Related papers: High-Contrast Transmission Resonances for the Lam\…
We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.
We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the…
A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…
Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering…
In this article, we present scattering and localization phenomena in a thin elastic plate comprising an aperiodic arrangement of scatterers. By analysing the form factor of the scattering cluster, we sample the reciprocal space which shows…
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of…
We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…
Different classes of physical systems with sizeable electron-phonon coupling and lattice distortions present anomalous resistivity behaviors versus temperature. We study a molecular lattice Hamiltonian in which polaronic charge carriers…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…
Response of a normally excited preloaded Hertzian contact is investigated in order to analyze the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…
We develop a classification of perfectly transmitting resonances occuring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…
We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been…
The theory of the high temperature superconducting cuprates, which is based on the condensation of holes into strings in checker-board geometry, was successful to explain the elastically scattered Neutrons by spin waves. Here it is extended…
Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…