Electrodynamics of Fractal Distributions of Charges and Fields
作者： Vasily E. Tarasov
DOI: 10.1007/978-3-642-14003-7_4
关键词: Distribution (number theory) 、 Quantum electrodynamics 、 Physics 、 Multipole expansion 、 Fractional calculus 、 Fractal 、 Development (differential geometry) 、 Continuous modelling
摘要: Joseph Liouville was a pioneer in development of fractional calculus to electrodynamics (Lutzen, 1985). The theory derivatives and integrals (Kilbas et al., 2006; Samko 1993) can be applied several specific electromagnetic problems (see, for example, (Engheta, 1997; Zelenyi Milovanov, 2004; 2009; Potapov, 2005; Tarasov, 2008, Bogolyubov 2009)). In this chapter, we consider fractal distribution charges fields the framework continuous model (Tarasov, 2005a,b, 2006a,b).
springer.com
sci-hub.st 参考文章(20)
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)
Vasily E. Tarasov, Magnetohydrodynamics of fractal media Physics of Plasmas. ,vol. 13, pp. 052107- ,(2006) , 10.1063/1.2197801
A. N. Bogolyubov, A. A. Potapov, S. Sh. Rehviashvili, An approach to introducing fractional integro-differentiation in classical electrodynamics Moscow University Physics Bulletin. ,vol. 64, pp. 365- 368 ,(2009) , 10.3103/S0027134909040031
Massimo Materassi, Giuseppe Consolini, Magnetic reconnection rate in space plasmas: a fractal approach. Physical Review Letters. ,vol. 99, pp. 175002- ,(2007) , 10.1103/PHYSREVLETT.99.175002
Gianluca Calcagni, Quantum field theory, gravity and cosmology in a fractal universe Journal of High Energy Physics. ,vol. 2010, pp. 120- ,(2010) , 10.1007/JHEP03(2010)120
Lev M Zelenyi, Aleksandr V Milovanov, Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics Physics-Uspekhi. ,vol. 47, pp. 749- 788 ,(2004) , 10.1070/PU2004V047N08ABEH001705
V. E. Tarasov, FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS FOR ELECTROMAGNETIC WAVES IN DIELECTRIC MEDIA Theoretical and Mathematical Physics. ,vol. 158, pp. 355- 359 ,(2009) , 10.1007/S11232-009-0029-Z
Vasily E. Tarasov, Electromagnetic field of fractal distribution of charged particles Physics of Plasmas. ,vol. 12, pp. 082106- 082106 ,(2005) , 10.1063/1.1994787
Vasily E. Tarasov, GRAVITATIONAL FIELD OF FRACTAL DISTRIBUTION OF PARTICLES Celestial Mechanics and Dynamical Astronomy. ,vol. 94, pp. 1- 15 ,(2006) , 10.1007/S10569-005-1152-2
Alexander V. Milovanov, Pseudochaos and low-frequency percolation scaling for turbulent diffusion in magnetized plasma Physical Review E. ,vol. 79, pp. 046403- ,(2009) , 10.1103/PHYSREVE.79.046403