Electromagnetic fields in fractal continua

Alexander S. Balankin; Baltasar Mena; Julián Patiño; Daniel Morales

doi:10.1016/j.physleta.2013.01.030

Electromagnetic fields in fractal continua

Alexander S. Balankin, Baltasar Mena, Julián Patiño, Daniel Morales

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

Abstract

Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ_D³∩E³ with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F^α accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.

Original language	English
Pages (from-to)	783-788
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	377
Issue number	10-11
DOIs	https://doi.org/10.1016/j.physleta.2013.01.030
State	Published - 1 Apr 2013

Keywords

Electrodynamics
Fractal media
Fractional metric

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10.1016/j.physleta.2013.01.030

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title = "Electromagnetic fields in fractal continua",

abstract = "Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum ΦD3∩E3 with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space Fα accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.",

keywords = "Electrodynamics, Fractal media, Fractional metric",

author = "Balankin, {Alexander S.} and Baltasar Mena and Juli{\'a}n Pati{\~n}o and Daniel Morales",

note = "Funding Information: The authors thank Rodolfo Camacho-Vel{\'a}zquez from the Mexican Petroleum Company (PEMEX), Yannis C. Yortsos (University of Southern California), Armando Garc{\'i}a Jaramillo (TEMPLE), Carlos Lira-Galeana (Mexican Petroleum Institute) and Michael Shapiro (National Polytechnic Institute) for fruitful and clarifying discussions. This work was supported by the PEMEX under the research SENER-CONACYT Grants No. 116458 and No. 143927 .",

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AU - Balankin, Alexander S.

AU - Mena, Baltasar

AU - Patiño, Julián

AU - Morales, Daniel

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N2 - Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum ΦD3∩E3 with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space Fα accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.

AB - Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum ΦD3∩E3 with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space Fα accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.

KW - Electrodynamics

KW - Fractal media

KW - Fractional metric

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 10-11

ER -

Electromagnetic fields in fractal continua

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Keywords

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