 2.5 x 108 N/m2. It can be assumed that the yield strength of the stainles steel is higher than that of copper. 

So far, in this model, we assume that all the particles are elastic and the collision is of specular reflection on a frictionless smooth surface. For inelastic particles, we may introduce the restitution coefficient e, which is defined as the ratio of the rebound speed to the incoming speed in a normal collision. Therefore, for a collision of an inelastic particle with a frictionless surface as shown in Fig. 5.9, we have... 

S. Shaik, S. Cohen, S. P. de Visser, P. K. Sharma, D. Kumar, S. Kozuch, F. Ogliaro, D. Danovich, Eur. J. Inorg. Chem. 207 (2004). The Rebound Controversy An Overview and Theoretical Modeling of the Robound Step in C—H Hydroxylation by Cytochrome P450. 

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