Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1993-12-21
Nonlinear Sciences
Chaotic Dynamics
LaTeX, 3 PostScript figures,(E-mail: ami@ami.e-burg.su)
Scientific paper
10.1088/0305-4470/26/23/014
A set of equations according to which the conducting medium consists of two fluids - laminar and vortex, has been obtained in the present paper by transforming MHD equations. In a similar way, an electronic fluid is assumed to consist of a laminar and a vortex fluid. This system allows one to study the formation and the dynamics of large-scale hydrodynamic fluctuations. From this model a model of a non-equilibrium phase transition belonging to a class of the Lorenz-type models has been developed [Lorenz E N 1963 J. Atmos. Sci. {\bf 20} 130]. Vortex structures resulting in the increase in an effective resistance of the conducting medium and the interruption of current have been shown to appear even at constant transport coefficients in a laminar electronic fluid. Critical exponents of the parameters of an order (amplitudes), which for a direct current coincide with the critical exponents in the Lorenz model, have been found. A spatial scale of the structure described by the theory is in good agreement with experiment. A further evolution of vortex structures has been shown to occur by splitting the spatial scale. A similarity, according to which the following sequence of splitting takes place: {\({k_0}{\rightarrow}{k_1}=0.5{k_0}{\rightarrow} {k_2}=2{k_0}{\rightarrow}{k_3}=2{k_2}\)}, etc. has been hypothesized.
Iskoldsky Alexander M.
Volkov Nickolas B.
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