Diffusion equations and different spatial fractional derivatives

We investigate for the diffusion equation the differences manifested by the solutions when three different types of spatial differential operators of noninteger (or fractional) order are considered for a limited and unlimited region.  In all cases, we verify an anomalous spreading of the system, which can be connected to a rich class of anomalous diffusion processes

Maturity Models for Testing and Calibration Laboratories: A Systematic Literature Review

Currently, testing and calibration laboratories are undergoing organizational restructuring in view of technical and regulatory requirements. To assist these laboratories, maturity models (MMs) can be used for the implementation and maintenance of management systems. The use of fuzzy logic is often found in association with the construction of MMs. Fuzzy logic helps in the construction of these models, removing subjective elements from the maturity assessment. Therefore, the objective of this study was to perform a systematic literature review (SLR) using the Methodi Ordinatio focused on MMs built with fuzzy logic that aim to evaluate the degree of maturity of testing and calibration laboratories that have implemented ISO/IEC 17025 for their quality management systems (QMSs). This analysis was performed with articles published between 2012 and 2022 in several databases using keywords such as “maturity model”, “fuzzy” and “ISO 17025” and resulted in 18 articles, which made up the bibliographic portfolio. After analyzing the content of these studies, it was possible to conclude that, although no study specifically discussed this MM, the discovered articles were important for presenting ideas and suggestions for future research

Solutions for a fractional diffusion equation with radial symmetry and integro-differential boundary conditions

The solutions for a dimensional system with radial symmetry and governed by a fractional diffusion equation have been investigated. More specifically, a spherical system was considered, being defined in the semi - infinity interval [R, ¥) and subjected to surface effects described in terms of integro - differential boundary conditions which has many practical applications. The analytical solutions were obtained by using the Green function approach, showing a broad range of different behaviors which can be related to anomalous diffusion. The analyses also considered the influence of the parameters of the analytical solution in order to describe a more realistic scenario

<b>Difusão anômala e equações fracionárias de difusão</b> - DOI: 10.4025/actascitechnol.v27i2.1476

Neste trabalho investigaremos as equações de difusão, usualmente aplicadas na descrição da difusão anômala, que empregam derivadas fracionárias tanto na variável temporal quanto na variável espacial. Em particular, para essas equações obteremos soluções exatas levando em conta uma condição inicial genérica e formularemos uma teoria de perturbação para o estudo de situações mais complexas. Também verificaremos que as derivadas fracionárias, quando aplicadas na parte temporal, possibilitam-nos o estudo de um processo de difusão anômala com o segundo momento finito, i.e., 2> &prop; t&alpha; (0 1, correspondendo aos casos, sub e superdifusivo, respectivamente). Em contraste, com a derivada fracionária aplicada na variável espacial que resulta em uma difusão anômala cujo segundo momento não é finito. Complementando o cenário acima, empregaremos o formalismo de caminhantes aleatórios para explorar as implicações obtidas por usar derivadas fracionárias na equação de difusã

Difusão anômala e equações fracionárias de difusão = Anomalous diffusion and fractional diffusion equations

Neste trabalho investigaremos as equações de difusão, usualmente aplicadas na descrição da difusão anômala, que empregam derivadas fracionárias tanto na variável temporal quanto na variável espacial. Em particular, para essas equações obteremos soluções exatas levando em conta uma condição inicial genérica e formularemos uma teoria deperturbação para o estudo de situações mais complexas. Também verificaremos que as derivadas fracionárias, quando aplicadas na parte temporal, possibilitam-nos o estudo de um processo de difusão anômala com o segundo momento finito, i.e., x 2 µ t a ( 0 < a < 1 , e a > 1 , correspondendo aos casos, sub e superdifusivo, respectivamente). Em contraste, com a derivada fracionária aplicada na variável espacial que resulta em uma difusão anômala cujo segundo momento não é finito. Complementando o cenário acima, empregaremos o formalismo de caminhantes aleatórios para explorar as implicações obtidas por usar derivadas fracionárias na equação de difusão.<br><br>In this work we investigate the anomalous diffusion equations, usually applied to describe the anomalous diffusion, which employ fractional derivatives for the time or the spatial variables. Inparticular, we obtain exact solutions by taking a generic initial condition into account and developing a perturbation theory to investigate complex situations. We also verify that the fractional derivatives, when applied to the time variable, lead us to a anomalous diffusion with second moment finite, i.e., x 2 µ t a ( 0 < a < 1 and a > 1 , corresponding to sub and superdifusive behavior, respectively). By way of contrast, the fractional derivative applied to the spatial variable results in a anomalous diffusion where the second moment is not finite. These equations generalize the usual diffusion equation in order to incorporate several situations. We also employ the continuous time random walking formalism to investigate the implications obtained by using fractional derivatives in the diffusion equation

Influence of Extreme Events in Electric Energy Consumption and Gross Domestic Product

The objective of this paper was to identify how extreme events can indicate periods of economic instability in variables from the economic and environmental context (per capita Gross Domestic Product (GDP), per capita electric energy consumption, and per capita carbon dioxide (CO2) emission). The research is limited to the population of the country (Brazil) and five cities of Paran&#225; (Curitiba, Londrina, Maring&#225;, Ponta Grossa, and Cascavel). Therefore, the major research interest was focused on finding information related to extreme events and other techniques that are used for interpretation of complex systems currently. The development was based on data collection. The results indicated that extreme events have influence in periods of economic instability. They also evidenced that there is greater correlation in GDP data/electric energy consumption than in GDP data/CO2 emissions or electric energy consumption/CO2 emissions