Related papers: On the problem of comparing graded metamaterials
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…
In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
Layered metal-dielectric metamaterials have filtering properties both in the frequency domain and in the spatial frequency domain. Engineering their spatial filtering response is a way of designing structures with specific diffraction…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
Most calibration schemes for reflection-based tissue spectroscopy in the mm-wave/THz-frequency range are based on homogenized, frequency-dependent tissue models where macroscopic material parameters have either been determined by…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two…
The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…
Optimization of functionally graded metamaterial arrays with a high dimensional and continuous geometric design space is cumbersome and could be accelerated via machine learning tools. Mechanical metamaterials can manipulate acoustic or…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective…
We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling…
We present the sliding basis computational framework to automatically synthesize heterogeneous (graded or discrete) material fields for parts designed using constrained optimization. Our framework uses the fact that any spatially varying…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…
Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…
In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such…