20 citations · 96 across the 22 of their papers we have counts for
28 papers
Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer
Lucas Chesnel, Sergei A. Nazarov, Jari Taskinen
We investigate the spectrum of a Laplace operator with mixed boundary conditions in an unbounded chamfered quarter of layer. This problem arises in the study of the spectrum of the…
Spectrum of the Dirichlet Laplacian in a thin cubic lattice
Lucas Chesnel, Sergei A. Nazarov
We give a description of the lower part of the spectrum of the Dirichlet Laplacian in an unbounded 3D periodic lattice made of thin bars (of width ) which have a s…
Acoustic waveguide with a dissipative inclusion
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov +1
We consider the propagation of acoustic waves in a waveguide containing a penetrable dissipative inclusion. We prove that as soon as the dissipation, characterized by some coeffici…
Spectral gaps in a double-periodic perforated Neumann waveguide
Delfina Gómez, Sergei A. Nazarov, Rafael Orive-Illera +1
We examine the band-gap structure of the spectrum of the Neumann problem for the Laplace operator in a strip with periodic dense transversal perforation by identical holes of a sma…
Acoustic passive cloaking using thin outer resonators
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov
We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can prop…
Design of a mode converter using thin resonant ligaments
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov
The goal of this work is to design an acoustic mode converter. More precisely, the wave number is chosen so that two modes can propagate. We explain how to construct geometries suc…
Modeling of fluid flow in a flexible vessel with elastic walls
V. Kozlov, S. Nazarov, G. Zavorokhin
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue an…
Gaps in the spectrum of two-dimensional square packing of stiff disks
L. D'Elia, S. A. Nazarov
In this paper we investigate via an asymptotic method the opening of gaps in the spectrum of a stiff problem for the Laplace operator in perforated by contiguou…
Design of an acoustic energy distributor using thin resonant slits
Lucas Chesnel, Sergei A. Nazarov
We consider the propagation of time harmonic acoustic waves in a device with three channels. The wave number is chosen such that only the piston mode can propagate. The main goal o…
Band-gap structure of the spectrum of the water-wave problem in a shallow canal with a periodic family of deep pools
Sergei A. Nazarov, Jari Taskinen
We consider the linear water-wave problem in a periodic channel , which is shallow except for a periodic array of deep potholes in it. Motivated by applic…
Abnormal acoustic transmission in a waveguide with perforated screens
Lucas Chesnel, Sergei A. Nazarov
We consider the propagation of the piston mode in an acoustic waveguide obstructed by two screens with small holes. In general, due to the features of the geometry, almost no energ…
Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
Lucas Chesnel, Sergei A. Nazarov, Jari Taskinen
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct n…
Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
Lucas Chesnel, Sergei A. Nazarov
We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid va…
Trapped modes in armchair graphene nanoribbons
V. A. Kozlov, S. A. Nazarov, A. Orlof
We study scattering on an ultra-low potential in armchair graphene nanoribbon. Using the continuous Dirac model and including a couple of artificial waves in the scattering process…
Plummeting and blinking eigenvalues of the Robin Laplacian in a cuspidal domain
Sergei A. Nazarov, Nicolas Popoff, Jari Taskinen
We consider the Robin Laplacian in the domains and , , with sharp and blunted cusps, respectively. Assuming that the Robin coefficient is lar…
"Blinking eigenvalues" of the Steklov problem generate the continuous spectrum in a cuspidal domain
Sergei A. Nazarov, Jari Taskinen
We study the Steklov spectral problem for the Laplace operator in a bounded domain , , with a cusp such that the continuous spectrum of the problem…
Non reflection and perfect reflection via Fano resonance in waveguides
Lucas Chesnel, Sergei A. Nazarov
We investigate a time-harmonic wave problem in a waveguide. By means of asymptotic analysis techniques, we justify the so-called Fano resonance phenomenon. More precisely, we show…
Self-adjoint and skew-symmetric extensions of the Laplacian with singular Robin boundary condition
Sergei A. Nazarov, Nicolas Popoff
We study the Laplacian in a smooth bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and…
Criteria for the Absence and Existence of Bounded Solutions at the Threshold Frequency in a Junction of Quantum Waveguides
Fedor L. Bakharev, Sergei A. Nazarov
In the junction of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray with a positive…
Invisibility and perfect reflectivity in waveguides with finite length branches
Lucas Chesnel, Sergei A. Nazarov, Vincent Pagneux
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem…
Trapped modes in zigzag graphene nanoribbons
V. A. Kozlov, S. A. Nazarov, A. Orlof
We study a scattering on an ultra-low potential in zigzag graphene nanoribbon. Using mathematical framework based on the continuous Dirac model and augumented scattering matrix, we…
Perfect transmission invisibility for waveguides with sound hard walls
Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Sergei A. Nazarov
We are interested in a time harmonic acoustic problem in a waveguide with locally perturbed sound hard walls. We consider a setting where an observer generates incident plane waves…
Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner
Lucas Chesnel, Xavier Claeys, Sergei A. Nazarov
We investigate the eigenvalue problem in a 2D domain divided into two regions . We are interested in situations where …
A fractal graph model of capillary type systems
Vladimir Kozlov, Sergei Nazarov, German Zavorokhin
We consider blood flow in a vessel with an attached capillary system. The latter is modeled with the help of a corresponding fractal graph whose edges are supplied with ordinary di…