Wave Propagation in Bifurcated Waveguides of Square Lattice Strips

Wave scattering on lattice structures involving an array of cracks

“…The discrete Wiener-Hopf equation (46) has the same form as Eq. (2.23) in [19] and in fact it is almost identical to (2.8) in [23], hence, employing the same kind of, elementary, multiplicative factorization of the kernel L (following the section §2.4 of [23]), i.e., L = L + L − on A , we find…”

“…Analogous result holds for the reflectance R (95). This is a special form of expression for R and T as it coincides with that for the bifurcated waveguides [23]. The analysis of R and T for finite cracks is provided in Appendix B.…”

Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

“…Each particle of such discrete nanoribbon structure is assumed to possess unit mass, and, interaction with atmost its four nearest neighbours through linearly elastic identical (massless) bonds with a spring constant 1/b 2 . The notation follows that introduced for an infinite lattice [33,34] and the square lattice waveguides [36,35]. Due to nature of the problem, the displacement of a particle, located at the site indexed by its lattice coordinates (x, y) ∈ Z 2 in S N and denoted by u x,y , is complex valued.…”

“…where A ∈ C is constant. The symbol a (κ in )· represents the mode shape corresponding to the specific wave mode indexed by κ in (see [36] or Appendix C of [35] for the detailed expressions).…”

“…The discrete Fourier transform u F y of {u x,y } x∈Z is well defined for all relevant values of (fixed) y [35] in an annulus A in the complex plane (same as that defined in [35], R ± are given in Appendix A of [35], namely, equation (A.1) R + = e −κ2 , R − = e +κ2 ).…”