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Article
Publication date: 24 November 2021

Rawid Banchuin

The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to…

Abstract

Purpose

The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to evaluate the appropriateness of such unconventional calculus.

Design/methodology/approach

The nonlocal fractal integro-differential equations describing RL, RC, LC and RLC circuits with arbitrary source terms defined on middle b cantor set have been formulated and solved by means of fractal Laplace transformation. Numerical simulations based on the derived solutions have been performed where an LC circuit has been studied by means of Lagrangian and Hamiltonian formalisms. The nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been derived and the local fractal calculus-based ones have been revisited.

Findings

The author has found that the LC circuit defined on a middle b cantor set become a physically unsound system due to the unreasonable associated Hamiltonian unless the local fractal calculus has been applied instead.

Originality/value

For the first time, the nonlocal fractal calculus-based analyses of electrical circuits with arbitrary source terms have been performed where those circuits with order higher than 1 have also been analyzed. For the first time, the nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been proposed. The revised contradiction free local fractal calculus-based Lagrangian and Hamiltonian equations have been presented. A comparison of local and nonlocal fractal calculus in terms of Lagrangian and Hamiltonian formalisms have been made where a drawback of the nonlocal one has been pointed out.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 26 January 2022

Rawid Banchuin

The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set.

Abstract

Purpose

The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set.

Design/methodology/approach

The fractal integrodifferential equations of resistor-inductor, resistor-capacitor, inductor-capacitor and resistor-inductor-capacitor circuits subjected to zero mean additive white Gaussian noise defined on fractal set have been formulated. The fractal time component has also been considered. The closed form expressions for crucial stochastic parameters of circuit responses have been derived from these equations. Numerical simulations of power spectral densities based on the derived autocorrelation functions have been performed. A comparison with those without fractal time component has been made.

Findings

We have found that the Hausdorff dimension of the middle b Cantor set strongly affects the power spectral densities; thus, the average powers of noise induced circuit responses and the inclusion of fractal time component causes significantly different analysis results besides the physical measurability of electrical quantities.

Originality/value

For the first time, the noise analysis of electrical circuit on fractal set has been performed. This is also the very first time that the fractal time component has been included in the fractal calculus-based circuit analysis.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 August 2022

Rawid Banchuin

The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.

Abstract

Purpose

The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.

Design/methodology/approach

For ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.

Findings

This study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.

Originality/value

To the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 11 April 2008

Yi Lin, Wujia Zhu, Ningsheng Gong and Guoping Du

The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the…

Abstract

Purpose

The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the material world.

Design/methodology/approach

Parallel comparison is used to reveal the underlying structure existing in human thoughts.

Findings

After highlighting all the relevant ideas and concepts, which are behind each and every crisis in the foundations of mathematics, it becomes clear that some difficulties in the authors' understanding of nature are originated from confusing actual infinities with potential infinities, and vice versa. By pointing out the similarities and differences between these two kinds of infinities, then some hidden contradictions existing in the system of modern mathematics are handily picked out. Then, theoretically, using the authors' yoyo model, it is predicted that the fourth crisis in the foundations of mathematics has appeared. And, a plan of resolution of this new crisis is provided.

Originality/value

This paper shows the first time in history that human thought, the material world, and each economic entity, share a common structure – the systemic yoyo structure. And it proves the arrival of the fourth crisis in mathematics by using systems modeling and listing several; contradictions hidden deeply in the foundations of mathematics.

Details

Kybernetes, vol. 37 no. 3/4
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 15 June 2012

Osama M. Abuzeid

The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

Abstract

Purpose

The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

Design/methodology/approach

For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.

Findings

An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.

Originality/value

This law is only valid as long as the creep is of the size of the surface roughness. The modified model admits an analytical solution for the case when the behavior is linear viscoelastic. The proposed model shows a good agreement when compared with experimental results available in the literature.

Details

Industrial Lubrication and Tribology, vol. 64 no. 4
Type: Research Article
ISSN: 0036-8792

Keywords

Article
Publication date: 1 June 2003

Osama M. Abuzeid

The objective of this paper is to construct a continuous model for the thermo‐visco‐elastic contact of a nominal flat, non‐smooth, punch and a smooth surface of a rigid…

Abstract

The objective of this paper is to construct a continuous model for the thermo‐visco‐elastic contact of a nominal flat, non‐smooth, punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied loads and temperatures. The proposed model assumes the punch surface material to behave according to the linear Kelvin‐Voigt visco‐elastic material. The punch surface, which is known to be fractal in nature, is modeled in this work using a deterministic Cantor structure. An asymptotic power low, deduced using approximate iterative relations, is used to express the punch surface approach as a function of the remote forces and bulk temperatures when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

Details

Journal of Quality in Maintenance Engineering, vol. 9 no. 2
Type: Research Article
ISSN: 1355-2511

Keywords

Article
Publication date: 16 September 2013

Osama M. Abuzeida and Nasim Alnumanb

– This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact.

Abstract

Purpose

This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact.

Design/methodology/approach

The rough surfaces, known to be physical fractal, are modelled using a deterministic Cantor structure. Such structure shows several levels of imperfections and including, therefore, several scales in the constriction of the flux lines. The proposed model will study the effect of the deformation (approach) of the two rough surfaces on the TCC as a function of the remotely applied load.

Findings

An asymptotic power law, derived using approximate iterative relations, is used to express the area of contact and, consequently, the thermal conductance as a function of the applied load. The model is valid only when the approach of the two surface in contact is of the order of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results both in trend and the numerical values.

Originality/value

The model obtained provides further insight into the effect that surface texture has on the heat conductance process. The proposed model could be used to conduct an analytical investigation of the thermal conductance of rough surfaces in contact. This model, although simple (composed of springs), nevertheless works well.

Article
Publication date: 1 December 2004

Osama M. Abuzeid

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half‐space. The considered…

Abstract

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied load. The proposed model assumes the punch surface material to behave according to Kelvin‐Voigt viscoelastic material. The punch surface, which is known to be fractal in nature, is modelled in this work using a deterministic Cantor structure. An asymptotic power law, deduced using iterative relations, is used to express the punch surface approach as a function of the remote force when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

Details

Industrial Lubrication and Tribology, vol. 56 no. 6
Type: Research Article
ISSN: 0036-8792

Keywords

Article
Publication date: 12 June 2009

Konstantinos Karamanos

The purpose of this paper is to discuss the recognizability of Cantorian stochastic automata by generalized entropy‐like qualities.

158

Abstract

Purpose

The purpose of this paper is to discuss the recognizability of Cantorian stochastic automata by generalized entropy‐like qualities.

Design/methodology/approach

The paper gives a necessary entropy condition, valid for all sequences on the alphabet {0, 1} read by lumping and generated by a Cantorian stochastic automaton.

Findings

The paper finds that, on this basis, once can determine that a given sequence is not generated by Cantorian stochastic automata and reconstruct the automaton when the sequence is generated by a Cantorian stochastic automaton.

Originality/value

This paper derives a new diagnostic for Cantorian stochastic automata, which could find a direct application to biology, where there is a recent claim that the coding regions of chromosomes form Cantor sets.

Details

Kybernetes, vol. 38 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 January 2005

Louis H. Kauffman

Discusses the notion of eigenform as explicated by Heinz von Foerster wherein an object is seen to be a token for those behaviors that lend the object its apparent stability in a…

Abstract

Purpose

Discusses the notion of eigenform as explicated by Heinz von Foerster wherein an object is seen to be a token for those behaviors that lend the object its apparent stability in a changing world.

Design/methodology/approach

Describes von Foerster's model for eigenforms and recursions and puts this model in the context of mathematical recursions, fractals, set theory, logic, quantum mechanics, the lambda calculus of Church and Curry, and the categorical framework of fixed points of Lawvere.

Findings

Determines that iterating a transformation upon itself is seen to be a key to understanding the nature of objects and the relationship of an observer and the apparent world of the observer.

Originality/value

Contemplates the concept of recursion in the context of second‐order cybernetics.

Details

Kybernetes, vol. 34 no. 1/2
Type: Research Article
ISSN: 0368-492X

Keywords

1 – 10 of 372