Fractional-order modelling of epoxy resin

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190292 ◽  
Author(s):  
J. A. Tenreiro Machado ◽  
António M. Lopes ◽  
Rui de Camposinhos
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Epoxy Resins ◽  
Clustering Algorithm ◽  
Electrical Impedance Spectroscopy ◽  
Advanced Materials ◽  
Mathematical Tool ◽  
Materials Modelling ◽  
Hierarchical Clustering Algorithm ◽  
Two Stages

This paper describes epoxy resins by means of electrical impedance spectroscopy (EIS) and the mathematical tool of fractional calculus (FC). Two stages are considered: first, the EIS is used for testing the samples and, second, the measured data are approximated using integer and fractional order models. The FC-based modelling describes the epoxy resins using a small number of parameters that reflect their main characteristics. The EIS data gathered for the epoxies samples are compared with those of different adhesives and sealants by means of a hierarchical clustering algorithm that unravels the relationships between the distinct materials. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Fractional Meissner–Ochsenfeld effect in superconductors

2019 ◽  
Vol 33 (26) ◽  
pp. 1950316 ◽  
Author(s):  
J. F. Gómez-Aguilar
Keyword(s):  
Magnetic Field ◽  
Critical Temperature ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Mathematical Tool ◽  
Conformable Derivative ◽  
Science And Engineering ◽  
Interest In Science ◽  
London Equation ◽  
Physical Phenomena

Fractional calculus (FC) is a valuable tool in the modeling of many phenomena, and it has become a topic of great interest in science and engineering. This mathematical tool has proved its efficiency in modeling the intermediate anomalous behaviors observed in different physical phenomena. The Meissner–Ochsenfeld effect describes the levitation of superconductors in a nonuniform magnetic field if they are cooled below critical temperature. This paper presents analytical solutions of the fractional London equation that describes the Meissner–Ochsenfeld effect considering the Liouville–Caputo, Caputo–Fabrizio–Caputo, Atangana–Baleanu–Caputo, fractional conformable derivative in Liouville–Caputo sense and Atangana–Koca–Caputo fractional-order derivatives. Numerical simulations were obtained for different values of the fractional-order.

scholarly journals Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190284 ◽  
Author(s):  
C. M. Ionescu ◽  
I. R. Birs ◽  
D. Copot ◽  
C. I. Muresan ◽  
R. Caponetto
Keyword(s):  
Fractional Order ◽  
Experimental Validation ◽  
Model Identification ◽  
Nonlinear Least Squares ◽  
Advanced Materials ◽  
Mathematical Framework ◽  
Nonlinear Identification ◽  
Proposed Model ◽  
Materials Modelling ◽  
Fluid Properties

The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals Advanced materials modelling via fractional calculus: challenges and perspectives

2020 ◽  
Vol 378 (2172) ◽  
pp. 20200050
Author(s):  
Giuseppe Failla ◽  
Massimiliano Zingales
Keyword(s):  
Fractional Calculus ◽  
Long Memory ◽  
Experimental Studies ◽  
Advanced Materials ◽  
Fractional Operators ◽  
Theme Issue ◽  
Materials Modelling ◽  
Local Media ◽  
Non Local ◽  
Complex Phenomena

Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals The Chronicles of Fractional Calculus

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
J.A.Tenreiro Machado ◽  
Virginia Kiryakova
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Mathematical Tool ◽  
Remarkable Progress

AbstractSince the 60s of last century Fractional Calculus exhibited a remarkable progress and presently it is recognized to be an important topic in the scientific arena. This survey analyzes and measures the evolution that occurred during the last five decades in the light of books, journals and conferences dedicated to the theory and applications of this mathematical tool, dealing with operations of integration and differentiation of arbitrary (fractional) order and their generalizations.

Application of fractional calculus methods to viscoelastic behaviours of solid propellants

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190291 ◽  
Author(s):  
Changqing Fang ◽  
Xiaoyin Shen ◽  
Kuai He ◽  
Chao Yin ◽  
Shasha Li ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivatives ◽  
Complex Modulus ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Advanced Materials ◽  
Solid Propellants ◽  
Static Modulus ◽  
Materials Modelling ◽  
Viscoelastic Constitutive Model

A three-branch viscoelastic model based on fractional derivatives is proposed for the viscoelastic behaviours of solid propellants. The simulation results show a satisfactory agreement with the stress relaxation modulus and complex modulus of solid propellants. As a comparison, the static modulus is also characterized by traditional viscoelastic model with integer-order derivatives. Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants. Moreover, a simple and effective direct search method based on simulated annealing and Powell's mothed is proposed for the data fitting. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives'.

Distributed Entropy Energy-Efficient Clustering algorithm for cluster head selection (DEEEC)

2020 ◽  
Vol 39 (6) ◽  
pp. 8139-8147
Author(s):  
Ranganathan Arun ◽  
Rangaswamy Balamurugan
Keyword(s):  
Energy Efficient ◽  
Clustering Algorithm ◽  
Cluster Head ◽  
Residual Energy ◽  
Energy Utilization ◽  
Sensor Nodes ◽  
Second Stage ◽  
Energy Efficient Clustering ◽  
Two Stages ◽  
Ch Selection

In Wireless Sensor Networks (WSN) the energy of Sensor nodes is not certainly sufficient. In order to optimize the endurance of WSN, it is essential to minimize the utilization of energy. Head of group or Cluster Head (CH) is an eminent method to develop the endurance of WSN that aggregates the WSN with higher energy. CH for intra-cluster and inter-cluster communication becomes dependent. For complete, in WSN, the Energy level of CH extends its life of cluster. While evolving cluster algorithms, the complicated job is to identify the energy utilization amount of heterogeneous WSNs. Based on Chaotic Firefly Algorithm CH (CFACH) selection, the formulated work is named “Novel Distributed Entropy Energy-Efficient Clustering Algorithm”, in short, DEEEC for HWSNs. The formulated DEEEC Algorithm, which is a CH, has two main stages. In the first stage, the identification of temporary CHs along with its entropy value is found using the correlative measure of residual and original energy. Along with this, in the clustering algorithm, the rotating epoch and its entropy value must be predicted automatically by its sensor nodes. In the second stage, if any member in the cluster having larger residual energy, shall modify the temporary CHs in the direction of the deciding set. The target of the nodes with large energy has the probability to be CHs which is determined by the above two stages meant for CH selection. The MATLAB is required to simulate the DEEEC Algorithm. The simulated results of the formulated DEEEC Algorithm produce good results with respect to the energy and increased lifetime when it is correlated with the current traditional clustering protocols being used in the Heterogeneous WSNs.

Handling WSD using Hierarchical Clustering Algorithm with sentences

2018 ◽  
pp. 83-88
Author(s):  
Mohana Priya K ◽  
Pooja Ragavi S ◽  
Krishna Priya G
Keyword(s):  
Hierarchical Clustering ◽  
Similarity Measure ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cosine Similarity Measure ◽  
Hierarchical Clustering Algorithm ◽  
Multiple Levels ◽  
Pos Tagger ◽  
Sentence Clustering ◽  
The Right

Clustering is the process of grouping objects into subsets that have meaning in the context of a particular problem. It does not rely on predefined classes. It is referred to as an unsupervised learning method because no information is provided about the "right answer" for any of the objects. Many clustering algorithms have been proposed and are used based on different applications. Sentence clustering is one of best clustering technique. Hierarchical Clustering Algorithm is applied for multiple levels for accuracy. For tagging purpose POS tagger, porter stemmer is used. WordNet dictionary is utilized for determining the similarity by invoking the Jiang Conrath and Cosine similarity measure. Grouping is performed with respect to the highest similarity measure value with a mean threshold. This paper incorporates many parameters for finding similarity between words. In order to identify the disambiguated words, the sense identification is performed for the adjectives and comparison is performed. semcor and machine learning datasets are employed. On comparing with previous results for WSD, our work has improvised a lot which gives a percentage of 91.2%

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

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