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In recent times the idea of cloaking has become very popular. After radar and sonar were discovered, problems of "visibility" reduction for physical bodies in air (by electromagnetic waves) or in water (by acoustical waves) have immediately become serious areas of research in physics. New technologies (sensors, actuators) of high spatial-temporal resolution, metamaterials and new computers with fast and accurate calculations, in combination with nontraditional versions of solutions to these boundary problems, have allowed physicists to obtain successful results in some cases. This e-book presents a rare attempt to understand the cloaking problem as a whole. The book should be useful for readers with a strong interest in contemporary problem solving approaches in the physics of waves.

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The conceptual possibilities of the design of thin absorbing (non-reflecting) coatings are considered using simple acoustical and mechanical models. Coating presents a thin layer with microscale stratification and fast time binary modulation of parameters following several algorithms of so-called cyclical wave-bolts. Algorithms of space-time modulation of the controlled layer's structure are thoroughly investigated for the one-dimensional boundary problem. These algorithms present: (a) control of boundary conditions in the discrete points; (b) control of the velocity of wave propagation; (c) control of the viscosity in layers. The algorithms do not require any measurements of the wave field and this removes the traditional stability problem for active systems. All kinds of control assume the existence of sufficient mechanical support or «vibrostat». Most of the algorithms of parametric control considered are converting low frequency incident waves into high frequency waves of technological range for which the waveguiding medium is assumed nontransparent (absorptive). Conditions for the effective application of all algorithms suggested have been formulated. It is shown that the absorbing layer can be arbitrarily thin relating to the minimum space scale of the incident wave and ensures effective absorption over a wide frequency range (beginning from zero frequency) limited only by finite space-time resolution of parametric control operations. On the base of one-dimensional boundary problems the structure of a 3-dimensional «black» parametric coating is formulated. The effectiveness of the absorbing coating does not depend on the incident wave direction. A general solution of the diffraction problem for this coating has been obtained through consideration of the object of disk shape. The possibilities of cyclical wave-bolt realization are based on the surplus of modern high space-time resolution in control, which is growing every year, relating to the space-time scales of location waves for instance remaining the same as years ago due to constant real conditions of far propagation.