Periodic current bursts observed in the dynamic current-voltage characteristic of a probe in the presence of a plasma fireball in dynamic state were modeled in the frame of the scale relativity model, based on both the fractal space-time concept and the generalization of Einstein’s principle of relativity to scale transformations. The bursts appear in the probe characteristic when a certain relation exists between the fireball dynamics frequency and the frequency of the probe voltage sweep. The double layer dynamics is described by a set of time-dependent Schrödinger-type equations and the self-structuring is given by means of the negative differential resistance. The obtained experimental and theoretical results are proven to be in very good agreement.

No abstract

Considering that the motions of the particles take place on fractals, a nondifferentiable mechanical model is built. Only if the spatial coordinates are fractal functions, the Galilean version of our model is obtained: the geodesics satisfy a Navier-Stokes-type of equation with an imaginary viscosity coefficient for a complex speed field or respectively, a Schrödinger-type of equation or hydrodynamic equations, in the case of irrotational movements. Moreover, in this approach, the analysis of the fractal fluid dynamics generates conductive properties in the case of movements synchronization both on differentiable and fractal scales, and convective properties in the absence of synchronization (e.g. laser ablation plasma is analyzed). On the other hand, if both the spatial and temporal coordinates are fractal functions, it results that, the geodesics satisfy a Klein-Gordon-type of equation on a Minkowskian manifold.

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.

Considering that the motions of the particles take place on ‘arbitrary’ fractals, an extended hydrodynamic model of the scale relativity is built. In this approach, static (particle in a box) and time-dependent (free particle) systems are analyzed. The particle in a box can be associated with a fractal fluid: the zero value of the real (differentiable) part of the complex speed field specifies the coherence, while the non-zero value of the imaginary (non-differentiable or fractal) part implies, through a quantization relation, a Reynolds criterion. For a minimal value of the Reynolds number, a Heisenberg's ‘egalitarian’ relationship results, whereas for big Reynolds numbers, the flow regime of the fractal fluid becomes turbulent. In such a context, the microscopic–macroscopic scale transition could be associated with an evolution scenario towards chaos. The free time-dependent particle can be associated with an incoherent fractal fluid: the differentiable and fractal components of the complex speed field are inhomogeneous in fractal coordinates due to the action of a fractal potential. There exists a momentum transfer on both speed components and the ‘observable’ in the form of a uniform motion is generated through a specific mechanism of ‘vacuum’ polarization induced by the same fractal potential.