Spectra of the Neumann Square Lattices
The classical 1D Pauling model of a planar square lattice of thin 3D acoustic waveguides involves the Kirchhoff transmission conditions at nodes of the graph.
Though this model does not provide an adequate description of the spectrum of the Neumann Laplacian in the 3D domain, because it indicates eigenvalues of infinite multiplicity (collapsed spectral bands) as well as it does not find open spectral gaps.
During his seminar, Prof. Narazor will present a refined 1D model which involves the Steklov-Robin transmission conditions at nodes and which is based on the two-term asymptotic decompositions. Thanks to this model, it can be demonstrated that the spectral bands in the low- and middle-frequency range cannot collapse and, indeed, a very narrow spectral gap may appear near them.