Related papers: Homogenization of one-dimensional layered and grad…
Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
Propagation of high amplitude acoustic pulses is studied in a 1D waveguide connected to a lattice of Helmholtz resonators. An homogenized model has been proposed by Sugimoto (J. Fluid. Mech., \textbf{244} (1992)), taking into account both…
We derived the geometrical parameters on the tube connections that homogenize the pressure drop in a multi-chamber vacuum system, where each chamber has a distinct volume and all are connected to the same vacuum pump. We start deriving the…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short- and long-range…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
A new construction of decomposition smoothness spaces of homogeneous type is considered. The smoothness spaces are based on structured and flexible decompositions of the frequency space $\mathbb{R}^d\backslash\{0\}$. We construct simple…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
We propose and analyze an HDG scheme for the Laplace-domain interaction between a transient acoustic wave and a bounded elastic solid embedded in an unbounded fluid medium. Two mixed variables (the stress tensor and the velocity of the…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff elastic matrix. We employ…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
Homogenization of a simultaneous heat and moisture flow in a masonry wall is presented in this paper. The principle objective is to examine an impact of the assumed imperfect hydraulic contact on the resulting homogenized properties. Such a…
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…