Fragment-size distribution in disintegration by maximum-entropy formalism

Nonextensive models for earthquakes

“…We note that, similarly to original version of SCP model, our approach, represented by Eqs. (8)- (12), provide a very good fit to the experimental data of the two catalogs here considered. It is worth emphasizing, however, that the energy density differ by several orders of magnitude from our model to the original SCP model.…”

“…In this regard, the authors studied the influence of the size distribution of fragments on the energy distribution of earthquakes. The theoretical motivation follows from the fragmentation phenomena [12] in the context of the geophysics systems. In this latter work, Englaman et al showed that the standard Botzmann-Gibbs formalism, although useful, cannot account for an important feature of fragmentation process, i.e., the presence of scaling in the size distribution of fragments, which is one of the main ingredients of the SCP approach.…”

A model for deformation and fragmentation in crushable brittle solids

“…However, this does not mean such models contradict thermodynamic principles, and in fact, many have been analyzed and justified using entropy methods from statistical mechanics [54][55][56][57]. So long as the energy consumed during damage and fragmentation is tracked correctly in the constitutive model, it is thought here that such approaches are reasonable from a thermodynamic perspective.…”

“…These include methods based on random disintegration of bodies in one or more dimensions leading to Poisson-type statistics, as well as geometry-based approaches partitioning areas or volumes in various ways [52,53]. Entropy maximization principles, by which the most chaotic distributions are deemed most probable, have also been used to construct fragment statistics [53] including methods accounting for elastic energy and damage [54] and rotational inertia thought important for granular microstructures [55]. Continuum micromechanicsbased models in which crack sizes are related to typical fragment sizes in dynamically fracturing brittle materials have also been developed [56].…”

Tsallis Entropy and the Transition to Scaling in Fragmentation

“…This transition has not been adequately explained in terms of any general principles, although in [1] the representation of the fragmentation process in terms of percolation on a Bethe lattice leads to a transition to a power law in the distribution of fragment sizes. Some attempts have been made to derive the fragment size distribution function from the maximum entropy principle [5,6], subject to some constraints which mainly came from physical considerations about the fragmentation phenomena. The resulting fragment distribution function describes the distribution of sizes of the fragments in a regime in which scaling is not present.…”