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In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications,…

Optics · Physics 2022-08-17 Amgad Abdrabou , Ya Yan Lu

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…

Numerical Analysis · Mathematics 2020-03-24 Da Li , Keran Li , Wenyuan Liao

We consider a model of an electron in a crystal moving under the influence of an external electric field: Schroedinger's equation in one spatial dimension with a potential which is the sum of a periodic function $V$ and a smooth function…

Mathematical Physics · Physics 2022-08-23 Alexander B. Watson , Michael I. Weinstein

Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…

Analysis of PDEs · Mathematics 2024-02-22 Mitia Duerinckx , Antoine Gloria , Matthias Ruf

We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…

Analysis of PDEs · Mathematics 2010-08-03 Aurora-Mihaela Marica , Enrique Zuazua

Here, we report a numerical implementation of the nonlocal homogenization approach recently proposed in [M. Silveirinha, Phys. Rev. B 75, 115104 (2007)], using the finite difference frequency-domain method to discretize the…

Materials Science · Physics 2015-05-13 Joao T. Costa , Mario G. Silveirinha , Stanislav I. Maslovski

Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…

Pattern Formation and Solitons · Physics 2013-12-19 Jakob Löber , Markus Bär , Harald Engel

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system $$ D_t w -\nabla\cdot \vec z = \nabla\cdot \vec h(x,t,x/\varepsilon), \qquad w\in \alpha(u,x/\varepsilon), \qquad \vec z\in…

Analysis of PDEs · Mathematics 2014-10-14 A. K. Nandakumaran , Augusto Visintin

This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…

Analysis of PDEs · Mathematics 2025-08-07 Yong Zhang

We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions,…

Classical Physics · Physics 2016-04-27 Ory Schnitzer , Richard V. Craster

Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be…

Mathematical Physics · Physics 2025-08-22 Harold Berjamin , Stephan Rudykh

In homogenization theory and multiscale modeling, typical functions satisfy the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in the second variable and $\epsilon$ is the smallest relevant wavelength,…

Numerical Analysis · Mathematics 2014-08-26 Björn Engquist , Christina Frederick

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

Analysis of PDEs · Mathematics 2016-05-31 Fernando A. Morales , Daniel E. Restrepo

The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…

Numerical Analysis · Mathematics 2022-12-21 R. Sancho , V. Rey de Pedraza , P. Lafourcade , R. A. Lebensohn , J. Segurado

This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…

Probability · Mathematics 2016-09-09 Martin Hairer , Gautam Iyer , Leonid Koralov , Alexei Novikov , Zsolt Pajor-Gyulai

We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of…

Analysis of PDEs · Mathematics 2020-11-24 Vivek Tewary

The periodic cellular topology characterizing the microscale structure of a heterogeneous material may allow the finest functional customization of its acoustic dispersion properties. The paper addresses the free propagation of elastic…

Applied Physics · Physics 2018-03-12 Francesca Vadalà , Andrea Bacigalupo , Marco Lepidi , Luigi Gambarotta

We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…

Numerical Analysis · Mathematics 2020-06-30 Stefan Sauter , Céline Torres

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…

Probability · Mathematics 2010-05-14 Martin Hairer , Charles Manson