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’.

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'.

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’.

scholarly journals On the thermodynamical restrictions in isothermal deformations of fractional Burgers model

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190278 ◽  
Author(s):  
Teodor M. Atanacković ◽  
Marko Janev ◽  
Stevan Pilipović
Keyword(s):  
Constitutive Equations ◽  
Fractional Derivatives ◽  
Qualitative Difference ◽  
Weak Form ◽  
Entropy Inequality ◽  
Advanced Materials ◽  
Creep Function ◽  
Theme Issue ◽  
Burgers Model ◽  
Materials Modelling

We investigate, in the distributional setting, the restrictions on the constitutive equation for a fractional Burgers model of viscoelastic fluid that follow from the weak form of the entropy inequality under isothermal conditions. The results are generalized, from the Burgers model, to an arbitrary class of linear constitutive equations with fractional derivatives. Our results show that the restrictions obtained here on the coefficients of constitutive equations are weaker when compared with the restrictions obtained by Bagley–Torvik method. We show the precise relation between restrictions derived here and those derived by Bagley–Torvik. We deal with the creep test, for the case when Bagley–Torvik conditions are violated, and new conditions obtained in this work are satisfied. The results show a qualitative difference in the form of creep function. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals Applications of Distributed-Order Fractional Operators: A Review

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 110
Author(s):  
Wei Ding ◽  
Sansit Patnaik ◽  
Sai Sidhardh ◽  
Fabio Semperlotti
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Transport Processes ◽  
Model Systems ◽  
Variable Order ◽  
Fractional Operators ◽  
Research Activity ◽  
Road Map ◽  
Real World Applications ◽  
Distributed Order

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

scholarly journals Complex partial synchronization patterns in networks of delay-coupled neurons

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180128 ◽  
Author(s):  
D. Nikitin ◽  
I. Omelchenko ◽  
A. Zakharova ◽  
M. Avetyan ◽  
A. L. Fradkov ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Temporal Dynamics ◽  
Delay Systems ◽  
Theme Issue ◽  
Partial Synchronization ◽  
Multiplex Network ◽  
Control Scheme ◽  
Non Local ◽  
Spatio Temporal ◽  
Fast Oscillations

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

New insights into soil arching behaviour in column supported embankments

2021 ◽  
Author(s):  
Edward Smith ◽  
Abdelmalek Bouazza ◽  
Louis King ◽  
R. Kerry Rowe
Keyword(s):  
Strain Softening ◽  
Experimental Studies ◽  
Bearing Failure ◽  
Arbitrary Lagrangian Eulerian ◽  
Soil Arching ◽  
Eulerian Formulation ◽  
Practical Design ◽  
Non Local ◽  
Punching Failure ◽  
Effective Design

The observation of failure surfaces within column supported embankments is critical to understanding how the embankment stresses are transferred towards the column heads. In this study, finite element simulations utilising a strain softening constitutive model, non-local regularisation and the Arbitrary Lagrangian-Eulerian formulation are used to examine these failure surfaces over various embankment geometries. This methodology offers insights into the nature of the failure mechanism, the development of a plane of equal settlement and the influence of the subsoil settlement profile. Depending on the embankment geometry, the results indicate either a punching failure, inverted general bearing failure, or a localised failure develops. The transition between punching and inverted general bearing failure is found to be closely related to the establishment of a plane of equal settlement within the embankment. The height of the plane of equal settlement and the range of failure mechanisms that develop were largely insensitive to the nature of the subsoil settlement profiles simulated. These findings have implications for the practical design of efficient embankments and the effective design of future experimental studies.

scholarly journals Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 240
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Order Of Convergence ◽  
Convergent Sequence ◽  
Scalar Function ◽  
Fixed Point Method ◽  
Point Method ◽  
Fractional Operators ◽  
Fixed Point Methods ◽  
Vector Valued Function

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and compact method to work the fractional calculus through the classification of fractional operators using sets. This new method of working with fractional operators, which may be called fractional calculus of sets, allows generalizing objects of conventional calculus, such as tensor operators, the Taylor series of a vector-valued function, and the fixed-point method, in several variables, which allows generating the method known as the fractional fixed-point method. Furthermore, it is also shown that each fractional fixed-point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed-point methods that generate convergent sequences. So, it is presented a method to estimate numerically in a region Ω the mean order of convergence of any fractional fixed-point method, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function. Finally, considering that the proposed method to classify fractional operators through sets allows generalizing the existing results of the fractional calculus, some examples are shown of how to define families of fractional operators that satisfy some property to ensure the validity of the results to be generalized.

scholarly journals Dynamic simulations of many-body electrostatic self-assembly

2018 ◽  
Vol 376 (2115) ◽  
pp. 20170143 ◽  
Author(s):  
Eric B. Lindgren ◽  
Benjamin Stamm ◽  
Yvon Maday ◽  
Elena Besley ◽  
A. J. Stace
Keyword(s):  
Self Assembly ◽  
Experimental Studies ◽  
Charged Particles ◽  
Theoretical Chemistry ◽  
Many Body ◽  
Single Particles ◽  
Theme Issue ◽  
Dynamic Simulations ◽  
The Subject ◽  
Small Clusters

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process. This article is part of the theme issue ‘Modern theoretical chemistry’.

Synthesis of bio-based 2-thiothiophenes

2021 ◽  
Vol 379 (2209) ◽  
pp. 20200350
Author(s):  
Yichen Qiu ◽  
Yunchao Feng ◽  
Ashley C. Lindsay ◽  
Xianhai Zeng ◽  
Jonathan Sperry
Keyword(s):  
Small Molecule ◽  
Chemical Industry ◽  
Emerging Technologies ◽  
Advanced Materials ◽  
Organosulfur Compounds ◽  
Theme Issue ◽  
Widespread Application ◽  
Fossil Carbon ◽  
Functionally Diverse

While the synthesis of bio-based compounds containing carbon, oxygen and (to a lesser extent) nitrogen is well studied, the production of organosulfur compounds from biomass has received virtually no attention, despite their widespread application throughout the chemical industry. Herein, we demonstrate that a range of bio-based 2-thiothiophenes are available from the biopolymer cellulose, proving that functionally diverse small-molecule organosulfurs can be prepared independent of fossil carbon. This article is part of the theme issue ‘Bio-derived and bioinspired sustainable advanced materials for emerging technologies (part 2)’.

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