Near universal values of social inequality indices in self-organized critical models

Success of social inequality measures in predicting critical or failure points in some models of physical systems

“…Next, discussed the numerical observations on g and k for site percolating systems in two dimensions and discussed, in particular, how their coincidence in magnitude (g = k ≃ 0.86) occurs preceding the imminent percolation or critical point. Similar results [17] (g = k ≃ 0.86) as the sandpile systems approach the self-organized critical point in the Bak-Tang-Wiesenfeld sandpile model, Manna model, and a centrally pulled self-organized fiber bundle model have been discussed. Finally, have discussed the numerical results (g ≃ 0.45 and k ≃ 0.65) as the global breaking point approach [22,23] in the equal-load-sharing fiber bundle models with irreversible local failures and collective load-share mechanism and their relevance in earthquake statistics [24].…”

“…The inequality indices (g and k) are obtained from the abovementioned Lorenz functions for the respective models. [17]. For a finite size scaling behavior of these values, see Figure 6.…”

“…Frontiers in Physics frontiersin.org (FBMs) ( [18][19][20][21]), when analyzed using the social inequality indices g and k [17,22], gives an intriguing possibility of predicting the imminent failure of the entire bundle.…”

“…Unlike the other cases discussed here, there are no dynamics on the other side of the critical point, as the system does not survive at all beyond the critical load. For self-organized-critical (SOC) systems, ([16]), as the average "height" h per site increases, our numerical study (in square lattice) [17] shows that g and k approach each other and become equal to about 0.863 (BTW), and 0.856 (Manna) at the respective values of average heights h ≃ 2.087 (little less than the actual critical value h c = 17/8 = 2.125) for the BTW model and h ≃ 0.6859 (compared to h c ≃ 0.7172) for the Manna model. For the other SOC models considered here [17,22], such as the driveninterface Edwards-Wilkinson model and the centrally pulled FBM, show similar growth (from g = 0 and k = 0.5) of the inequality indices to about g = k ≃ 0.86 a little below the respective SOC points.…”

“…At occupation concentration p both below and above the percolation threshold p c ≃ 0.5927 [6] gave g = k ≃ 0.865 at a site occupation probability p ≃ 0.565, somewhat below the percolation threshold p c . The statistics of avalanches (successive failures in one go, without any increase in the external perturbation), following the self-organizing critical dynamics of the sand-pile models ([16]) have also recently been analyzed in terms of the behavior of social inequality indices g and k [17]. Finally, the avalanche statistics due to collective dynamics of failure or breaking of individual elements (in non-brittle materials), studied using the fiber bundle models…”