Agnes Lamacz

Dispersive effective models for waves in heterogeneous media

We study the long-time behavior of waves in a strongly heterogeneous medium, starting from the one-dimensional scalar wave equation with variable coefficients. We assume that the coefficients are periodic with period e and e > 0 is a small length parameter. Our main result concerns homogenization and consists in the rigorous derivation of two different dispersive models. The first is a fourth-order equation with constant coefficients including powers of e. In the second model, the e-dependence is completely avoided by considering a third-order linearized Korteweg–de Vries equation. Our result is that both simplified models describe the long-time behavior well. An essential tool in our analysis is an adaption operator which modifies smooth functions according to the periodic structure of the medium.

Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations

We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in

Effective Maxwell Equations in a Geometry with Flat Rings of Arbitrary Shape

\mathbb{R}^n

A well-posed hysteresis model for flows in porous media and applications to fingering effects

,

Dispersive homogenized models and coefficient formulas for waves in general periodic media

n\in\{1,2,3\}

Effective acoustic properties of a meta-material consisting of small Helmholtz resonators

. Standard homogenization theory provides, for the limit of a small periodicity length

Dispersive effective equations for waves in heterogeneous media on large time scales

\varepsilon>0

Outgoing wave conditions in photonic crystals and transmission properties at interfaces

, an effective second order wave equation that describes solutions on time intervals

Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

[0,T]

A negative index meta-material for Maxwell´s equations

. In order to approximate solutions on large time intervals