Fractals in wave processes
V.V. Zosimov a
L.M. Lyamshev b
a Research Institute of Applied Acoustics, Dubna, Moscow Region, Russian Federation
b N.N. Andreev Acoustics Institute, Russian Academy of Sciences, ul. Shvernika 4, Moscow, 117036, Russian Federation
A review of fundamental results on fractal structure manifestation in wave processes is presented. Elastic properties and dispersion of fractal materials are discussed; their distribution density, and the shape of wave functions of their localised elastic oscillations, fractons. Examples of their application for the explanation of amorphic properties of solids are presented. Patterns of wave scattering and emission by fractal structures are examined. Principal methods of random signal analysis employed to reveal different fractal structures associated with these signals are described. Data on fractal properties of wave fields are discussed.