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Current Status of Radio Physical Applications of Fractals, Fractional Operators and Scaling


A.A. Potapov

It's increased now the interest to the recognition of such conception as simplicity and complexity, recognition of different unique features of complex systems of organic and inorganic nature, including dissipative, self-organization, fractional, scaling, non-Markovian, non-Gaussian, linear and non-linear response on the exposure. One of the main signal analysis problems, made by complex systems is adequate parameterization of the contributions characterized by formed investigation signal. Features of complex systems are commonly becomes at the different space/time scales. More adequate estimations of the investigated system state and dynamic of the state changes of subsystem are realize by using fractal theory and signal processing in space of fractal dimension with indispensable accounting of scaling effects, what was the first suggested and developed by author. Creation of the first standard fractal sign dictionary of the aim classes and constant improvement of the algorithm support are the main stages in development of the first in the world fractal non-parametric soft signal detection. Formerly author with members of the Central Design Department “ALMAZ” (1990 – 1992 years) was worked on the design first in the Russia fractal slit antenna (it was exotica at that time) in the range of millimeter wave length. In spite of classical methods, where a smooth radiation pattern were synthesized, in the base of fractal synthesis theory was putted the idea of radiation characteristic realization with repeated structure on the arbitrary scale. This gives us an ability to create new regimes of fractal electrodynamics, and also give principal new features. Physical modeling of fractional integral and differential operators allows us on the base of nanotechnology create a radio elements on the passive elements, modeled fractal impedance with a frequency scaling. In the article the main results of theoretical and experimental investigations carried by the author since eightieth years of XX century resulting in formation and de-velopment of new fundamental scientific direction "Fractal radio physics and fractal radio electronics: Designing of fractal radio systems" have been briefly systematized. It has been shown that fractals, fractional operators and scaling are important investigation instrument which is good adapted both practice needs and abstract constructions of modern mathematics. Using of the term “fractal” in the radio physic is not only reasonably, but it’s necessary. It is needed a principal changes in a preconceived idea in the work of scientists and engineers. Now we are free on psychological chains of the hypothesis, which give a special role to smooth analog continuously differentiable functions and integer-valued measures. Search of possible fractal methods and fractional operators applications can’t be started from the attempt to solve know problems, cause who are used to continuously differentiable functions and integer-valued measures, will never leave the scope of problems having a simple solution.

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