Chain survival probability

This function provides the chain survival probability, which is the probability for a given active chain with end-to-end vector r at time t to remain active until time t with end vector r. 

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. 

The density distribution of distance between the chain ends corresponding to SAWs statistics has been presented by Pietronero as multiplication of two functions w R) S (R) G (R). where one is the Gaussian function G (R) - cxp -dR /2a N and determines the probability that the trajectory of end-chain RW via N steps ends in a spherical layer R,R + dR. The survival probability function S(R) selects these trajectories of RW which are not self-avoided. Such function has been determined starting from the following point of view... 

Since aU links of are required for a chain to function and the survival probability of each individual link is independent of each other, the survival probability of the entire chain as the product of its individual probabilities is calculated according to the rules of the probability theory as follows ... 

Hypothesis the rupture of a chain with N undifferentiated Unks is set off by the rupture of the weakest link. Let be the survival probability of a link the survival probability of the chain can be written as PsN that is, by reasoning on the rupture probabilities 1 - = (1 - Pj) or also ... 

The a- and ajS-processes are characterized by a broad asymmetric dielectric relaxation spectrum, which can be well represented by the Kohlrausch Williams-Watts (KWW) decay function (cf. eqn. (4.17)). The major factor leading to the broad DR spectra for a- and ajS-relaxations is that chain segments relax in cooperation with their environment. In order to explain the mechanism of this relaxation, the concepts of defect diffusion and free-volume fluctuation are used. For example, Bendler has proposed a model in which the KWW function is interpreted as the survival probability of a frozen segment in a swarm of hopping defects with a stable waiting-time distribution At for defect motion. 

In the end, it seems most likely that only these two types of industry networks will survive in this segment, and that the e-distributors may possibly have the advantage in some segments. The individual supplier extranet will probably not succeed in this segment of high supply chain complexity because of the sheer number of websites a customer would have to handle in order to achieve transparency. 

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