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.

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Implications of the fractal potential in the system dynamics using an extended scale relativity model assuming the fractal character of the particle movements, are established. So, in the dissipative approximation of the model it is shown that the fractal potential comes from the non-differentiability of the space-time, i.e. by means of imaginary part of a complex speed field. In the dispersive approximation of the same model, the fractalization of the differential part of the complex speed field induces a normalized fractal potential which controls through coherence the system dynamics. In such context the type I superconductivity results: the temperature dependences of the superconducting parameter, the accumulator effect etc.

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