The present status of research and understanding regarding the dynamics and the statistical properties of earthquakes is reviewed, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture, which provides a microscopic basis for our understanding of an earthquake instability, and on the statistical physical modelling of earthquakes, which provides macroscopic aspects of such phenomena. Recent numerical results from several representative models are reviewed, with attention to both their critical and their characteristic properties. Some of the relevant notions and related issues are highlighted, including the origin of power laws often observed in statistical properties of earthquakes, apparently contrasting features of characteristic earthquakes or asperities, the nature of precursory phenomena and nucleation processes, and the origin of slow earthquakes, etc.

We present here the exact solution of an infinite range, discrete, opinion formation model. The model shows an active-absorbing phase transition, similar to that numerically found in its recently proposed continuous version [Lallouache et al., Phys. Rev E 82, 056112 (2010)]. Apart from the two-agent interactions here we also report the effect of having three-agent interactions. The phase diagram has a continuous transition line (two-agent interaction dominated) and a discontinuous transition line (three-agent interaction dominated) separated by a tricritical point.

The two principal ingredients determining the failure modes of disordered solids are the strength of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage—the two extreme natures of the failure modes. In this study, using the random fiber bundle model as a prototype for disordered solids, we classify all failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes. As the fiber bundle model is a long-standing model for interpreting various features of stressed disordered solids, the general phase diagram can serve as a guiding principle in anticipating the responses of disordered solids in general.

A national voting population, when segmented into groups such as, for example, different states, can yield a counterintuitive scenario in which the winner may not necessarily get the highest number of total votes. A recent example is the 2016 presidential election in the United States. We model the situation by using interacting opinion dynamics models, and we look at the effect of coarse graining near the critical points where the spatial fluctuations are high. We establish that the sole effect of coarse graining, which mimics the “winner take all” electoral college system in the United States, can give rise to finite probabilities of events in which a minority candidate wins even in the large size limit near the critical point. The overall probabilities of victory of the minority candidate can be predicted from the models, which indicate that one may expect more instances of minority candidate winning in the future.