"Physical basis of the self-organization at critically concept"
The theory of the self-organized at critically concept suggests a general interpretation of signals of all sizes and durations produced when a dynamic system, driven in a critical state, produces chain reactions. Usually the self-organized at criticality concept is related to the ubiquity of flicker noise experimentally emphasized by the presence of a 1/f power spectra. Because systems revealing flicker noise contain many components and are governed by different kinds of interactions it was not possible hitherto to construct a mathematical model to be both totally realistic and theoretically manageable. In this paper we will show that chain reactions in plasma conductors are related both to the instability whose result is a structure emerged after self-organization as well as to its spontaneously de-aggregation (catastrophic disruption). For proving this we appeal to a new phenomenological model of self-organization suggested by plasma experiments . Its consideration offers, in our opinion, the physical basis for the missed realistic theoretical model of flicker noise and implicitly to the concept of self-organization at criticality. As known, flicker noise appears in plasma devices in connection with the emergence and de-aggregation of complex space charge configurations (CSCC) . Similarly with the “construction” of the sand-pile, the self-assembling of the CSCC can also be controlled by the experimentalist. This is not the case when the CSCC reaches the critical state for which it de-aggregates. Since during the breakdown (collapse) of the framework of the CSCC chain processes of different sizes and durations are produced the system emits electrical signals whose frequency distribution reveals the presence of flicker noise. This distribution is related to the energies stored in the electric fields of the different patterns of the CSCC framework, which are released during its de-aggregation. Thus the double layer (DL) as a whole disrupts because of the presence of stochastic phenomena in time intervals in the range of 10-2 s. Between every disruption the DL performs a proper dynamics with frequencies of around tens of kHz. Signals of hundred of MHz are emitted during every disruption of the DL since this involves the release of the electric fields energy stored in the structure of “mini-double layers” located at its negative side. The superposition of these durations explains the appearance of the 1/f spectra in the current transported by the plasma conductor. Related to the flicker noise is the anomalous transport of matter and energy whose intrinsic mechanism is another challenging problem with interest for all branches of science. Since matter and energy are stored in every DL during its self-assembling phase, it is evident that its detachment from the CSCC and its propagation through the conductor, followed by its de-aggregation, involve a transport that can not be described by the classic transport theories. References: M. Sanduloviciu et al., Chaos, Solitons & Fractals 17 (2003) 183 and 203, and the references therein.