Abstract: There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems sym...

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster’s model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave...

Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical pen-and-paper p...

We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component....

[1] A general acoustic model for a frequency sweep rod-liquid-rod interferometer applicable to high-temperature silicate liquids is presented. The wave propagations in the acoustic model are solved according to the accurate elastic wave equation and the acoustic wave equation. The solutions indicate that when a pulsed wave is sent down a buffer rod, which is partially immersed in a silicate liq...

We first review the basic existence results for exterior boundary value problems for the Helmholtz equation via boundary integral equations. Then we describe the numerical solution of these integral equations in two dimensions for a smooth boundary curve using trigonometric polynomials on an equidistant mesh. We provide a comparison of the NystrGm method, the collocation method and the Gale&in ...