Lamellar heterogeneous objects with interfaces. Using transfer matrices in applications
In this paper heterogeneous subjects are investigated, namely laminated nanoparticles and flat-layered media. Common feature of objects under consideration is presence of surfaces divided into slabs with different physical characteristics. The aim of the work is to demonstrate large possibilities and certain preferences of transfer matrices method for solution different problems of applied physics and generalization of the results taken out by author early. The method is especially convenient for analysis of such systems under action of different external physical fields. The method makes possible to transfer boundary conditions from slab to slab, to avoid the necessity of consideration of high order algebraical systems and matrices inversion problem is reduced to theirs simple multiplication. We presented a general scheme of building transfer matrices based on conversion of partial differential equations to ordinary differential equations with using expansion by a system of orthogonal functions. In addition to known results, the transfer matrices for inhomogeneous differential equations are constructed, i.e. those for physical systems with internal energy sources. Transfer matrix method has been used to solve some applied problems, especially problems of electromagnetic scattering on ellipsoidal nanoparticles (electrostatic approximation), spherical particles (electrostatic and wave approximations), expressions for calculations of electrical energy in slabs are found. Solution of Eigen value problems for multilayer panels is constructed, design formulas for determination of oscillation Eigen frequencies of multilayer panel with using three-dimensional elasticity theory are also obtained. Design formulas and some typical artwork are presented.