Nonextensive Statistical Mechanics

7.1 Physics 235Fig. 7.16 The vertical ((a) and(c)) and horizontal ((b) and(d)) displacement normalized distributionsapproach a q-Gaussian with q ≃ 1.5 intheintermediate regime ((a) and (b)), and aGaussian in the fully developed regime ((c) and (d)). The symbols indicate the silo aperture: circlesfor 3.8d and squares for 11d. The blue (red) solid line is a Gaussian (q-Gaussian with q = 3/2)(from [451, 452]).7.1.5.2 Silo DrainageComputational simulations have been recently done [451, 452] for the discharge ofgranular matter out of the bottom of a vertical silo: see Fig. 7.15. Although the outcomeprecision of the simulations is not very high, our interest in these experimentslies on the fact that they seem to provide one more verification of the predictedscaling (4.16): see Figs. 7.16 and 7.17.7.1.6 Condensed Matter PhysicsManganites are a family of magnetic materials having “exotic” magnetic and electricproperties (such as giant magnetoresistance), as well as ferro-paramagneticfirst- and second-order phase transitions. Their theoretical approach has considerabledifficulties. Several papers by the same group, [454–459] among others, haveadopted a phenomenological approach based on q-statistics, using the index q asa tunable fitting parameter to reflect the consequences of the well-known fractalnature (at the level of microstructures) of the family. The attempt has been successfulin substances such as La 0.60 Y 0.07 Ca 0.33 MnO 3 as can be judged from sayFigs. 7.18, 7.19, 7.20, 7.21, and 7.22. The deep understanding of this fact on microscopicor mesoscopic grounds remains, nevertheless, an open question. Especially if