Publications
354 results found
Ungureanu B, Guenneau S, Achaoui Y, et al., 2019, The influence of building interactions on seismic and elastic body waves, EPJ Applied Metamaterials, Vol: 6, Pages: 1-12, ISSN: 2272-2394
We outline some recent research advances on the control of elastic waves in thin and thick plates, that have occurred since the large scale experiment [S. Brûlé, Phys. Rev. Lett. 112, 133901 (2014)] that demonstrated significant interaction of surface seismic waves with holes structuring sedimentary soils at the meter scale. We further investigate the seismic wave trajectories of compressional body waves in soils structured with buildings. A significant substitution of soils by inclusions, acting as foundations, raises the question of the effective dynamic properties of these structured soils. Buildings, in the case of perfect elastic conditions for both soil and buildings, are shown to interact and strongly influence elastic body waves; such site-city seismic interactions were pointed out in [Guéguen et al., Bull. Seismol. Soc. Am. 92, 794–811 (2002)], and we investigate a variety of scenarios to illustrate the variety of behaviours possible.
Huidobro PA, Galiffi E, Guenneau S, et al., 2019, Fresnel drag in space-time-modulated metamaterials, Publisher: arXiv
A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actual material motion. We discuss how both the permittivity and permeability need to be modulated in order to achieve these effects, and we present an equivalent transmission line model.
Ponti JMD, Colombi A, Ardito R, et al., 2019, Graded metasurface for enhanced sensing and energy harvesting
In elastic wave systems, combining the powerful concepts of resonance andspatial grading within structured surface arrays enable resonant metasurfacesto exhibit broadband wave focusing, mode conversion from surface (Rayleigh)waves to bulk (shear) waves, and spatial frequency selection. Devices builtaround these concepts allow for precise control of surface waves, often withstructures that are subwavelength, and utilise rainbow trapping that separatesthe signal spatially by frequency. Rainbow trapping yields large amplificationsof displacement at the resonator positions where each frequency componentaccumulates. We investigate whether this amplification, and the associatedcontrol, can be used to create energy harvesting devices; the potentialadvantages and disadvantages of using graded resonant devices as energyharvesters is considered. We concentrate upon elastic plate models for whichthe A0 mode dominates, and take advantage of the large displacement amplitudesin graded resonant arrays of rods, to design innovative metasurfaces that focuswaves for enhanced piezoelectric sensing and energy harvesting. Numericalsimulation allows us to identify the advantages of such graded metasurfacedevices and quantify its efficiency, we also develop accurate models of thephenomena and extend our analysis to that of an elastic half-space and Rayleighsurface waves.
Chaplain GJ, Craster R, 2019, Flat lensing by graded line meta-arrays, Publisher: AMER PHYSICAL SOC
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- Citations: 10
Makwana M, Craster R, Guenneau S, 2019, Topological beam-splitting in photonic crystals, Optics Express, Vol: 27, Pages: 16088-16102, ISSN: 1094-4087
We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric and magnetic polarisation. We do so by considering arrangements of Indium Phosphide dielectric pillars in air, in particular we place several inclusions within a cell that is then extended periodically upon a square lattice. Hexagonal lattice structures are more commonly used in topological valleytronics but, as we discuss, three-way splitting is only possible using a square, or rectangular, lattice. To achieve splitting and transport around a sharp bend we use accidental, and not symmetry-induced, Dirac cones. Within each cell pillars are either arranged around a triangle or square; we demonstrate the mechanism of splitting and why it does not occur for one of the cases. The theory is developed and full scattering simulations demonstrate the effectiveness of the proposed designs.
Makwana M, Craster R, Guenneau S, 2019, Topological beam-splitting in photonic crystals, Publisher: OPTICAL SOC AMER
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- Citations: 43
Palmer S, Xiao X, Pazos-Perez N, et al., 2019, Extraordinarily transparent compact metallic metamaterials, Nature Communications, Vol: 10, ISSN: 2041-1723
The design of achromatic optical components requires materials with high transparency and low dispersion. We show that although metals are highly opaque, densely packed arrays of metallic nanoparticles can be more transparent to infrared radiation than dielectrics such as germanium, even when the arrays are over 75% metal by volume. Such arrays form effective dielectrics that are virtually dispersion-free over ultra-broadband ranges of wavelengths from microns up to millimeters or more. Furthermore, the local refractive indices may be tuned by altering the size, shape, and spacing of the nanoparticles, allowing the design of gradient-index lenses that guide and focus light on the microscale. The electric field is also strongly concentrated in the gaps between the metallic nanoparticles, and the simultaneous focusing and squeezing of the electric field produces strong ‘doubly-enhanced’ hotspots which could boost measurements made using infrared spectroscopy and other non-linear processes over a broad range of frequencies.
Martin RJ, Kearney MJ, Craster R, 2019, Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes, Journal of Physics A: Mathematical and Theoretical, Vol: 52, ISSN: 1751-8113
The first-passage problem of the Ornstein–Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a starting-point, and extending to a general mean-reverting process, we investigate the long- and short-time asymptotics using a combination of Hopf–Cole and Laplace transform techniques. As a result we are able to give a single formula that is correct in both limits, as well as being exact in certain special cases. We demonstrate the results using a variety of other models.
Dubois M, Perchoux J, Vanel AL, et al., 2019, Acoustic flat lensing using an indefinite medium, Physical Review B: Condensed Matter and Materials Physics, Vol: 99, ISSN: 1098-0121
Acoustic flat lensing is achieved here by tuning a phononic array to have indefinite medium behavior in a narrow frequency spectral region along the acoustic branch in the irreducible Brillouin zone (IBZ). This is confirmed by the occurrence of a flat band along an unusual path in the IBZ and by interpreting the intersection point of isofrequency contours on the corresponding isofrequency surface; coherent directive collimated beams are formed whose reflection from the array surfaces create lensing. Theoretical predictions using a mass-spring lattice approximation of the phononic crystal (PC) are corroborated by time-domain experiments, airborne acoustic waves generated by a source with a frequency centered about 10.6 kHz, placed at three different distances from one side of a finite PC slab, constructed from polymeric spheres, yielding distinctive focal spots on the other side. These experiments evaluate the pressure field using optical feedback interferometry and demonstrate precise control of the three-dimensional wave trajectory through a sonic crystal.
Vanel AL, Craster RV, Schnitzer O, 2019, Asymptotic modelling of phononic box crystals, SIAM Journal on Applied Mathematics, Vol: 79, Pages: 506-524, ISSN: 0036-1399
We introduce phononic box crystals, namely arrays of adjoined perforated boxes, as a three-dimensional prototype for an unusual class of subwavelength metamaterials based on directly coupling resonating elements. In this case, when the holes coupling the boxes are small, we create networks of Helmholtz resonators with nearest-neighbour interactions. We use matched asymptotic expansions, in the small hole limit, to derive simple, yet asymptotically accurate, discrete wave equations governing the pressure field. These network equations readily furnish analytical dispersion relations for box arrays, slabs and crystals, that agree favourably with finite-element simulations of the physical problem. Our results reveal that the entire acoustic branch is uniformly squeezed into a subwavelength regime; consequently, phononic box crystals exhibit nonlinear-dispersion effects (such as dynamic anisotropy) in a relatively wide band, as well as a high effective refractive index in the long-wavelength limit. We also study the sound field produced by sources placed within one of the boxes by comparing and contrasting monopole- with dipole-type forcing; for the former the pressure field is asymptotically enhanced whilst for the latter there is no asymptotic enhancement and the translation from the microscale to the discrete description entails evaluating singular limits, using a regularized and efficient scheme, of the Neumann's Green's function for a cube. We conclude with an example of using our asymptotic framework to calculate localized modes trapped within a defected box array.
Chaplain GJ, Makwana MP, Craster R, 2019, Rayleigh-Bloch, topological edge and interface waves for structured elastic plates, Wave Motion, Vol: 86, Pages: 162-174, ISSN: 0165-2125
Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal arrangements. We model array and interface waves for structured thin elastic plates, so-called platonic crystals, that share many analogies with their electromagnetic and acoustic counterparts, photonic and phononic crystals, and much of what we present carries across to those systems. These crystals support several forms of edge or array-guided modes, that decay perpendicular to their direction of propagation. To rapidly, and accurately, characterise these modes and their decay we develop a spectral Galerkin method, using a Fourier–Hermite basis, to provide highly accurate dispersion diagrams and mode-shapes, that are confirmed with full scattering simulations. We illustrate this approach using Rayleigh Bloch modes, and generalise high frequency homogenisation, along a line array, to extract the envelope wavelength along the array. Rayleigh–Bloch modes along graded arrays of rings of point masses are investigated and novel forms of the rainbow trapping effect and wave hybridisation are demonstrated. Finally, the method is used to investigate the dispersion curves and mode-shapes of interfacial waves created by geometrical differences in adjoining media.
Movchan AB, McPhedran RC, Carta G, et al., 2019, Platonic localisation: one ring to bind them, Archive of Applied Mechanics, Vol: 89, Pages: 521-533, ISSN: 0939-1533
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring–mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring–mass resonators can be tuned to produce a “negative inertia” input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes.
Martin R, Craster RV, Pannier A, et al., 2019, Analytical approximation to the multidimensional Fokker--Planck equation with steady state, Journal of Physics A: Mathematical and Theoretical, Vol: 52, ISSN: 1751-8113
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.
Proctor M, Maier SA, Craster RV, et al., 2019, Unidirectional edge states in two dimensional plasmonic arrays, Pages: 1559-1560
The combination of topologically protected states with plasmonic systems presents the opportunity to control electromagnetic waves reliably on the nanoscale. Motivated by these effects we investigate arrays of plasmonic nanoparticles with hallmarks of topological effects, including band inversion and unidirectional edge states. These states are a result of particular lattice symmetries. By treating the nanoparticles as point dipoles and applying the coupled dipole method, we model infinite arrays and semi-infinite ribbons.
Ungureanu B, Brûlé S, Achaoui Y, et al., 2019, Modeling large scale metamaterials for elastic waves control, Pages: 946-947
We’ve studied and proposed to apply the large scale metamaterials properties, which are based on the negative values of the Bulk modules K and G; the Young modulus, of longitudinal elasticity, as well as on the negative mass density, in order to obtain elastic waves control. These negative values are obtained with the help of the local resonance of the elementary cells that lead to very dispersive properties of the metamaterials.
Makwana M, Craster R, Guenneau S, et al., 2019, Exotic symmetry-induced effects in photonic and phononic systems, Pages: 948-949
Predictive theory to geometrically engineer materials in continuum systems to have desired symmetry-induced effects is developed here by bridging the gap between quantum and continuum descriptions. We emphasise a predictive approach, the strength of which is demonstrated by the ability to design well-defined broadband edge states, valley-Hall networks and anisotropic quasicrystalline effects. We solely use semi-analytical models; this means we can concentrate cleanly upon issues such as group theory, and its influence upon the effects we see, without numerical distractions.
De Ponti JM, Colombi A, Craster R, et al., 2019, Graded metasurface for elastic energy harvesting
Metamaterial designs combining graded arrays of resonators and elastic wave excitation allows a precise control of the propagation of mechanical waves in solid media. In this study metamaterial’s broadband control capacities are used to design an innovative piezoelectric energy harvester.
Ungureanu B, Guenneau S, Brule S, et al., 2019, Controlling seismic elastic surface waves via interacting structures, 13th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), Publisher: IEEE, Pages: 438-440
Berte R, Della Picca F, Poblet M, et al., 2018, Acoustic far-field hypersonic surface wave detection with single plasmonic nanoantennas, Physical Review Letters, Vol: 121, ISSN: 0031-9007
The optical properties of small metallic particles allow us to bridge the gap between the myriad of subdiffraction local phenomena and macroscopic optical elements. The optomechanical coupling between mechanical vibrations of Au nanoparticles and their optical response due to collective electronic oscillations leads to the emission and the detection of surface acoustic waves (SAWs) by single metallic nanoantennas. We take two Au nanoparticles, one acting as a source and the other as a receptor of SAWs and, even though these antennas are separated by distances orders of magnitude larger than the characteristic subnanometric displacements of vibrations, we probe the frequency content, wave speed, and amplitude decay of SAWs originating from the damping of coherent mechanical modes of the source. Two-color pump-probe experiments and numerical methods reveal the characteristic Rayleigh wave behavior of emitted SAWs, and show that the SAW-induced optical modulation of the receptor antenna allows us to accurately probe the frequency of the source, even when the eigenmodes of source and receptor are detuned.
Makwana MP, Craster R, 2018, Designing multidirectional energy splitters and topological valley supernetworks, PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950
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- Citations: 49
Makwana MP, Craster R, 2018, Geometrically navigating topological plate modes around gentle and sharp bends, PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950
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- Citations: 40
Bennetts LG, Peter MA, Craster R, 2018, Graded resonator arrays for spatial frequency separation and amplification of water waves, Journal of Fluid Mechanics, Vol: 854, ISSN: 0022-1120
A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.
Kahouadji L, Nowak E, Kovalchuk N, et al., 2018, Simulation of immiscible liquid-liquid flows in complex microchannel geometries using a front-tracking scheme, MICROFLUIDICS AND NANOFLUIDICS, Vol: 22, ISSN: 1613-4982
The three-dimensional two-phase flow dynamics inside a microfluidic device of complex geometry is simulated using a parallel, hybrid front-tracking/level-set solver. The numerical framework employed circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The device considered in the present work is constructed via a module that defines solid objects by means of a static distance function. The construction combines primitive objects, such as a cylinder, a plane, and a torus, for instance, using simple geometrical operations. The numerical solutions predicted encompass dripping and jetting, and transitions in flow patterns are observed featuring the formation of drops, ‘pancakes’, plugs, and jets, over a wide range of flow rate ratios. We demonstrate the fact that vortex formation accompanies the development of certain flow patterns, and elucidate its role in their underlying mechanisms. Experimental visualisation with a high-speed imaging are also carried out. The numerical predictions are in excellent agreement with the experimental data.
Craster RV, Sassi R, 2018, Spectral algorithms for reaction-diffusion equations, Publisher: arXiv
A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches. The examples are chosen from the literature to illustrate points and queries that naturally arise.
Choi W, Shi F, Lowe MJS, et al., 2018, Rough surface reconstruction of real surfaces for numerical simulations of ultrasonic wave scattering, NDT and E International, Vol: 98, Pages: 27-36, ISSN: 0963-8695
The scattering of waves by rough surfaces plays a significant role in many fields of physical sciences including ultrasonics where failure surfaces are often rough and their accurate identification is critical. The prediction of the strength of scattering can be hampered when the roughness is not adequately characterised and this is a particular issue when the surface roughness is within an order of the incident wavelength. Here we develop a methodology to reconstruct, and accurately represent, rough surfaces using an AutoRegressive (AR) process that then allows for rapid numerical simulations of ultrasonic wave rough surface scattering in three dimensions. Gaussian, exponential and AR surfaces are reconstructed based on real surface data and the statistics of the surfaces are compared with each other. The statistics from the AR surfaces agree well with those from actual rough surfaces, taken from experimental samples, in terms of the heights as well as the gradients, which are the two main factors in accurately predicting the wave scattering intensities. Ultrasonic rough surface scattering is simulated numerically using the Kirchhoff approximation, and comparisons with Gaussian, exponential, AR and real sample surfaces are performed; scattering intensities found using AR surfaces show the best agreement with the real sample surfaces.
Craster R, Guenneau S, Hutridurga Ramaiah H, et al., 2018, Cloaking via mapping for the heat equation, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Vol: 16, Pages: 1146-1174, ISSN: 1540-3459
This paper explores the concept of near-cloaking in the context of time-dependentheat propagation. We show that after the lapse of a certain threshold time, the boundary measure-ments for the homogeneous heat equation are close to the cloaked heat problem in a certain Sobolevspace norm irrespective of the density-conductivity pair in the cloaked region. A regularised trans-formation media theory is employed to arrive at our results. Our proof relies on the study of the longtime behaviour of solutions to the parabolic problems with high contrast in density and conductivitycoefficients. It further relies on the study of boundary measurement estimates in the presence of smalldefects in the context of steady conduction problem. We then present some numerical examples to illustrate our theoretical results.
Skelton E, Craster RV, Colombi A, et al., 2018, The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion, New Journal of Physics, Vol: 20, ISSN: 1367-2630
We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.
Smith ER, Theodorakis PE, Craster RV, et al., 2018, Moving contact lines: linking molecular dynamics and continuum-scale modeling, Langmuir, Vol: 34, Pages: 12501-12518, ISSN: 0743-7463
Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.
Seungwon S, Chergui J, Juric D, et al., 2018, A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant, Journal of Computational Physics, Vol: 359, Pages: 409-435, ISSN: 0021-9991
A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737–757) is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.
Shi F, Lowe M, Skelton EA, et al., 2018, A time-domain finite element boundary integral approach for elastic wave scattering, Computational Mechanics, Vol: 61, Pages: 471-483, ISSN: 0178-7675
The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.
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