By S. Abdullaev
This special and well timed paintings is dedicated to the issues of ray idea of long-range wave propagation in frequently inhomogeneous media utilizing the trendy idea of dynamic structures. the writer, updating an previous box with smooth equipment, makes use of the final ideas of ray dynamics and a few rather uncomplicated notions of nonlinear dynamics to outline the topic, making the rading effortless for even non-specialists. the basic principles are before everything formulated with waveguides and resonators, and then the extra advanced difficulties of nonlinear ray dynamics in cellular and heterogeneous media are mentioned. This unique fabric encompasses such recommendations as nonlinear resonance, chaos, the devil's ladder, and kinetics.
S.S. Abdullaev is on the Institute for Biocybernetics, Uzbekistan Academy of Sciences, Tashkent. He has been specialising within the conception of wave propagation on the grounds that 1975.
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It is not realistic but, as a system of overlapping fractals, it has the essential feature. Since the Cantor set is a fractal with a simple construction procedure, it allows us to study in detail the statistics of the overlap of one fractal object on another. The two fractal overlap magnitude changes in time as one fractal moves over the other. The overlap (magnitude) time series can, therefore, be studied as a model time series of earthquake avalanche dynamics . The statistics of overlaps between two fractals are not studied much yet, although their knowledge is often required in various physical contexts.
Chaos and dynamics of rays in waveguide media by S. Abdullaev