Evaluation of Electric Field for a Dielectric Cylinder Placed in Fractional Space
Evaluation of Electric Field for a Dielectric Cylinder Placed in Fractional Space
DOI:
https://doi.org/10.53560/PPASA(59-2)758Keywords:
FD-Space, Laplacian-equation, Ising-limit, Quantum-Field-TheoryAbstract
The problem related to the dielectric cylinder placed in non-integer dimensional space (FD space) isthoroughly investigated in this paper. The FD space describes complex phenomena of physics and electromagnetism. We have solved Laplacian equation in FD space to obtain the solution of a dielectric cylinder in low frequency. The problem is solved by the method of separation of variables analytically. The classical solution of the problem can be easily recovered from the derived solution in non-integer dimensional space.
References
C.G. Bollini, J.J. Giambiagi, Dimensional renormalization: The number of dimensions as a regularizing parameter, Nuovo Cimento B 12 (1972) 2026.
J.F. Ashmore, On renormalization and complex space time dimensions, Commun. Math. Phys. 29 (1973) 177-187.
K.G. Wilson, Quantum field-theory models in less than 4 dimension, Phys. Rev. D 7 (10) (1973) 2911- 2926.
F.H. Stillinger, Axiomatic basis for spaces with noninteger dimension, J. Math. Phys. 18 (6) (1977) 1224-1234.
X.F. He, Excitons in anisotropic solids: The model of fractional-dimensional space, Phys. Rev. B 43 (3) (1991) 2063-2069.
C.M. Bender, S. Boettcher, Dimensional expansion for the Ising limit of quantum field theory, Phy. Rev. D 48 (10) (1993) 4919-4923.
C.M. Bender, K.A. Milton, Scalar Casimir effect for a D-dimension sphere, Phys. Rev. D 50 (10) (1994) 6547-6555.
V.E. Tarasov, Fractional generalization of Liouville equations, Chaos 14 (2004) 123-127.
V.E. Tarasov, Electromagnetic fields on fractals, Modern Phys. Lett. A 21 (20) (2006) 1587-1600.
A. Zeilinger, K. Svozil, Measuring the dimension of space time, Phys. Rev. Lett. 54 (1985) 2553-2555.
S. Muslih, D. Baleanu, Fractional multipoles in fractional space, Nonlinear Anal. 8 (2007) 198-203.
C. Palmer, P.N. Stavrinou, Equations of motion in a noninteger-dimensionspace, J. Phys. A 37 (2004) 6987-7003.
J.D. Jackson, Classical Electrodynamics, 3rd ed., John Wiley, New York, 1999.
Julius Adams Stratton, Electromagnetic Theory, 640 Pages, 1941, Wiley-IEEE Press.
T. Myint-U, L. Debnath, Linear Partial Differential Equations for Scientists and Engineers, 4th ed., 2007.
V.E. Tarasov, Gravitational field of fractals distribution of particles, Celestial Mech. and Dynam. Astronom. 94 (2006) 1-15.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II, pages 1184-1185, New York: McGraw-Hill, 1953.
Dumitru Baleanu, Alireza K. Golmankhaneh, Ali K. Golmankhaneh, On electromagnetic field in fractional space, Nonlinear Analysis: Real World Applications 11 (2010) 288-292.
V.E. Tarasov, Vector Calculus in Non-Integer Dimensional Space and its Applications to Fractal Media, Eq.(77), Commun Nonlinear Sci Numer Simulat 20 (2015) 360-374.
