Survival probability regions

Yet unless very detailed information is available to describe the initial distribution of separations, p(r, 0), it will not be possible to use measured time-dependent survival probabilities to probe details of dynamic liquid structure. Currently, experimental uncertainties at 30% are so large that such a probe is not possible, since the effects of the short-range caging region are only 30%, at the most, of the rate coefficient or escape probability. 

Many years ago Polya [20] formulated the key problem of random walks on lattices does a particle always return to the starting point after long enough time If not, how its probability to leave for infinity depends on a particular kind of lattice His answer was a particle returns for sure, if it walks in one or two dimensions non-zero survival probability arises only for the f/iree-dimensional case. Similar result is coming from the Smoluchowski theory particle A will be definitely trapped by B, irrespectively on their mutual distance, if A walks on lattices with d = 1 or d = 2 but it survives for d = 3 (that is, in three dimensions there exist some regions which are never visited by Brownian particles). This illustrates importance in chemical kinetics of a new parameter d which role will be discussed below in detail. 

An original formalism for the treatment of many-particle effects in the A + B — B reaction was developed in a series of papers by Berezhkovskii, Machnovskii and Suris [54-59]. It is based on the so-called Wiener trajectories and related the Wiener sausages concept (the spatial region visited by a spherical Brownian particle during its random walks) [55, 60, 61]. It was shown that the convential survival probability for a walker among traps, which could be presented in a form [47]... 

Whether the inactive region is a true continuum (e.g., photofragmentation) or a quasi-continuum comprised of an enormous density of rigorously bound eigenstates (polyatomic molecule dynamics, Section 9.4.14) is often of no detectable consequence. The dynamical quantities discussed in Section 9.1.4 (probability density, density matrix, autocorrelation function, survival probability, transfer probability, expectation values of coordinates and conjugate momenta) describe the active space dynamics without any reference to the detailed nature of the inactive space. 

In the case of our systems it is in principal possible to measure the probability of hydrogen to stay in the cluster. In the molecular dynamics simulation the survival probability is calculated by integrating the square of the wavefunction over the cluster region P t) = l /(r, t) dr, where l//(r, t) is the time-dependent... 

Since the survival probability may be ditficult to measure, some decay analyses discuss other quantities, such as the nonescape probability from a region of space [57, 58], the probability density at chosen points of space [25, 59, 60], the flux [61-63], and the arrival time [64]. For initially localized wave packets, there is no major discrepancy between survival probability and the nonescape probability [3, 57, 59, 65-67]. Examination of densities, fluxes, or arrival time distributions may be interesting since a new variable is introduced (we shall see later some applications), but at the price of losing the simplicity and directness of the survival probability. 

Recently the same problem has been reanalyzed by Dicus et al. [86], and indeed they confirmed that the survival probability deviates from exponential at long times. This model and its variants have been applied to study the effect of a distant detector (by adding an absorptive potential) [87], anomalous decay from a flat initial state [44], resonant state expansions [3], initial state reconstruction (ISR) [58], or the relevance of the non-Hermitian Hamiltonian concept (associated with a projector formalism for internal and external regions of space) in potential scattering [88]. In Ref. [88] the model was extended to a chain of delta functions to study overlapping resonances. 

If there are any identifiable gross lesions, they often differ between animals that die, and those that survive to the end of the observation period. The reason for these differences is very simple. An animal that dies less than 24 hours after chemical exposure probably has not had sufficient time to develop a well-defined lesion. As mentioned earlier, most deaths occur within 24 hours. Animals that survive for the two-week observation period have probably totally recovered and rarely have apparent lesions. Hence, the animals that provide the best chance to identify test-article-specific lesions are those that die in the region of 24 to 96 hours postdosing. 

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