Poissonian temporal

The temporal evolution of spatial correlations of both similar and dissimilar particles for d = 1 is shown in Fig. 6.15 (a) and (b) for both the symmetric, Da = Dft, and asymmetric, Da = 0 cases. What is striking, first of all, is rapid growth of the non-Poisson density fluctuations of similar particles e.g., for Dt/r = 104 the probability density to find a pair of close (r ro) A (or B) particles, XA(ro,t), by a factor of 7 exceeds that for a random distribution. This property could be used as a good aggregation criterion in the study of reactions between actual defects in solids, e.g., in ionic crystals, where concentrations of monomer, dimer and tetramer F centres (1 to 3 electrons trapped by anion vacancies which are 1 to 3nn, respectively) could be easily measured by means of the optical absorption [22], Namely in this manner non-Poissonian clustering of F centres was observed in KC1 crystals X-irradiated for a very long time at 4 K [23],... 

T = J0°° w(t)tdt —> oo, manifesting the self-similar nature of this waiting process that has also prompted the coinage of fractal time processes [48]. Note that in the limit a —> 1, this waiting time pdf reduces to the singular form Lf (t/x) — 5(t - x) with finite T = % that leads back to the temporally local Markovian formulation of classical Brownian transport. In fact, for any waiting time pdf with a finite characteristic time T, one recovers the Brownian picture, such as for the Poissonian form w(t) = x xe t x. 

From the point of view of modeling the temporal behavior of earthquakes, the recurrence models can be divided in two main classes. The first class contains the memoryless model, i.e., the Poisson model, whereas the second class includes the non-Poissonian models, i.e., time-dependent models. While the Poisson model is extensively used in PSHAs, its adequacy is limited since the mechanism of earthquake interactions at regional scale has highlighted the tendency to a spatiotemporal clustering of earthquake occurrence, even for moderate earthquakes. Moreover, due to the memoryless ... 

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