Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions
is investigated. It is shown that if the tube is non-straight and its curvature vanishes …

A brief survey on graph models for wave propagation in thin structures is presented. Such
models arise in many areas of mathematics, physics, chemistry and engineering (dynamical …

We consider a pair of parallel straight quantum waveguides coupled laterally through a
window of a width l in the common boundary. We show that such a system has at least one …

We consider a quantum mechanical particle living on a graph and discuss the behaviour of
its wavefunction at graph vertices. In addition to the standard (or-type) boundary conditions …

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long
cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid …

Abstract We consider the Dirichlet Laplacian for astrip in R^ 2 with one straight boundary
and a width a (1+ λ f (x)), where f is a smooth function of acompact support with a length 2 b …

We consider rectangular graph superlattices of sides l 1, l 2 with the wave-function coupling
at the junctions either of the δ type, when they are continuous and the sum of their …

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary
conditions in an open geometry given by two straight leads of the same width which cross at …

We discuss the Nöckel model of an open quantum dot, ie a straight hard-wall channel with a
potential well. If this potential depends on the longitudinal variable only, there are …

We study the nature of the essential spectrum of the Dirichlet Laplacian in tubes about
infinite curves embedded in Euclidean spaces. Under suitable assumptions about the decay …