On-off intermittency and hard turbulence in the flow of fluid in the magnetic field

Abstract

This work provides an analysis of experiments in which various modes of mercury flow in a constant external magnetic field were observed; we examined the temperature oscillations in the mercury flow in a heated pipe at various Reynolds and Hartmann numbers. In some modes, the temperature oscillations have specific forms of strong aperiodic “bursts” over the weak irregular background, which are specific to the developed turbulent flow. To determine the nature of these temperature oscillations and the characteristics of the fluid flow, we examined them through the apparatus of nonlinear dynamics. The totality of all the results (autocorrelation function, correlation integral, maximum Lyapunov exponents, and Fourier transform) provide evidence of the chaotic nature of the observed flow modes despite the relative weakness of high-frequency harmonics in comparison to low-frequency ones. In the case of separate bursts of turbulence, the duration of the laminar phase τ follows the known distribution ∼τ–3/2, derived from the theory of on-off intermittency.

Chaotic intermittency with non-differentiable M(x) function

“…Figures 2 and 3 show the complete M (x) function and the RPD function, respectively. The M (x) function is given by equations ( 16)-( 17), and the RPD function is determined by Equation (12). From the figures, we observe that the theory here described works accurately regarding the numerical results.…”

“…First, we study the case with reinjection overlap or superposition in the lower part of the laminar interval. Then, the complete RPD function results in equation (12), Where k is a real number, and b is evaluated from the normalization condition, which is (see [1,2])…”

“…The laminar or regular phases are pseudo-equilibrium or pseudo-periodic solutions, while the bursts correspond to chaotic evolution [1][2][3]. The phenomenon of chaotic intermittency has been found in different fields of science as physics, chemistry, medicine, engineering, and economics [4][5][6][7][8][9][10][11][12][13][14][15][16]. Therefore, a better description and understanding of the chaotic intermittency phenomenon would contribute to several fields of knowledge.…”

“…Figure3RPD function given by map given by equation(12) for a1 = 0.9, a2 = 2, ε = 0.001, and x = −0.2. Black points: theoretical RPD function.…”

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

“…25,26 The Lorentz group is a Lie group of symmetries of the Minkowski spacetime in special relativity. Many physics laws, equations, and theories, e.g., Maxwell's field equations in the theory of electromagnetism, 27,28 the Dirac equation in the theory of the electron, 29,30 and the Standard Model of particle physics, 31,32 respect the Lorentz symmetry. Besides, in engineering, the Lorentz group is also used to characterize the catadioptric fundamental matrices that are applied to study the catadioptric cameras.…”