Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation

We analyse a bidimensional nonlinear Fokker-Planck equation by considering an anisotropic case, whose diffusion coefficients are $D_x \propto |x|^{-\theta}$ and $D_y \propto |y|^{-\gamma}$ with $\theta, \gamma \in {\cal{R}}$. In this context, we also investigate two situations with the drift force $\vec{F}(\vec{r},t)=(-k_{x}x, -k_y y)$. The first one is characterized by $k_x/k_y=(2+\gamma)/(2+\theta)$ and the second is given by $k_{x}=k$ and $k_{y}=0$. In these cases, we can verify an anomalous behavior induced in different directions by the drift force applied. The found results are exact and exhibit, in terms of the $q$-exponentials, functions which emerge from the Tsallis formalism. The generalization for the $D$-dimensional case is discussed.Comment: 6 pages, tex fil

q-exponential, Weibull, and q-Weibull distributions: an empirical analysis

In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law (q-exponential with q > 1) controversy.Comment: 6 pages, Latex. To appear in Physica

On the equivalence of the self-dual and Maxwell-Chern-Simons models coupled to Fermions

We study the exact equivalence between the self-dual model minimally coupled with a Dirac field and the Maxwell-Chern-Simons model with non-minimal magnetic coupling to fermions. We show that the fermion sectors of the models are equivalent only if a Thirring like interaction is included. Using functional methods we verify that, up to renormalizations, the equivalence persists at the quantum level.Comment: 8 pages, revte

Regularities in football goal distributions

Besides of complexities concerning to football championships, it is identified some regularities in them. These regularities refer to goal distributions by goal-players and by games. In particular, the goal distribution by goal-players it well adjusted by the Zipf-Mandelbrot law, suggesting a conection with an anomalous decay.Comment: (Universidade Estadual de Maringa - Brazil) Latex, 3 pages, 3 ps figure

Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions

We obtain new exact classes of solutions for the nonlinear fractional Fokker-Planck-like equation partial_t rho = partial_x{D(x) partial^{mu -1}_x rho^{nu} - F(x) rho} by considering a diffusion coefficient D = D|x|^{-theta} (theta in R and D>0) and a drift force F = -k_1 x + k-bar_{gamma} x|x|^{gamma-1} (k_1, k-bar_{gamma}, gamma in R). Connection with nonextensive statistical mechanics based on Tsallis entropy is also discussed.Comment: latex, 5 pages. Submitted to Physica

An Improved Description of the Dielectric Breakdown in Oxides Based on a Generalized Weibull distribution

In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown $(Q_{BD})$ and/or time-to-breakdown $(t_{BD})$ during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution ($q$-Weibull), which properly describes $(t_{BD})$ data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown $(t_{BD})$ extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the $q$-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze $t_{BD}$ data of SiO$_2$-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the $q$-Weibull distribution.Comment: 5 pages, 3 figure

Dynamics of tournaments: the soccer case

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.Comment: To appear in EPJ

Path Integral Approach to the Nonextensive Canonical Density Matrix

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path integral formulation with unnormalized constraints, and this generalization is worked out through two different ways, which are shown to be equivalent. These formulations with unnormalized constraints are solutions to two generalized Bloch equations proposed in this work. The first form of the generalized Bloch equation is linear, but with a temperature-dependent effective Hamiltonian; the second form is nonlinear and resembles the anomalous correlated diffusion equation (porous medium equation). Furthermore, we can extend these results to the prescription of field theory using integral representations. The second development is dedicated to analyzing the path integral formulation with normalized constraints. To illustrate the methods introduced here, we analyze the free particle case and a non-interacting scalar field. The results herein obtained are expected to be useful in the discussion of generic nonextensive contexts.Comment: (Univ. Est. de Maringa, PR- Brazil),17 pages, Late

Integrating expertises and ambitions for data-driven digital building permits - the EUNET4DBP

The digitalization of the process for building permit (involving the use of 3D information systems) is seen as a priority in a wide part of the world. Since it is a very multidisciplinary use case, involving a variety of stakeholders tackling complex issues and topics, some of them joined their efforts and skills in the European Network for Digital Building Permit. The initial activity of the network, after a review of on-going experiences, was a workshop to share knowledge about the topics involved and to identify the main ambitions of the network with respect to three pillars (i.e. Process - Rules and Requirements - Technology) and the related requirements. It was achieved through a collective brainstorming activity guided by digital tools, whose results were further analysed in a post-processing phase. Such results are presented in this paper and will be the base for planning the future network activity. © Authors 2020

Remarks on (1−q)(1-q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and normalized constrainsts. We show that these approxiamtions can not be accurate in the analysis of systems with many degrees of freedom.Comment: Latex, 6 pages, 2 figure