About some applications of the theory of block structures in Earth sciences, seismology, building and construction and material science

Abstract

The work discusses the issues of using the theory of block structures in related fields and demonstrates the ways of its application. The theory of block structures makes it possible to study physical-and-mechanical fields in an aggregate of contacting domains occupied by the media with different properties. This theory can be used in the applications in various fields of science, i.e. mechanics of a deformable solid, material science, seismology, geophysics, acoustics, building and construction, technical sciences and engineering applications. In theoretical physics and quantum mechanics, crystallography, construction of large integral schemes, acousto-electronics, methods of the theory of block structures can be convenient components of the research. The theory of block structures is much more complex in development than the theory of layered structures, which is considered to be studied in detail. To develop this theory, mathematical methods are applied, which are rarely used in other applications, such as topological algebra, external analysis, theory of functions of many complex variables, multivariable Leray residue forms, and matrix-functions factorization. Matrix-functions factorization, which is not required in the theory of layered structures, is an integral component of the developed theory of block structures.