Non-extensive statistical mechanics (or q-statistics) is based on the so-called non-additive Tsallis entropy. Since its introduction by Tsallis, in 1988, as a generalization of the Boltzmann–Gibbs equilibrium statistical mechanics, it has steadily gained ground as a suitable theory for the description of the statistical properties of non-equilibrium complex systems. Therefore, it has been applied to numerous phenomena, including real seismicity. In particular, Tsallis entropy is expected to provide a guiding principle to reveal novel aspects of complex dynamical systems with catastrophes, such as seismic events. The exploration of the existing connections between Tsallis formalism and real seismicity has been the focus of extensive research activity in the last two decades. In particular, Tsallis q-statistics has provided a unified framework for the description of the collective properties of earthquakes and faults. Despite this progress, our present knowledge of the physical processes leading to the initiation of a rupture, and its subsequent growth through a fault system, remains quite limited. The aim of this paper was to provide an overview of the non-extensive interpretation of seismicity, along with the contributions of the Tsallis formalism to the statistical description of seismic events.

We have explored the idea of producing the equilibrium equation of state, i.e. the pressure as a function of packing fraction, βP(φ), of a confined system up to very high pressures to yield the configuration that leads to the maximum packing fraction. For this purpose we have massively implemented the replica exchange Monte Carlo algorithm in graphics processing units (GPUs), in such a way that each GPU core handles a single simulation cell. This yields a very easy scheme to implement parallelization for a very large amount of replicas (thousands), which densely sample configuration space. We have tested this idea with a very well studied system, i.e. discs confined in a circular cavity, for a number of particles N ≤ 125. In all cases, our outcomes for configurations having maximum packing fractions are in perfect agreement with those already reported and conjectured optimal in the literature, for which there is no formal mathematical proof, strongly suggesting that they are indeed optimal configurations. Furthermore, in most cases, we have obtained the same function βP(φ), by compressing loose random configurations and by decompressing copies of the configuration having the largest packing fraction. This reveals numerically that the so obtained maximum packing configurations are the correct answer.

The understanding of the dynamical behavior of seismic phenomena is currently an open problem, mainly because seismic series can be considered to be produced by phenomena exhibiting dynamic phase transitions; that is, with some complexity. For this purpose, the Middle America Trench in central Mexico is considered a natural laboratory for examining subduction because of its heterogenous natural structure. In this study, the Visibility Graph method was applied to study the seismic activity of three regions within the Cocos plate: the Tehuantepec Isthmus, the Flat slab and Michoacan, each one with a different level of seismicity. The method maps time series into graphs, and it is possible to connect the topological properties of the graph with the dynamical features underlying the time series. The seismicity analyzed was monitored in the three areas studied between 2010 and 2022. At the Flat Slab and Tehuantepec Isthmus, two intense earthquakes occurred on 7 and 19 September 2017, respectively, and, on 19 September 2022, another one occurred at Michoacan. The aim of this study was to determine the dynamical features and the possible differences between the three areas by applying the following method. First, the time evolution of the a- and b-values in the Gutenberg–Richter law was analyzed, followed by the relationship between the seismic properties and topological features using the VG method, the k–M slope and the characterization of the temporal correlations from the γ-exponent of the power law distribution, P(k) ∼ k^−γ, and its relationship with the Hurst parameter, which allowed us to identify the correlation and persistence of each zone.

Based on a recently published theoretical model, in this work we experimentally studied the problem of gravity water drainage due to continuous steam injection into an elliptical porous chamber made of glass beads and embedded in a metallic, quasi-2D, massive cold slab. This configuration mimics the process of steam condensation for a given time period during the growth stage of the steam-assisted gravity drainage (SAGD) process, a method used in the recovery of heavy and extra-heavy oil from homogeneous reservoirs. Our experiments validate the prediction of the theoretical model regarding the existence of an optimal injected steam mass flow rate per unit length, ${\varphi }_{opt}$, to achieve the maximum recovery of a condensate (water). We found that the recovery factor is close to 85% when measured as the percentage of the mass of water recovered with respect to the injected mass. Our results can be extended to actual oil-saturated reservoirs because the model involves the formation of a film of condensates close to the chamber edge that allows for gravity drainage of a water/oil emulsion into the recovery well.

The flow of water through a channel with a heterogeneous porous layer in its central core is simulated using the method of Smoothed-Particle Hydrodynamics (SPH). Three different porous substrates are considered that differ in the geometry of their grain arrays. The heterogeneity is modeled by dividing the porous substrate into four zones that each have a different porosity. The pressure loss and the flow across the channel are simulated at two different scales, the pore scale and the Representative Elementary Volume (REV) scale, based on use of the Ergun equation. Since the computational cost at the REV scale is much lower than at the pore scale, it is therefore important to assess how accurately the REV-scale calculation reproduces the pore-scale results. The REV-scale simulation predicts cross-sectional mainstream velocity profiles and head losses through the channel that differ from the pore-scale results by root-mean-square errors of about 0.01% and 0.3%, respectively.

The use of polymer microspheres is becoming increasingly widespread. Along with their most common applications, they are beginning to be used in the synthesis of photonic crystals, microstructure analysis and multiplexed diagnostics for disease control purposes. This paper presents a simple mathematical model that allows us to study the transport mechanisms involved in the deformation of an elastic microchannel under the flow stream of a power-law fluid. In particular, we analyze the momentum transfer to a non-Newtonian fluid (Polydimethylsiloxane, PDMS) due to the deformation of the elastic ceiling of a rectangular microchannel. Hooke’s law is used to represent the stress–deformation relationship of the PDMS channel ceiling. Stop-flow lithography is modeled, and the pressure exerted by the deformed PDMS ceiling on the fluid when the microchannel returns to its original form is taken into account. It is found that the response time of the elastic ceiling deformation increases with the channel width and length and decreases with the channel height independently of the power-law exponent of the injected fluid. However, an increase in the power-law exponent beyond unity causes an increase in the wall-deformation response time and the maximum deformation of the channel height compared to a Newtonian fluid.