Related papers: Macroscopic Wave Propagation for 2D Lattice with R…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…
This paper introduces a micro-lattice based metamaterial for low frequency wide-band vibration attenuation, that is enabled by engineering the metamaterial's building blocks to induce local resonance bandgaps for elastic waves in all…
We present a systematic theoretical and numerical investigation of the propagation properties of linear magnetohydrodynamic (MHD) waves in a spatially periodic magnetic field, referred to as a magneto-lattice. Two types of central…
We study time-harmonic scattering by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength…
We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a…
In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation (WKE). This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
Fully coherent searches (over realistic ranges of parameter space and year-long observation times) for unknown sources of continuous gravitational waves are computationally prohibitive. Less expensive hierarchical searches divide the data…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…
We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
We establish long-time existence and uniqueness for the 2D wave equation with a harmonic potential in one direction. This proof relies on a fine study of the so-called space-time resonances of the equation. Then we derive a resonant system…
In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections.…