Related papers: Bloch Spectra for High Contrast Elastic Media
We introduce the concept of effective phononic crystals, which combine periodicity with varying isotropic material properties to force periodic coefficients in the elastic equations of motion in a non-Cartesian basis. Periodic coefficients…
We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized…
We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a unified method based on layer potential techniques to…
The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to be a fractal function of the so-called electric matching ratio which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a…
The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…
A method for homogenization of a heterogeneous (finite or periodic) elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations.…
Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable…
Using adiabatic expansions formalism, upper bounds for interband transitions for Bloch electrons in slowly varying in time electric fields are obtained. These bounds imply the validity of one-band approximation on long time scales.
The radiation dynamics of a dipole antenna embedded in a Photonic Crystal are modeled by an initially excited harmonic oscillator coupled to a non--Markovian bath of harmonic oscillators representing the colored electromagnetic vacuum…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…
We study Bragg spectroscopy of strongly interacting one dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard…
This paper is concerned with the high-frequency homogenization of bubbly phononic crystals. It is a follow-up of the works [H. Ammari et al., Sub-wavelength phononic bandgap opening in bubbly media, J. Diff. Eq., 263 (2017), 5610--5629]…
We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of three-dimensional linear…
An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in…
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an…
We derive analytical solutions based on singular Green's functions, which enable efficient computations of scattering simulations or Floquet-Bloch dispersion relations for waves propagating through an elastic plate, whose surface is…
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the…