A CONTRIBUTION TO MAGNETIC RECONNECTION: A BOLTZMANN CORRECTION TO THE MAGNETIC INDUCTION EQUATION FOR FARADAY VORTEX TUBES
Анотація
The Boltzmann correction to the Maxwell induction law for a moving medium
lled with vortex tubes of Faraday has been implemented.
Ключові слова
Повний текст:
PDF (English)Посилання
V. I. Arnold, B. A. Khesin, Topological Methods in Hydrodynamics, Springer, New York, 1998.
T. W. Barrett, Topological Foundations of Electromagnetism, World Scientic, Hackensack, 2008.
G. K. Batchelor, On the spontaneous magneticeld in a conducting liquid in turbulent motion, Proc. R. Soc. Lond. A, 201 (1950), 405 - 416.
L. Boltzmann, Uber Faraday's Kraftlinien von Maxwell, Ostwalds Klassiker der Exacten Wissenschaften, No. 69, W. Engelmann, Leipzig, 1895.
L. Boltzmann, _ Uber Physikalische Kraftlinien, Ostwalds Klassiker der Exacten Wissenschaften, No. 102, W. Engelmann, Leipzig, 1898.
L. Boltzmann, Some errata in Maxwell's paper 'On Faraday's lines of force, Nature, 57 (1897), 77 - 79.
V. L. Borsch, The Faraday induction law after the Boltzmann correction and the problem of magnetic reconnection, in International Conference on Methods of Aerophysical Research, ICMAR 2010, Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of RAS, Novosibirsk, Russia, November 1 - 6, 2010.
V. L. Borsch, Derivation of the magnetic induction equation from the hypothesis of molecular vortices after Boltzmann, in Russian conference Nonlinear Waves: Theory and New Applications, NW 2011, Lavrientiev Institute of Hydrodynamics, Siberian Branch of RAS, Novosibirsk, Russia, March 2 - 4, 2011.
V. L. Borsch, The original Maxwell electromagnetism as a _uent microcontinuum theory. A fresh look based on Boltzmann comments, in Colloquium EuroMech 531 Vortices and Waves: Identifications and Mutual Inuences , Lomonosov Moscow State University, Moscow, Russia, June 21 - 24, 2011.
J. Cat, One understanding: Maxwell on the methods of illustration and scientic metaphor, Stud. Hist. Mod. Phys., 32 (2001), 395 - 441.
O. Darrigol, The electrodynamics of moving bodies from Faraday to Hertz, Centaurus, 36 (1993), 245 - 360.
O. Darrigol, Electrodynamics from Ampere to Einstein, Oxford University Press, Oxford, 2000.
O. Darrigol, Les Equations de Maxwell: de MacCullagh a Lorentz, Belin, Paris, 2005.
P. A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge, 2001.
M. Faraday, Experimental researches in electricity. First series, Phil. Trans. R. Soc. Lond., 122 (1832), 126 - 162.
J. P. Goedbloed, S. Poedts, Principles of Magnetohydrodynamics with Applications to Laboratory and Astrophysical Plasmas, Cambridge University Press, Cambridge, 2004.
J. P. Goedbloed, R. Keppens, S. Poedts, Advanced Magnetohydrodynamics with Applications to Laboratory and Astrophysical Plasmas, Cambridge University Press, Cambridge, 2010.
M. E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, Cambridge, 2009.
H. Helmholtz, Uber Integrale der Hydrodynamischen Gleichungen welche den Wirbelbewegungen Entsprechen, J. Reine Angew. Math., 55 (1858), 25 - 55.
G. Hornig, K. Schindler, Magnetic topology and the problem of its invariant definition, Phys. Plasmas, 3 (1996), 781 - 791.
A. Jeffrey, Magnetohydrodynamics, Oliver & Boyd, Edinburgh, 1966.
B. B. Kadomtsev, Magnetic _eld line reconnection, Rep. Progr. Phys., 50 (1987), 115 143.
Lord Kelvin (W. Thomson), Vibration of columnar vortex, Phil. Mag., 10 (1880), 155 - 168.
V. V. Kozlov, The frozen-in condition for a direction field, small denominators and chaotization of steady flows of a viscous fluid, J. Appl. Math. Mech., 63 (1999), 229 - 235.
H. Lamb, Hydrodynamics, Cambridge University Press, London, 1975.
K. Lambert, The uses of analogy: James Clerk Maxwell's 'On Faraday's lines of force' and early Victorian analogical argument, British J. Hist. Sci., 44 (2011), 61 - 68.
L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1984.
H. A. Lorentz, The Theory of Electrons and its Applications to the Phenomena of Light and Radiant Heat, Teubner, Leipzig, 1916.
J. C. Maxwell, On Faraday's lines of force, Trans. Camb. Phil. Soc., 10 (1864), 27 - 83. (Part I read 1855, part II read 1856.)
J. C. Maxwell, On physical lines of force. Part I. The theory of molecular vortices applied to magnetic phenomena, Phil. Mag., 21 (1861), 161 - 175.
J. C. Maxwell, On physical lines of force. Part II. The theory of molecular vortices applied to electric currents, Phil. Mag., 21 (1861), 281 - 291, 338 - 348.
J. C. Maxwell, On physical lines of force. Part III. The theory of molecular vortices applied to statical electricity, Phil. Mag., 23 (1862), 12 - 24.
J. C. Maxwell, On physical lines of force. Part IV. The theory of molecular vortices applied to the action of magnetism on polarized light, Phil. Mag., 23 (1862), 85 - 95.
Maxwell J. C., A Dynamical Theory of the Electromagnetic Field, Phil. Trans. R. Soc. Lond., CLV (1865), 459 - 512.
J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. I, Clarendon Press, Oxford, 1873.
J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. II, Clarendon Press, Oxford, 1873.
H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge University Press, Cambridge, 1978.
K. Moffatt, Vortex Dynamics: The legacy of Helmholtz and Kelvin, in A. V. Borisov et al. (eds.), IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, and Turbulence, Steklov Mathematical Institute, RAS, Moscow, August 25 - 30, 2006, Springer, Dordrecht, 2008, 1 - 10.
N. J. Nersessian, Maxwell and 'The method of physical analogy': model-based reasoning, generic abstraction, and conceptual change, in D. B. Malament (ed.), Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, Open Court, Chicago, 2002, 129 - 166.
W. Pauli, Theory of Relativity, Pergamon Press, London, 1958.
E. Priest, T. Forbes, Magnetic Reconnection: MHD Theory and Aplications, Cambridge University Press, Cambridge, 2000.
R. Prim, C. Truesdell, A derivation of Zorawski's criterion for permanent vector-lines, Proc. AMS, 1 (1950), 32 - 34.
M. I. Pudovkin, V. S. Semenov, Magnetic _eld reconnection theory and the solar wind-magnetosphere interaction: A review, Space Sci. Rev., 41 (1985), 1 - 89.
L. I. Sedov, On the Ponderomotive Forces of Interaction of Electromagnetic Field and an Accelerating Material Continuum, taking into Account Finite Deformations, J. Appl. Math. Mech., 29 (1965), 4 - 17.
L. I. Sedov, On the Addition of Motions Relative to Deformable Reference Systems, J. Appl. Math. Mech., 42 (1978), 181 - 184.
D. M. Siegel, Innovation in Maxwell's Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light, Cambridge University Press, Cambridge, 1991.
G. I. Taylor, Production and dissipation of vorticity in a turbulent _uid, Proc. R. Soc. Lond. A, 164 (1938), 15 - 23.
C. Truesdell, The kinematics of vorticity, Indiana University Press, Bloomington, 1954.
C. Truesdell, R. A. Toupin, The classical fields theories. Principles of classical mechanics and field theories, in S. Flugge (ed.), Encyclopedia of Physics, Vol. III / 1, Springer, Berlin, 1960, 226 - 793.
A. Tsinober, How analogous is generation of vorticity and passive vectors (magnetic fields)?, in S. Molokov et al. (eds), Magnetohydrodynamics: Historical Evolution and Trends, Springer, Dordrecht, 2007, 223 - 230.
M. Yamada, R. Kulsrud, H. Ji, Magnetic Reconnection, Rev. Mod. Phys., 82 (2010), 603 - 664.
E. G. Zweibel, M. Yamada, Perspectives on magnetic reconnection, Proc. R. Soc. Lond. A, 472 (2016), 1 - 30.
K. Zorawski, Uber die Erhaltung der Wirbelbewegung, C. R. Acad. Sci. Cracovie, 1900, 335 - 341.
DOI: http://dx.doi.org/10.15421/141803
Посилання
- Поки немає зовнішніх посилань.
Індексування журналу
Журнал розміщено у наукометричних базах, репозитаріях та пошукових системах:
Адреса редколегії: 49050, Україна, Дніпровський національний університет імені Олеся Гончара, вул. Козакова 18, корп. 14, механіко-математичний факультет, д-р фіз.-мат. наук, проф. Когут П.І.
email: p.kogut@i.ua
Це видання має доступ за ліцензією Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.