Abstract
Abstract In this chapter we particularize the general results of Chapters 3 and 4 to the first nontrivial terms in the low frequency expansions known as Rayleigh approximations or Rayleigh terms of both the near and the far fields. Also included are the leading terms in the scattering cross sections. These results are given for general shapes in terms of the potential functions to which they have been reduced in Chapters 3 and 4. For acoustics and electromagnetics, most of the material in this chapter refers to results obtained in the 1960s and the 1970s by a number of researchers such as D. S. Jones, R. E. Kleinman, T. B. A. Senior, V. Twersky, J. Van Bladel and many others. The corresponding material in elasticity was developed in the 1980s by G. Dassios, K. Kiriaki, D. Polyzos and others.
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