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Articles

Scattering of electromagnetic plane wave from a low contrast circular cylinder buried in non-integer dimensional Half Space

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Pages 263-283 | Received 08 Sep 2016, Accepted 29 Nov 2016, Published online: 16 Jan 2017

References

  • Stillinger FH. Axiomatic basis for spaces with non-integer dimensions. J Math Phys. 1977;18:1224–1234.
  • Palmer C, Stavrinou PN. Equations of motion in a non-integer-dimensional space. J Phys A. 2004;37:6987–7003.
  • Attiya AM. Reflection and transmission of electromagnetic wave due to a quasi-fractional-space slab. Prog Electromagnet Res Lett. 2011;24:119–128.
  • Tarasov VE. Acoustic waves in fractal media: non-integer dimensional space approach. Wave Motion. 2016;63:18–22.
  • Ahmadi A, Neyshabouri MR, Rouhipour H, et al. Fractal dimension of soil aggregates as an soil erodibility. J Hydrol. 2011;400:305–311.
  • Sandev T, Petreska I, Lenzi EK. Harmonic and anharmonic quantum- mechanical oscillators in noninteger dimensions. Phys Lett A. 2014;378:109–116.
  • Zubair M, Mughal MJ, Naqvi QA. Fractional fields and waves in fractional dimensional space. New York (NY): Springer-verlag; 2012.
  • Zubair M, Mughal MJ, Naqvi QA. The wave equation and general plane wave solution in fractional space. Prog Electromn Res Lett. 2011;19:137–146.
  • Zubair M, Mughal MJ, Naqvi QA. An exact solution of cylindrical wave equation for electromagnetic field in fractional dimensional space. Prog Electromn Res. 2011;114:443–455.
  • Zubair M, Mughal MJ, Naqvi QA. An exact solution of spherical wave in D dimensional fractional space. J Electromn Waves Appl. 2011;25:1481–1491.
  • Zubair M, Mughal MJ, Naqvi QA. On electromagnetic wave propagation in fractional space. Nonlinear Anal Real World Appl. 2011;12:2844–2850.
  • Zubair M, Mughal MJ, Naqvi QA, et al. Differential electromagnetic equations in fractional space. Prog Electromagnet Res. 2011;114:255–269.
  • Asad H, Mughal MJ, Zubair M, et al. Electromagnetic Green’s function for fractional space. J Electromn Waves Appl. 2012;26:1903–1910.
  • Asad H, Zubair M, Mughal MJ. Reflection and transmission at dielectric-fractal interface. Prog Electromagnet Res. 2012;125:543–558.
  • Naqvi QA, Zubair M. On cylindrical model of electrostatic potential in fractional dimensional space. Optik-Int J Light Electron Opt. 2016;127:3243–3247.
  • Abbas M, Rizvi AA, Naqvi QA. Two dimensional Green’s function for non-integer dimensional dielectric half space geometry. Optik-Int J Light Electron Opt. 2016;127:8530–8535.
  • Zubair M, Ang LK. Fractional-dimensional Child-Langmuir law for a rough cathode. Phys Plasmas, (1994-present). 2016;23:072118
  • Hameed A, Omar M, Syed AA, et al. Power tunneling and rejection from fractal chiral-chiral interface. J Electromagnet Waves Appl. 2014;28:1766–1776.
  • Noor A, Syed AA, Naqvi QA. Quasi-static analysis of scattering from a layered plasmonic sphere in fractional space. J Electromagnet Waves Appl. 2015;29:1047–1059.
  • Tarasov VE. Continuous medium model for fractal Media. Phys Lett A. 2005;336:167–174.
  • Tarasov VE. Anisotropic fractal media by vector calculus in non-integer dimensional space. J Math Phys. 2014;55:083510.
  • Tarasov VE. Elasticity of fractal materials using the continuum model with non-integer dimensional space. C R Mec. 2015;343:57–73.
  • Tarasov VE. Flow of fractal fluid in pipes: Non-integer dimensional space approach. Chaos Solitons Fractals. 2014;67:26–37.
  • Tarasov VE. Vector calculus in non-integer dimensional space and its applications to fractal media. Commun Nonlinear Sci Numer Simul. 2015;20:360–374.
  • Tarasov VE. Electromagnetic waves in non-integer dimensional spaces and fractals. Chaos Solitons Fractals. 2015;81:38–42.
  • Tarasov VE. Fractal electrodynamics via non-integer dimensional space approach. Phys Lett A. 2015;379:2055–2061.
  • Tarasov VE. Acoustic waves in fractal media: Non-integer dimensional spaces approach. Wave Motion. 2016;63:18–22.
  • Palmer C, Stavrinou PN. Equations of motion in a non-integer-dimensional space. J Phys A: Math Gen. 2004;37:6987.
  • Balankin AS, Mena B, Patio J, et al. Electromagnetic fields in fractal continua. Phys Lett A. 2013;377:783–788.
  • Balankin AS. Effective degrees of freedom of a random walk on a fractal. Phys Rev E. 2015;92:062146.
  • Balankin AS, Bory-Reyes J, Shapiro M. Towards a physics on fractals: differential vector calculus in three-dimensional continuum with fractal metric. Phys A. 2016;444:345–359.
  • Muslih S, Baleanu D, Rabei E. Gravitational potential in fractional space. Open Phys. 2007;5:285–292.
  • Gomez-Aguilar JF. Fractional space waves in conductors. Progr Fract Differ Appl. 2015;1(4):259–267.
  • G’omez-Aguilara JF, Escobar-Jimenezb RF, Lopez-Lopeza MG, et al. Electromagnetic waves in conducting media described by a fractional derivative with non-singular kernel. J Electromagnet Waves Appl. 2016;30:1493–1503.
  • Ostoja-Starzewski M. Electromagnetism on anisotropic fractal media. Zeitschrift fur angewandte Mathematik und Physik. 2013;64:381–390.
  • Kreh M. Bessel functions: project for the Penn State--Gttingen summer school on number theory. Available form: http://www.math.psu.edu/papikian/Kreh.pdf.
  • Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. New York (NY): Dover books on mathematics, Courier Corporation; 2012.
  • Ahmed S, Naqvi QA. Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space. Prog Electromagnet Res. 2008;78:25–38.
  • Naqvi QA, Rizvi AA. Low contrast circular cylinder buried in a grounded dielectric layer. J Electromagnet Waves Appl. 1998;12:1527–1537.
  • Lawrence DE, Sarabandi K. Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface. IEEE Trans Antennas Propag. 2002;50:1368–1376.
  • Fiaz MA, Frezza F, Pajewski L, et al. Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach. IEEE Trans Antennas Propag. 2012;60:2834–2842.
  • Balanis CA. Advanced engineering elecvtromagnetics. 2nd ed. New York (NY): Wiley; 2012.
  • Bender CM, Orszag SA. Advanced mathematical methods for scientists and engineering. New York (NY): McGraw-Hill.

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