Precessing ball solitons (PBS) in a ferromagnet during the first order phase transition is induced by a magnetic field directed along the axis of anisotropy, while the action of the periodic field perpendicular to the main magnetic field has been analyzed. Under these conditions, the characteristics of arising equilibrium PBS are uniquely determined by the frequency of the periodic field, but the solitons with other frequencies are impossible. For such structure, the entropy increase connected with dissipation is compensated by the decrease of the entropy due to the external periodic field. It is shown that the equilibrium PBS are essentially the “self-organizing systems” that can arise spotaneously in a metastable state of ferromagnet.
Cite this paper
V. Nietz, "Precessing Ball Solitons as Self-Organizing Systems during a Phase Transition in a Ferromagnet," Applied Mathematics
, Vol. 4 No. 10, 2013, pp. 78-83. doi: 10.4236/am.2013.410A3010
 P. Glansdorff and I. Prigogine, “Thermodynamic Theory of Structure, Stability and Fluctuations,” Wiley and Sons, London, 1971.
 G. Nicolis and I. Prigogine, “Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations,” Wiley and Sons, London, New York, 1977.
 H. Haken, “Advanced Synergetics, Instability Hierarchies of Self-Organizing Systems and Devices,” Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983.
 D. Kondepudi and I. Prigogine, “Modern Thermodynamics: From Heat Engines to Dissipative Structures,” Wiley and Sons, Chichester, 1998.
 A. M. Zhabotinskiy, “Oscillatory Processes in Biological and Chemical Systems,” Moscow, 1967. (in Russian)
 A. M. Zhabotinskiy, “Biophysics,” Vol. 9, 1964, p. 306. (in Russian)
 S. Chandrasekhar, “Hydrodynamic and Hydromagnetic Stability,” Oxford, 1961.
 V. Nietz, “Kinetics of Precessing Ball Solitons in Ferromagnetic at the First-Order Transition,” European Physical Journal B, Vol. 85, 2012, p. 133.
 L. D. Landau and E. M. Lifshitz, Physikalische Zeitschrift der Sowjetunion, Vol. 6, 1935, p. 153.