Application of Cairns-Tsallis distribution to the dipole-type Hamiltonian mean-field model.

We found that the rare distribution of velocities in quasisteady states of the dipole-type Hamiltonian mean-field model can be explained by the Cairns-Tsallis distribution, which has been used to describe nonthermal electron populations of some plasmas. This distribution gives us two interesting parameters which allow an adequate interpretation of the output data obtained through molecular dynamics simulations, namely, the characteristic parameter q of the so-called nonextensive systems and the α parameter, which can be seen as an indicator of the number of particles with nonequilibrium behavior in the distribution. Our analysis shows that fit parameters obtained for the dipole-type Hamiltonian mean-field simulated system are ad hoc with some nonthermality and nonextensivity constraints found by different authors for plasma systems described through the Cairns-Tsallis distribution.

Griffith theory of physical fractures, statistical procedures and entropy production: Rosetta stone's legacy.

A physical model, based on energy balances, is proposed to describe the fractures in solid structures such as stelae, tiles, glass, and others. We applied the model to investigate the transition of the Rosetta Stone from the original state to the final state with three major fractures. We consider a statistical corner-breaking model with cutting rules.

Complexity and disequilibrium in the dipole-type Hamiltonian mean-field model.

This research studies information properties, such as complexity and disequilibrium, in the dipole-type Hamiltonian mean-field model. A fundamental analytical assessment is the partition function in the canonical ensemble to derive statistical, thermodynamical, and information measures. They are also analytical, dependent on the number of particles, consistent with the theory for high temperatures, and rising some limitations at shallow temperatures, giving us a notion of the classicality of the system defining an interval of temperatures where the model is well working.

Quantitative methods to determine the student workload. I. Empirical study based on digital platforms.

We present a quantitative study of an online course developed during COVID19 sanitary emergency in Chile. We reconstruct the teaching-learning process considering the activity logs on digital platforms in order to answer the question of How do our students study? The results from the analysis evidence the complex adaptive character of the academic environment, which exhibits regularities similar to those found in financial markets (e.g.

Quantitative methods to determine the student workload: II. Statistical models for the microcurricular performance indicators.

Previously, we observed that the student workload follows an inverse relation with the learning rate (an application of the kinematic notion of speed contextualized to the learning process). Motivated by this finding, we propose a quantitative estimation of the learning rate using a different source of information: the historical records of final grades of a given course. According to empirical data analyzed in other similar studies, the distribution functions of final grades exhibit a regular pattern: a Gaussian behavior for the approval region and a homogeneous distribution for the failed one.