We present an effective model of “space-coiled metacrystals” composed of a periodic array
of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block …

This paper deals with the existence of guided waves and edge states, in particular two-
dimensional media obtained by perturbing a reference periodic medium with honeycomb …

We study the band structure of self-adjoint elliptic operators A_g=-∇⋅g∇, where \sigma_g
has the symmetries of a honeycomb tiling of R^2. We focus on the case where g is a real …

We consider the bifurcations of standing wave solutions to the nonlinear Schr\" odinger
equation (NLS) posed on a quantum graph consisting of two loops connected by a single …

We leverage quantum graph theory to quickly and accurately characterise acoustic
metamaterials comprising networks of interconnected pipes. Anisotropic bond lengths are …

The goal of this thesis is to develop efficient numerical methods for the solution of the time-
harmonic wave equation in quasiperiodic media, in the spirit of methods previously …

The spectrum of the Dirichlet problem on the planar square lattice of thin quantum
waveguides has a band-gap structure with short spectral bands separated by wide spectral …

This work analyzes structural waves that propagate freely along taut cables, characterized
by a discrete array of scatter elements. The outcomes underline the role played by the …

Trapping and transmission of waves through an acoustic waveguide with a set of perforated
cross-walls are studied. Eigenvalues of the corresponding spectral Neumann problem for …

We study the essential spectrum of a formally self-adjoint system of partial differential
equations, for example the elasticity system, in periodic domains with non-periodic …