By F I Frankl, E. A. Karpovich
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In an interday context, the question of the applicability of the models of Ref.  to Omori regimes has already been raised in Ref. . This note is organized as follows. In Sect. 2 we briefly recall the model of Refs. [2, 3] and present the procedure of calibration. In Sect. 3 we discuss the selection of Omori-like processes from our database and show how our model can be used to analytically describe these processes. In Sect. 4 we compare the results of the properly calibrated model with the statistical records at our disposal for the S&P 500 index.
The presence of a powerlaw relaxation is often found in various complex systems (see [3, 4] for example, and references therein). The origin of Omori law even in the case of earthquake is not fully understood. Nevertheless, many proposed mechanisms are based on the basic idea that the entire region of aftershocks is composed of a number of small and heterogeneous regions containing faults, among which the stress of main earthquake is released subsequently with delayed fractures of the faults. The idea of delayed fractures is quite analogous to our case.
The bottom one shows the total amounts of debt of those failed firms. One can see that not only the Tokyo prefecture (at center) but also the northeast prefecture of Hokkaido (top) and east prefectures in Kyushu island (leftmost) were influenced seriously, even if they are all located far away from the Tohoku area. The paper is organized as follows. In Sect. 2 we define aftershocks in terms of chained failures, where a chain refers to neighborhood on the supplier-customer network. We give a basic idea behind the method of counting the number of chained failures.
Gas Dynamics of Thin Bodies by F I Frankl, E. A. Karpovich