Escape probability, application

This equation shows that at low electric fields, the escape probability is a linear function of F, and the slope-to-intercept ratio of this dependence is given by erJlk T. It is worth noting that this ratio is independent of /-q. Therefore plots of (p F)l(p 0) vs. 7 may be used to test the applicability of the presented theory to describe real systems, even if the distribution of electron thermalization distances is unknown. 

An interesting and useful application of the concepts developed for the purely absorbing medium is in the calculation of escape probabilities from arbitrarily shaped volumes. If P(r) is the probability that a... 

An important application of this general result is given in Chap. 10 in connection with the problem of computing the resonance-escape probability for fuel lumps in a heterogeneous reactor. 

The increase in the resonance-escape probability has been attributed to two effects, namely, the self-shielding of the fuel lump and the physical separation of the two materials (refer to Secs. 10.1c and d). The purpose of the present section is to study these effects in detail. The treatment begins with an elementary analysis of the latter effect, which arises from purely geometric considerations. This study is followed by an outline of an analytical procedure (based on nuclear-resonance parameters) for computing the integrals which appear in the expression for the resonance-escape probability [see, for example, (10.25) and (10.37)]. Application is made first to homogeneous systems, and the results are later extended to heterogeneous systems. 

Application of these theoretical escape probabilities to measured data of emission into liquid argon requires an assumption on the kinetic energy distribution of the emitted electrons. The simple distribution... 

There are basically two ways to overcome such problems. Firstly, one can thermally excite the system so that it can escape from local minima and continue to search the surrounding conformational space. This is the principle behind molecular dynamics simulations, which generate the trajectory of a molecule in time by numerically integrating Newton s equations of motion. This technique is discussed in another section of the present volume. It is also the principle behind Monte Carlo simulations, which build up a thermodynamic ensemble of molecular conformations based on their Boltzmann probabilities. Application of this approach to nucleic acids is discussed below. 

Areas of the North and South Atlantic, and North and South Pacific present continual extreme and hostile ambient conditions that make survival exposed to such conditions a very limited probability with adequate protection measures. In these locations the probability of survival is increased with the provision of a fixed safe refuge rather than the provision of an immediate means of escape. For offshore facilities historical evidence indicates that both helicopter and lifeboat mechanism may be unavailable in some catastrophic incidents. Remote onshore facilities may also experience severe winter conditions that also render this philosophy applicable. 

The epoxy matrix, containing multiple hydroxyl and amino groups, has a high tendency to adsorb water, a major cause of material failure in many applications. Finally, when one uses the epoxy as a fiber matrix, there is a distinct probability that voids will appear due to reaction by-products which do not escape during cure. Once the material vitrifies, the mobility of the molecules is reduced, making it difficult for the small molecular weight products to be eliminated. 

This simple expression, which gives the probability that a pair of charges initially separated by ro and performing a diffusive motion in the mutual Coulomb field will escape recombination, has found numerous applications in various fields of physics and chemistry. 

It is unfortunate that the general literature does not contain more detailed information regarding this important development. However, the process patents are relatively recent and the whole matter is involved with the earlier basic patents on hydrocarbon oxidation. It is probable that a number of applications are still on file for which no patents have as yet been issued. Escaping, as it has, the attention of academic investigators in the past, the pressure oxidation process has been an industrial development, and the general public will necessarily have to wait for operating details. 

The ultimate in avoiding autotoxicity is for the wamingly colored prey to forego a toxin altogether. This seems to contradict what was said earlier about toxins vj. distastefulness. Indeed, we should probably not find it common, but Gibson (1980) has shown that birds can be taught to avoid models when the only stimulus is complete frustration, i.e., the models escape . This concept may be applicable to certain brightly colored leafhoppers, but it has received little attention. 

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