On fractal theory in radio engineering, micro- and nanoelectronics

A.A.Potapov

Russia

Main results of theoretical and experimental investigations since eighties of XX that led to formation and developing of new fundamental science discipline: "Fractal Radio Physics and Fractal Radio Electronics: Fractal Radio Systems Designing" are briefly classified in the paper. For a long time stationary behaviors and periodical motions were assumed to be the only possible conditions. However the discoveries of the latter part of XX century principally changed our idea of dynamic processes behavior. Now we realize that our world is not only non-linear but also is fractal. At present the lack of conventional physical models is obviously felt. In other words the full description of signals and fields up-to-date processing is impossible via classical mathematics formulas.

It is absolutely evident for the author that the application of scale invariance ("scaling") conceptions and of modern functional analysis, which are related with set theory, theory of fractional dimension, general topology, geometrical measure theory and dynamic systems theory, to modern informational technologies reveals great potential opportunities and new prospects in multidimensional signals processing and in the related scientific and technical areas. In the end of XX century the possibility of assuming the fractals as a basis of new idea in radio physics and radar appeared due to fractal conception creation by B.Mandelbrot. Therefore since the eighties of XX century the author and his subordinate team intensively and successively search the new radio physical approaches that somehow or other related to application of fractal theory, deterministic chaos, scaling effects and fractional operators. Twenty first century is characterized by broad development of the large new radio physical applications that totally standing on ground of the fractal conceptions proposed by the author.

In fact, it is a question of new fundamental trend in radio physics and radio electronics - application of fractal theory, deterministic chaos theory, fractional measure and scaling invariants in the problems of radio systems and different oriented elements self-descriptiveness increase. The main principles of this trend are worked up by the author, as mentioned above, in IREE RAS since the eighties of XX century. In the beginning these principles concerned the issues of super poor radio signals and images filtration in essentially non-Gaussian noise. Then it became absolutely clear that such a "fractal" approach is useful also for other problems.

It is necessary note, that the effectiveness of radio physical investigations can be significantly improved by taking into account fractality of wave phenomena that are progressing at every stage of wave radiation, scattering and propagation in different mediums. The fundamental steps consisted in transfer of integer measuring signals received by radio system into fractional measuring space using scaling relations, allow to introduce absolutely new conceptions and approaches in conventional fields of the classical radio physics and radio electronics and to obtain sufficiently unexpected for practice but physically validated results on the basis of these conceptions (see references). Basic difference between fractal and classical radio physics is due to principally different approach to the main components of a signal and a field.

Fractal theory formation - striking example of new science trend that is based equally on both progress in abstract mathematics areas and on a new view on a long known empiric material which could not be interpreted and described scientifically before the valid models appear. Basing on a great explanatory power the fractal theory stimulates the natural science development. Fractal theory application allows us to discover a great deal of previously unused reserves and to apply it in different technical applications field.

Thus progressive advance of conceptions of the numerous reports, articles and monographs which are presented in Bibliographic list allows to formulate the main principles and methods of physical construction of fractal radio systems and fractal radio elements.

The author makes bold to state that the approach briefly present here defines new stage of the radio physics and radio electronics development.