Experimental and theoretical evidence for the chaotic dynamics of complex structures

Abstract

This paper presents the experimental results on the formation, dynamics and evolution towards chaos of complex space charge structures that emerge in front of a positively biased electrode immersed in a quiescent plasma. In certain experimental conditions, we managed to obtain the so-called multiple double layers (MDLs) with non-concentric configuration. Our experiments show that the interactions between each MDL's constituent entities are held responsible for the complex dynamics and eventually for its transition to chaos through cascades of spatio-temporal sub-harmonic bifurcations. Further, we build a theoretical model based on the fractal approximation (scale relativity theory) in order to reproduce the experimental results (plasma self-structuring and scenario of evolution to chaos). Comparing the experimental results with the theoretical ones, we observe a good correlation between them.

Dynamics Control of the Complex Systems via Nondifferentiability

“…We note that the results from the present paragraph permit the chaoticity and self-structuring control by means of nondifferentiability. Thus the experimental results on the formation, dynamics, and evolution towards chaos of complex space charge structures that emerge in front of a positively biased electrode immersed in a quiescent plasma from [20] are in agreement with our previous theoretical results.…”

“…This topic was developed in [12][13][14][19][20][21][22][23] using the scale relativity theory (SRT) [12][13][14]. In the framework of SRT we assume that the movements of complex system entities take place on continuous but nondifferentiable curves (fractal curves) so that all physical phenomena involved in the dynamics depend not only on the space-time coordinates but also on the space-time scales resolution.…”

“…The first equation 9is the momentum conservation law, the second equation 10is the density conservation law, and they define together the fractal hydrodynamics (FH) model. We note that, for Peano-type movements in fractal dimension = 2 and supposing that fractal potential is assimilated with the pressure, the fractal hydrodynamic model becomes the standard hydrodynamic (for details see [19][20][21][22][23]).…”

Solid components separation from heterogeneous mixtures through turbulence control

“…Plasma is a very favourable medium for the development of instabilities and transitions to chaos, a large variety of scenarios of transition to chaos being experimentally observed: intermittencies [64,65], quasi-periodicity (Ruelle-Takens scenario) [66,67], period doubling (Feigenbaum scenario) [68,69], cascade of sub-harmonic bifurcations [70,71], or torus breakdown [72]. It can be described as a fluid governed by a combination of Maxwell's equations and Navier-Stokes equations.…”

Fractal Information by Means of Harmonic Mappings and Some Physical Implications

“…These instabilities imply both chaos through different routes (intermittencies, quasi-periodicity, cascade of period-doubling bifurcations, sub-harmonic bifurcations, torus breakdown) and self-structuring through the generation of complex structures [3][4][5]. According to the classical concepts, all theoretical complex systems models (fluid models, kinetic models, etc.)…”