We adapt tools of transformation optics, governed by a (elliptic) wave equation, to thermodynamics, governed by the (parabolic) heat equation. We apply this new concept to an invibility cloak in ...order to thermally protect a region (a dead core) and to a concentrator to focus heat flux in a small region. We finally propose a multilayered cloak consisting of 20 homogeneous concentric layers with a piecewise constant isotropic diffusivity working over a finite time interval (homogenization approach).
Control of waves with metamaterials is of great topical interest, and is fueled by rapid progress in broadband acoustic and electromagnetic cloaks. We propose a design for a cloak to control bending ...waves propagating in isotropic heterogeneous thin plates. This is achieved through homogenization of a multilayered concentric coating filled with piecewise constant isotropic elastic material. Significantly, our cloak displays no phase shift for both backward and forward scattering. To foster experimental efforts, we provide a simplified design of the cloak which is shown to work in a more than two-octave frequency range (30 Hz to 150 Hz) when it consists of 10 layers using only 6 different materials overall. This metamaterial should be easy to manufacture, with potential applications ranging from car industry to anti-earthquake passive systems for smart buildings, depending upon the plate dimensions and wavelengths.
It was recently shown theoretically that the time-dependent heat conduction equation is form invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, ...fictitious transformed space can be mapped onto (meta)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a microstructured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating while maintaining the same downstream heat flow as without object and cloak.
Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated ...with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400-600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.
Electromagnetic cloaking, as challenging as it may be to the physicist and the engineer has become a topical subject over the past decade. Thanks to the transformations optics (TO) invisibility ...devices are in sight even though quite drastic limitations remain yet to be lifted. The extreme material properties which are deduced from TO can be achieved in practice using dispersive metamaterials. However, the bandwidth over which a metamaterial cloak is efficient is drastically limited. We design and simulate a spherical cloak which takes into account the dispersive nature of relative permittivity and permeability tensors realized by plasma-like metamaterials. This spherical cloak works over a broad frequency-band even though these materials are of a highly dispersive nature. We establish two equations of state that link the eigenvalues of the permittivity and permeability tensors in every spherical cloak regardless of the geometrical transformation. Frequency dispersive properties do not disrupt cloaking as long as the equations of states are satisfied in the metamaterial cloak.
Following the advent of electromagnetic metamaterials, researchers working in wave physics have translated concepts of engineered media to acoustics, elastodynamics and diffusion processes. In ...elastodynamics, seismic metamaterials have emerged in the last decade for soft soils structured at the meter scale, and have been tested with full-scale experiments on holey soils. Born in the soil, seismic metamaterials have emerged from the field of tuned-resonators buried in the soil, around building's foundations or near the soil-structure interface as local seismic isolators. Forests of trees have been interpreted as above-surface resonators, and coined natural seismic metamaterials. We first review some advances made in seismic metamaterials and dress an inventory of which material parameters can be achieved and which cannot, from the effective medium theory perspective. We envision future developments of large scale auxetic metamaterials for building's foundations, above surface resonators for seismic protection and metamaterial-like transformed urbanism at the city scale.
•An array of boreholes in soft soil can filter Rayleigh waves below 10 Hz.•A forest of trees above soil can reflect and convert Rayleigh waves below 100 Hz.•Geometric transforms underpin the design of seismic cloaks with concrete columns in soil.•Conformal maps can help design city maps with an ‘earthquake protected’ area in the city center.
Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to ...nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3-10 Hz, and for low-speed sedimentary soil (vs: 300-500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency.
Abstract
Previous theory and experiment has shown that introducing strong (nonlocal) beyond-nearest-neighbor interactions in addition to (local) nearest-neighbor interactions into rationally designed ...periodic lattices called metamaterials can lead to unusual wave dispersion relations of the lowest band. For roton-like dispersions, this especially includes the possibility of multiple solutions for the wavenumber at a given frequency. Here, we study the one-dimensional frequency-dependent acoustical phonon transmission of a slab of such nonlocal metamaterial in a local surrounding. In addition to the usual Fabry-Perot resonances, we find a series of bound states in the continuum. In their vicinity, sharp Fano-type transmission resonances occur, with sharp zero-transmission minima next to sharp transmission maxima. Our theoretical discussion starts with a discrete mass-and-spring model. We compare these results with solutions of a generalized wave equation for heterogeneous nonlocal effective media. We validate our findings by numerical calculations on three-dimensional metamaterial microstructures for one-dimensional acoustical wave propagation.
We present a finite element analysis of a diffusion problem involving a coated cylinder enabling the rotation of heat fluxes. The coating consists of a heterogeneous anisotropic conductivity deduced ...from a geometric transformation in the time dependent heat equation. In contrast to thermal cloak and concentrator, specific heat and density are not affected by the transformation in the rotator. Therein, thermal flux diffuses from region of lower temperature to higher temperature, leading to an apparent negative conductivity analogous to what was observed in transformed thermostatics. When a conducting object lies inside the rotator, it appears as if rotated by certain angle to an external observer, what can be seen as a thermal illusion. A structured rotator is finally proposed inspired by earlier designs of thermostatic and microwave rotators.
PDF
