Publications
336 results found
Putley HJ, Guenneau S, Porter R, et al., 2022, A tunable electromagnetic metagrating, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 478, ISSN: 1364-5021
<jats:p>We explore electromagnetic (EM) wave incidence upon gratings of reconfigurable metamaterial cylinders, which collectively act as a metagrating, to identify their potential as reconfigurable subwavelength surfaces. The metacylinders are created by a closely spaced, microstructured array of thin plates that, in the limit of small inter-plate spacing, are described by a semi-analytical continuum model. We build upon metacylinder analysis in water waves, translating this to EM for TE polarization (longitudinal magnetic field) for which the metacylinders exhibit anisotropic scattering; this is exploited for the multiple scattering of light by an infinite metagrating of uniform cylinder radius and angle, for which we retrieve the far-field reflection and transmission spectra for plane-wave incidence. These spectra reveal unusual effects including perfect reflection and a negative Goos–Hänchen shift in the transmitted field, as well as perfect symmetry in the far-field scattering coefficients. The metagrating also hosts Rayleigh–Bloch surface waves, whose dispersion is contingent on the uniform cylinder angle, shifting under rotation towards the light-line as the cylinder angle approaches the horizontal. For both plane-wave scattering and the calculation of the array-guided modes, the cylinder angle is the principal variable in determining the wave interaction, and the metagrating is tunable simply through rotation of the constituent metacylinders.</jats:p>
Wang Y-T, Shen Z, Neil TRR, et al., 2022, Models for resonant acoustic metasurfaces with application to moth wing ultrasound absorption, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 380, ISSN: 1364-503X
Aguzzi G, Thomsen HR, Nooghabi AH, et al., 2022, Architected frames for elastic wave attenuation: Experimental validation and local tuning via affine transformation, APPLIED PHYSICS LETTERS, Vol: 121, ISSN: 0003-6951
Davies B, Craster RV, 2022, Symmetry-induced quasicrystalline waveguides, Wave Motion, Vol: 115, Pages: 1-16, ISSN: 0165-2125
Introducing an axis of reflectional symmetry in a quasicrystal leads to thecreation of localised edge modes that can be used to build waveguides. Wedevelop theory that characterises reflection-induced localised modes inmaterials that are formed by recursive tiling rules. This general theory treatsa one-dimensional continuous differential model and describes a broad class ofboth quasicrystalline and periodic materials. We present an analysis of amaterial based on the Fibonacci sequence, which has previously been shown tohave exotic, Cantor-like spectra with very wide spectral gaps. Our approachprovides a way to create localised edge modes at frequencies within thesespectral gaps, giving strong and stable wave localisation. We also use ourgeneral framework to make a comparison with reflection-induced modes inperiodic materials. These comparisons show that while quasicrystallinewaveguides enjoy enhanced robustness over periodic materials in certainsettings, the benefits are less clear if the decay rates are matched. Thisshows the need to carefully consider equivalent structures when makingrobustness comparisons and to draw conclusions on a case-by-case basis,depending on the specific application.
Kahouadji L, Liang F, Valdes JP, et al., 2022, The transition to aeration in turbulent two-phase mixing in stirred vessels, Flow, Turbulence and Combustion, Vol: 2, Pages: 1-20, ISSN: 0003-6994
We consider the mixing dynamics of an air–liquid system driven by the rotation of a pitched blade turbine (PBT) inside an open, cylindrical tank. To examine the flow and interfacial dynamics, we use a highly parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation strategy. Our numerical technique is designed to capture faithfully complex interfacial deformation, and changes of topology, including interface rupture and dispersed phase coalescence. As shown via transient, a three-dimensional (3-D) LES (large eddy simulation) using a Smagorinsky–Lilly turbulence model, the impeller induces the formation of primary vortices that arise in many idealised rotating flows as well as several secondary vortical structures resembling Kelvin–Helmholtz, vortex breakdown, blade tip vortices and end-wall corner vortices. As the rotation rate increases, a transition to ‘aeration’ is observed when the interface reaches the rotating blades leading to the entrainment of air bubbles into the viscous fluid and the creation of a bubbly, rotating, free surface flow. The mechanisms underlying the aeration transition are probed as are the routes leading to it, which are shown to exhibit a strong dependence on flow history.
Georgiades E, Lowe MJS, Craster RV, 2022, Leaky wave characterisation using spectral methods, JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, Vol: 152, Pages: 1487-1497, ISSN: 0001-4966
Chaplain GJ, De Ponti JM, V Craster R, 2022, Elastic Orbital Angular Momentum (vol 128, 064301, 2022), PHYSICAL REVIEW LETTERS, Vol: 128, ISSN: 0031-9007
Hennessy MG, Craster R, Matar OK, 2022, Drying-induced stresses in poroelastic drops on rigid substrates, Physical Review E, Vol: 105, ISSN: 2470-0045
We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a nonmonotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localize the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.
Palmer SJ, Ignatov Y, Craster RV, et al., 2022, Asymptotically exact photonic approximations of chiral symmetric topological tight-binding models, New Journal of Physics, Vol: 24, ISSN: 1367-2630
Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is often broken by long-range interactions. We look to overcome this difficulty by exploiting the topology of networks, consisting of voids and narrow connecting channels, formed by the spaces between closely spaced perfect conductors. In the limit of low frequencies and narrow channels, these void-channel systems have a direct mapping to analogous discrete mass-spring systems in an asymptotically rigorous manner and therefore only have short-range interactions. We demonstrate that topological tight-binding models that are protected by chiral symmetries, such as the SSH model and square-root semimetals, are reproduced for these void-channel networks with appropriate boundary conditions. We anticipate, moving forward, that this paper provides a basis from which to explore continuum photonic topological systems, in an asymptotically exact manner, through the lens of a simplified tight-binding model.
Aguzzi G, Kanellopoulos C, Wiltshaw R, et al., 2022, Octet lattice-based plate for elastic wave control (vol 12, 1088, 2022), Scientific Reports, Vol: 12, Pages: 1-1, ISSN: 2045-2322
Chaplain GJ, De Ponti JM, Craster RV, 2022, Elastic orbital angular momentum, Physical Review Letters, Vol: 128, ISSN: 0031-9007
We identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe.
Aguzzi G, Kanellopoulos C, Wiltshaw R, et al., 2022, Octet lattice-based plate for elastic wave control, Scientific Reports, Vol: 12, ISSN: 2045-2322
Motivated by the importance of lattice structures in multiple fields, we numerically investigate the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses. The cellular architecture of this plate invokes the well-known octet topology, while the metadevices rely on novel customized octets either comprising spherical masses added to the midpoint of their struts or variable node thickness. We numerically determine the dispersion curves of a doubly-periodic array of octets, which produce a broad bandgap whose underlying physics is elucidated and leveraged as a design paradigm, allowing the construction of a metabarrier effective for inhibiting the transmission of waves. More sophisticated effects emerge upon parametric analyses of the added masses and node thickness, leading to graded designs that spatially filter waves through an enlarged bandgap via rainbow trapping. Additionally, Luneburg and Maxwell metalenses are realized using the spatial modulation of the tuning parameters and numerically tested. Wavefronts impinging on these structures are progressively curved within the inhomogeneous media and steered toward a focal point. Our results yield new perspectives for the use of octet-like lattices, paving the way for promising applications in vibration isolation and energy focusing.
Davies B, Craster RV, 2022, Homogenisation of topologically protected edge states, Pages: X122-X124
We have developed a succinct approach for using homogenisation to derive explicit estimates for the properties of topologically protected edge states. Our approach uses transfer matrices to reduce the wave transmission problem to a set of difference equations, which can be handled concisely using high-frequency homogenisation. This gives estimates for the eigen-frequency and the decay rate of topologically protected edge states. We use a medium based on the Su-Schrieffer-Heeger model to demonstrate the method and show how it can be extended to more complex geometries.
Chaplain GJ, Craster R, Cole N, et al., 2021, Underwater focusing of sound by Umklapp diffraction, Physical Review Applied, Vol: 21, Pages: 1-11, ISSN: 2331-7019
Scholte modes that are localized between a submerged axisymmetric structured elastic plate and surrounding fluid can undergo mode conversion via Umklapp diffraction into radiative modes; this radiative response is verified by experiments that show focusing of underwater sound across a broad range of frequencies. The diffracted beams, that form a cone, are engineered to exist at a desired spatial position, associated with an abrupt change in the patterning of the plate. These structures take the form of grooves present only on one side of the plate, yet the focusing phenomena is achieved on both sides, even as viewed from the flat surface.
Huidobro et al, 2021, Correction for Huidobro et al., Fresnel drag in space–time-modulated metamaterials, Proceedings of the National Academy of Sciences, Vol: 118, Pages: 1-1, ISSN: 0027-8424
Putley HJ, Chaplain GJ, Rakotoarimanga-Andrianjaka H, et al., 2021, Whispering-Bloch elastic circuits, Wave Motion, Vol: 105, Pages: 1-19, ISSN: 0165-2125
We investigate structured arrays and rings in elasticity to design elastic platonic circuitsthat utilise resonant phenomena. Creating ring resonators, and understanding theircoupling to input and output arrays, allows for the development of platonic circuitsincluding add–drop filters (ADFs) and coupled resonator elastic arrays (CREAs), andhence we envisage integrated platonic devices. Structured rings of point-masses placedatop a thin elastic plate lead to highly confined quasi-modes that leak energy; theleakage being quantified by the limiting quality factor Q. The conditions of resonanceare deduced using highly accurate numerical simulations based on a Green’s functionapproach to solve the dispersion relation associated with the structured ring resonators.The sharp resonances that emerge are then used to filter and direct wave energy basedon input frequency, and this is illustrated through analogy with devices used in optics,e.g. integrated photonic circuits. The potential applications of the elastic devices includeelastic delay lines and passive energy harvesters.
Balmforth NJ, Craster R, Hewitt DR, 2021, Building on Oldroyd's viscoplastic legacy: Perspectives and new developments, Journal of Non-Newtonian Fluid Mechanics, Vol: 294, ISSN: 0377-0257
The decade following the second world war heralded the publication of a collection of important papers on non-Newtonian fluid mechanics; Oldroyd’s work featured heavily in this collection. Not only did these articles establish important results, but Oldroyd’s style and methods set the scene for subsequent work in the area, exploiting mathematical analysis to formulate problems, establish results and guide further research. While Oldroyd’s name will forever be linked with the study of elastic fluids, the purpose of the present paper is to offer a modern perspective on a number of Oldroyd’s papers on viscoplastic fluids from 1947–1951 [1], [2], [3], [4], [5], [6], [7], [8]. Along the way, we sprinkle in a brief review of some of the subsequent developments stemming from Oldroyd’s advances, together with a few new results guided by his work. Following the approach of most of Oldroyd’s original papers, we focus on unidirectional flow down conduits. In an Appendix, we complement this discussion with a lubrication analysis, extending, clarifying and correcting the important original analysis of Walton and Bittleston (1991) [9]; although lubrication theory was not directly utilized by Oldroyd, the methodology aligns with his philosophy of using asymptotic and analytical approaches.
Laforge N, Wiltshaw R, Craster RV, et al., 2021, Acoustic topological circuitry in square and rectangular phononic crystals, Physical Review Applied, Vol: 15, Pages: 1-13, ISSN: 2331-7019
We systematically engineer a series of square and rectangular phononiccrystals to create experimental realisations of complex topological phononiccircuits. The exotic topological transport observed is wholly reliant upon theunderlying structure which must belong to either a square or rectangularlattice system and not to any hexagonal-based structure. The phononic systemchosen consists of a periodic array of square steel bars which partitionsacoustic waves in water over a broadband range of frequencies (~0.5 MHz). Anultrasonic transducer launches an acoustic pulse which propagates along adomain wall, before encountering a nodal point, from which the acoustic signalpartitions towards three exit ports. Numerical simulations are performed toclearly illustrate the highly resolved edge states as well as corroborate ourexperimental findings. To achieve complete control over the flow of energy,power division and redirection devices are required. The tunability afforded byour designs, in conjunction with the topological robustness of the modes, willresult in their assimilation into acoustical devices.
Quadrelli DE, Craster R, Kadic M, et al., 2021, Elastic wave near-cloaking, Extreme Mechanics Letters, Vol: 44, Pages: 1-8, ISSN: 2352-4316
Cloaking elastic waves has, in contrast to the cloaking of electromagnetic waves, remained a fundamental challenge: the latter successfully uses the invariance of Maxwell’s equations, from which the field of transformational optics has emerged, whereas the elastic Navier equations are not invariant under coordinate transformations. Our aim is to overcome this challenge, at least in practical terms, and thereby unlock applications in mechanics, ultrasound, vibration mitigation, non-destructive evaluation and elastic wave control. We achieve near-cloaking by recognizing that, despite the lack of invariance, a decoupling into a system of form invariant potential equations together with a quantifiable approximation, can be used effectively in many cases to control the flow of elastodynamic waves. Here, in particular we focus on the efficiency and practicability of the proposed near-cloaking which is illustrated using carpet cloaks to hide surface defects from incoming compressional and shear in-plane waves and from surface elastic Rayleigh waves.
Chaplain GJ, Craster RV, 2021, Surface corrugated laminates as elastic grating couplers: Splitting of SV- and P-waves by selective diffraction, Journal of Applied Physics, Vol: 129, Pages: 1-10, ISSN: 0021-8979
The phenomenon of selective diffraction is extended to in-plane elastic waves, and we design surface corrugated periodic laminates that incorporate crystal momentum transfer, which, due to the rich physics embedded within the vector elastic system, results in frequency, angle, and wave-type selective diffraction. The resulting devices are elastic grating couplers, with additional capabilities as compared to analogous scalar electromagnetic couplers, in that the elastic couplers possess the ability to split and independently redirect, through selective negative refraction, the two body waves present in the vector elastic system: P- (compressional) and SV- (shear-vertical) elastic waves. The design paradigm, and interpretation, is aided by obtaining isofrequency contours via a non-dimensionalized transfer matrix method.
Batchvarov A, Kahouadji L, Constante-Amores CR, et al., 2021, Three-dimensional dynamics of falling films in the presence of insoluble surfactants, Journal of Fluid Mechanics, Vol: 906, Pages: A16-1-A16-13, ISSN: 0022-1120
We study the effect of insoluble surfactants on the wave dynamics of vertically falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (AIChE J., vol. 49, 2003, pp. 2715–2727). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi-two-dimensional shape. In addition, the presence of Marangoni stresses is found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near-complete rigidification of the interface is observed.
Haslinger SG, Lowe MJS, Craster R, et al., 2021, Prediction of reflection amplitudes for ultrasonic inspection of rough planar defects, Insight, Vol: 63, Pages: 28-36, ISSN: 2156-485X
The characteristics of planar defects (no loss of material volume) that arise during industrial plant operation are difficult to predict in detail, yet these can affect the performance of non-destructive testing (NDT) used to manage plant structural integrity. Inspection modelling is increasingly used to design and assess ultrasonic inspections of such plant items. While modelling of smooth planar defects is relatively mature and validated, issues have remained in the treatment of rough planar defect species. The qualification of ultrasonic inspections for such defects is presently very conservative, owing to the uncertainty of the amplitudes of rough surface reflections. Pragmatic solutions include the addition of large sensitivity thresholds and more frequent inspection intervals, which require more plant downtime. In this article, an alternative approach has been developed by the authors to predict the expected surface reflection from a rough defect using a theoretical statistical model. Given only the frequency, angle of incidence and two statistical parameter values used to characterise the defects, the expected reflection amplitude is obtained rapidly for any scattering angle and size of defect, for both compression and shear waves. The method is applicable for inspections of isotropic media that feature surface reflections such as pulse-echo or pitch-catch, rather than for tip signal-dependent techniques such as time-of-flight diffraction. The potential impact for inspection qualification is significant, with the new model predicting increases of up to 20 dB in signal amplitude in comparison with models presently used in industry. All mode conversions are included and rigorous validations using numerical and experimental methods have been performed. The model has been instrumental in obtaining new statistically significant results related to the effect of tilt; the expected pulse-echo backscattered amplitude for very rough planar defects is independent of til
Ungureanu B, Tournat V, Craster R, et al., 2021, Theory and experiments for seismic waves propagating within an array of clamped inclusions in a soft matrix, 15th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), Publisher: IEEE, Pages: X438-X441
Makwana M, Wiltshaw R, Craster R, et al., 2021, Topological guidance in novel photonic crystal fibers, 15th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), Publisher: IEEE, Pages: X144-X147
Craster R, Diatta A, Guenneau S, et al., 2021, On near-cloaking for linear elasticity, Multiscale Modeling & Simulation, Vol: 19, Pages: 633-664, ISSN: 1540-3459
We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosseratand Willis frameworks are shown to be equivalent to certain high-contrast small defect problems forthe usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study thesharpness of the estimates from [H. Ammari, H. Kang, K. Kim, and H. Lee, J. Differential Equations,254 (2013), pp. 4446--4464], wherein the convergence of the solutions to the transmission problems isinvestigated, when the Lam\'e parameters in the inclusion tend to extreme values. Both soft and hardinclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose anapproximate isotropic cloak algorithm for a symmetrized Cosserat cloak.
Fu S, Li G, Craster R, et al., 2021, Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains, Multiscale Modeling & Simulation, Vol: 19, Pages: 1684-1709, ISSN: 1540-3459
Wiltshaw R, Craster R, Makwana M, 2020, Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers, Wave Motion, Vol: 99, ISSN: 0165-2125
We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet-Bloch waves through an infinite array of scatterers. The approach also lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on some topical examples from topological wave physics.
Tang K, Makwana MP, Craster RV, et al., 2020, Observations of symmetry induced topological mode steering in a reconfigurable elastic plate, Physical Review B, Vol: 102, ISSN: 2469-9969
We experimentally investigate the valley-Hall effect for interfacial edge states, highlighting the importance of the modal patterns between geometrically distinct regions within a structured elastic plate. These experiments, for vibration, are at a scale where detailed measurements are taken throughout the system and not just at the input/output ports; this exposes the coupling between geometrically distinct modes that underlie the differences between wave transport around gentle and sharp bends.
Chaplain GJ, Ponti JMD, Aguzzi G, et al., 2020, Topological rainbow trapping for elastic energy harvesting in graded Su-Schrieffer-Heeger systems, Applied Physics Letters, Vol: 14, Pages: 054035 – 1-054035 – 15, ISSN: 0003-6951
We amalgamate two fundamental designs from distinct areas of wave control in physics, and place them in the setting of elasticity. Graded elastic metasurfaces, so-called metawedges, are combined with the now classical Su-Schrieffer-Heeger (SSH) model from the field of topological insulators. The resulting structures form one-dimensional graded-SSH-metawedges that support multiple, simultaneous, topologically protected edge states. These robust, enhanced localised modes are leveraged for applications in elastic energy harvesting using the piezoelectric effect. The designs we develop are first motivated by applying the SSH model to mass-loaded Kirchhoff-Love thin elastic plates. We then extend these ideas to using graded resonant rods, and create SSH models, coupled to elastic beams and full elastic half-spaces.
De Ponti JM, Colombi A, Riva E, et al., 2020, Experimental investigation of amplification, via a mechanical delay-line, in a rainbow-based metamaterial for energy harvesting, Applied Physics Letters, Vol: 117, Pages: 143902-1-143902-6, ISSN: 0003-6951
We experimentally demonstrate that a rainbow-based metamaterial, created by a graded array of resonant rods attached to an elastic beam, operates as a mechanical delay-line by slowing down surface elastic waves to take advantage of wave interaction with resonance. Experiments demonstrate that the rainbow effect reduces the amplitude of the propagating wave in the host structure. At the same time, it dramatically increases both the period of interaction between the waves and the resonators and the wavefield amplitude in the rod endowed with the harvester. Increased energy is thus fed into the resonators over time: we show the enhanced energy harvesting capabilities of this system.
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