Localized and pseudolocalized stationary elastic waves at a plane defect in a crystal

Quantization of Energy in 1D Model of Crystal Lattice with Local Perturbations Induced by Ion-Beam Impact

“…In this case, we consider only interaction between the nearest neighbours of each ion, that means that only those members in the sum (8) are nonzero indexes of which are satisfying the conditions s = n-1, s = n and s = n+1. Owing to (12) and (14), the potential energy of linear chain in the tight binding approximation can be written as: Given the large number of ions in the chain, the solution of the problem changes only insignificantly if the index of each member in the last two sums in the right side of relation [18] will be reduced by one (i.e. [22] for the reason of transformation of formula (20) to different representation.…”

“…For example in ref. (18), the boundary conditions consist of a local perturbation of the elastic moduli at the interface.…”

Excitation of Bulk Spin Waves by Acoustic Wave at the Plane Defect of a Ferromagnet

“…Let's consider the magnetically homogeneous system with equal magnetic parameters, i.e., tM 01 u tM 01 u M 0 , α α 1 pzq α 2 pzq and β β 1 pzq β 2 pzq, extended also on the interface, i.e., we will treat the whole system as a homogeneous media for SWs. The solution of the wave equation for KAW is [9]: …”

“…As comes from the symmetry considerations of coupled LandauLifshitz (LL) and wave motion equations, Rayleigh wave couples linearly to the forward volume SW, while Love wave couples linearly to the Damon-Eshbach mode. In the long-wavelength limit, the Love wave can be approx- * corresponding author; e-mail: yuleva1313@gmail.com imated by the solution given by Kosevich [9] for a shear horizontal wave localized at the planar defect. We will further refer to this localized wave as a "Kosevich wave" (KAW).…”

Dissipative interaction and anomalous surface absorption of bulk phonons at a two-dimensional defect in a solid

“…In the case of a homogeneous 2D defect which does not possess complex internal structure and intrinsic dynamical degrees of freedom, these boundary conditions can be reduced in the simplest case to the continuity of the elastic displacements u i and to the discontinuity of surface-projected bulk stresses σ zi , i = 1, 2, 3 (for more general boundary conditions which account for the discontinuity both of surface-projected bulk stresses and elastic displacements, see Refs. [5,15]). For the problem under consideration, the following boundary conditions will be used: u (1) x − u (2) x = 0, u (1) z − u (2) z = 0, ( 5)…”