scholarly journals Application of Fractional Calculus to Modeling the Non-Linear Behaviors of Ferroelectric Polymer Composites: Viscoelasticity and Dielectricity

Membranes ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 409
Author(s):  
Ruifan Meng
Keyword(s):  
Dielectric Loss ◽  
Fractional Calculus ◽  
Polymer Composites ◽  
Fractional Order ◽  
Dielectric Constants ◽  
Viscoelastic Deformation ◽  
Ferroelectric Polymer ◽  
Linear Behavior ◽  
Dielectric Model ◽  
Non Linear

Ferroelectric polymer composites normally show non-linear mechanical and electrical behaviors due to the viscoelastic and dielectric relaxation of polymer matrixes. In this paper, a fractional calculus approach is used to describe the non-linear behavior of ferroelectric polymer composites from both viscoelastic and dielectric perspectives. The fractional elements for viscoelasticity and dielectricity are “spring-pot” and “cap-resistor”, which can capture the intermediate properties between spring and dashpot or capacitor and resistor, respectively. For modeling the viscoelastic deformation, the “spring-pot” equation is directly used as the fractional mechanical model. By contrast, for the dielectricity of ferroelectric polymer composites, which is usually characterized by dielectric constants and dielectric losses, the “cap-resistor” equation is further formulated into the frequency domain by Fourier transform to obtain the fractional order dielectric model. The comparisons with experimental results suggest that the proposed models can well describe the viscoelastic deformation as well as the frequency dependence of the dielectric constant and dielectric loss of ferroelectric polymer composites. It is noted that the fractional order dielectric model needs to be separated into two regions at low and high frequencies due to the polarization effect. Additionally, when the dipole relaxations occur at higher frequencies, the proposed model cannot describe the rise of the dielectric loss curve.

Novel Ferroelectric Polymer Composites with High Dielectric Constants

2003 ◽  
Vol 15 (19) ◽  
pp. 1625-1629 ◽  
Author(s):  
Z.-M. Dang ◽  
Y.-H. Lin ◽  
C.-W. Nan
Keyword(s):  
Polymer Composites ◽  
Dielectric Constants ◽  
Ferroelectric Polymer ◽  
High Dielectric

scholarly journals Simulation of Chaotic Oscillators of Fractional Order

2019 ◽  
pp. 11-17
Author(s):  
Alejandro Silva-Juárez ◽  
Miguel De Jesús Salazar-Pedraza ◽  
Juan Jorge Ponce-Mellado ◽  
Gustavo Herrera-Sánchez
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Arbitrary Order ◽  
Chaotic Behavior ◽  
Pid Controllers ◽  
Chaotic Oscillators ◽  
Non Linear ◽  
Derivatives Of ◽  
Corrective Method

In 1695 the theory of fractional calculus was introduced, but it only developed as a pure mathematical branch. Currently several research groups have focused on the control, the implementation of filters, PID controllers, synchronization, the implementation of circuits of chaotic systems of fractional order, etc. Currently, the number of applications of fractional calculus is increasing rapidly, these mathematical phenomena have allowed us to describe and model a real object more accurately than the classical "integer" methods. Along with the development of the fractional calculation, it was shown that many fractional-order nonlinear dynamic systems behave in a chaotic manner. This is the type of non-linear systems that are addressed in this research topic with the focus on derivatives of arbitrary order, where numerical simulations of chaotic behavior are presented in non-linear, fractional-order autonomous models. The case studies are six chaotic oscillators of fractional order; The systems of Lorenz, Rӧssler, Financiero, Lui, Chen and Lü, whose attractors are obtained by applying the definitions of the Grünwald-Letnikov definitions and the predictive corrective method of Adams-Bashforth-Moulton.

Nonlinear Time Series Analysis with R

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Particle Physics ◽  
Linear Time ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Linear Behavior ◽  
Non Linear ◽  
Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

Behaviour of Axially Loaded Composite Wall Panel by Using Finite Element Analysis

2015 ◽  
Vol 815 ◽  
pp. 49-53
Author(s):  
Nur Fitriah Isa ◽  
Mohd Zulham Affandi Mohd Zahid ◽  
Liyana Ahmad Sofri ◽  
Norrazman Zaiha Zainol ◽  
Muhammad Azizi Azizan ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Composite Structures ◽  
Element Analysis ◽  
Steel Sheets ◽  
Linear Behavior ◽  
Non Linear ◽  
Composite Wall ◽  
Experimental Values ◽  
Civil Engineering Infrastructure

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to behavior is concerned, it is well known that a key step is to investigate the influence of geometric differences on the non-linear behavior of the panels. One possible approach is to use the validated numerical model based on the non-linear finite element analysis (FEA). The validation of the composite panel’s element using Trim-deck and Span-deck steel sheets under axial load shows that the present results have very good agreement with experimental references. The developed finite element (FE) models are found to reasonably simulate load-displacement response, stress condition, giving percentage of differences below than 15% compared to the experimental values. Trim-deck design provides better axial resistance than Span-deck. More concrete in between due to larger area of contact is the factor that contributes to its resistance.

Electric poling effect on capacitance of ferroelectric polymer composites

2021 ◽  
Author(s):  
S. S. Kulkarni ◽  
Arundhati H. Patil ◽  
U. V. Khadke
Keyword(s):  
Polymer Composites ◽  
Ferroelectric Polymer

scholarly journals Dielectric Properties of Wood-Polymer Composites: Effects of Frequency, Fiber Nature, Proportion, and Chemical Composition

2021 ◽  
Vol 5 (6) ◽  
pp. 141
Author(s):  
Imen Elloumi ◽  
Ahmed Koubaa ◽  
Wassim Kharrat ◽  
Chedly Bradai ◽  
Ahmed Elloumi
Keyword(s):  
Dielectric Properties ◽  
Polymer Composites ◽  
Wide Frequency Range ◽  
Dielectric Constants ◽  
Cellulose Content ◽  
Wood Fibers ◽  
Low Frequencies ◽  
Wood Polymer ◽  
Wood Polymer Composites ◽  
New Applications

The characterization of the dielectric properties of wood–polymer composites (WPCs) is essential to understand their interaction with electromagnetic fields and evaluate their potential use for new applications. Thus, dielectric spectroscopy monitored the evolution of the dielectric properties of WPCs over a wide frequency range of 1 MHz to 1 GHz. WPCs were prepared using mixtures of different proportions (40%, 50%, and 60%) of wood and bark fibers from various species, high-density polyethylene, and maleated polyethylene (3%) by a two-step process, extrusion and compression molding. Results indicated that wood fibers modify the resistivity of polyethylene at low frequencies but have no effect at microwave frequencies. Increasing the fiber content increases the composites’ dielectric properties. The fibers’ cellulose content explains the variation in the dielectric properties of composites reinforced with fibers from different wood species. Indeed, composites with high cellulose content show higher dielectric constants.

Mitigating the Effects of Non-Linear Distortion Using Polarizers in Microwave Photonic Link

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarika Singh ◽  
Sandeep K. Arya ◽  
Shelly Singla
Keyword(s):  
Dynamic Range ◽  
Extinction Ratio ◽  
Polarization Angle ◽  
Third Order ◽  
Microwave Photonic ◽  
Linear Behavior ◽  
Spurious Free Dynamic Range ◽  
Non Linear ◽  
Intermodulation Distortions ◽  
Insertion Losses

AbstractA scheme to suppress nonlinear intermodulation distortion in microwave photonic (MWP) link is proposed by using polarizers to compensate inherent non-linear behavior of dual-electrode Mach-Zehnder modulator (DE-MZM). Insertion losses and extinction ratio have also been considered. Simulation results depict that spurious free dynamic range (SFDR) of proposed link reaches to 130.743 dB.Hz2/3. A suppression of 41 dB in third order intermodulation distortions and an improvement of 15.3 dB is reported when compared with the conventional link. In addition, an electrical spectrum at different polarization angles is extracted and 79^\circ is found to be optimum value of polarization angle.

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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