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459

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Introduction

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## Publications

Publications (459)

In this paper, we propose a new model to approximate the wave response of waveguides containing an arbitrary number of small inclusions. The theory is developed for general one-dimensional elastic waveguides to study various types of modes, e.g. longitudinal, flexural, shear, torsional or coupled modes. The precise problem assumes the host material...

In this work, we present a comprehensive method for determining the dispersion relation in one-dimensional waveguides, applicable to a wide range of structures, regardless of their specific characteristics. This general framework employs a unified mathematical model, referred to as *generalized beams*, where varying types of waveguides and scattere...

This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional elastic waveguide with several point resonators by utilizing the Green's matrix approach. The derivations inclu...

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three...

Elastic wave manipulation using large arrays of resonators is driving the need for advanced simulation and optimization methods. To address this we introduce and explore a robust framework for wave control: Quasi-normal modes (QNMs). Specifically we consider the problem for thin elastic plates, where the Green's function formalism is well known and...

A variety of scientific fields like proteomics and spintronics have created a new demand for on-chip devices capable of sensing parameters localized within a few tens of micrometers. Nano and microelectromechanical systems (NEMS/MEMS) are extensively employed for monitoring parameters that exert uniform forces over hundreds of micrometers or more,...

In this work we investigate the computation of dispersion relation (i.e., band functions) for three-dimensional photonic crystals, formulated as a parameterized Maxwell eigenvalue problem, using a novel hp-adaptive sampling algorithm. We develop an adaptive sampling algorithm in the parameter domain such that local elements with singular points are...

Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances while simultaneously being physically compact. To aid this design challenge, we develop a methodology to allow isospectral twinning of reference cavities with...

Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method of low-frequency homogenization, it was so far only possible to obtain non-reciprocal effective media when both material properties are modulated in time, in the form of...

We propose a new model to approximate the wave response of waveguides containing an arbitrary number of small inclusions. The theory is developed to consider any one-dimensional waveguide (longitudinal, flexural, shear, torsional waves or a combination of them by mechanical coupling), containing small inclusions with different material and/or secti...

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with ca...

The energy harvesting capability of a graded metamaterial is maximised via reinforcement learning (RL) under realistic excitations at the microscale. The metamaterial consists of a waveguide with a set of beam-like resonators of variable length, with piezoelectric patches, attached to it. The piezo-mechanical system is modelled through equivalent l...

Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances whilst simultaneously being physically compact. To aid this design challenge we develop a methodology to allow isospectral twinning of reference cavities with...

High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter. Abstract Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method of low frequency homogenisation, it was so far on...

Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems, and meta...

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 properties are obtained near a given point of the dispersion diagram in frequency-wavenumber space. The asymptotic...

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to characterise; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues wi...

The rainbow trapping phenomenon of graded metamaterials can be combined with the fractal spectra of quasiperiodic waveguides to give a metamaterial that performs fractal rainbow trapping. This is achieved through a graded cut-and-project algorithm that yields a projected geometry for which the effective projection angle is graded along its length....

Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the...

Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient d...

Precise manipulation of the direction and redirection of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite framelike structure and the requirement to channel energy away from critical regions, leaving them vibration free, and redirect energy along edges toward energy concentrators for damp...

The study of dispersion curves and wave propagation characteristics has been of great interest in the non-destructive evaluation community for developing efficient and accurate guided wave inspection techniques. Leaky Lamb waves, which radiate from a waveguide into a surrounding fluid or elastic material, exhibit exponential growth in amplitude awa...

We experimentally demonstrate the capability of architected plates, with a frame-like cellular structure, to inhibit the propagation of elastic flexural waves. By leveraging the octet topology as a unit cell to design the tested prototypes, a broad and easy-to-tune bandgap is experimentally generated. The experimental outcomes are supported by exte...

Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. The cantilever experiment allows the stress in a drying film that has been deposited onto a thin plate to be quantified. Mechanical stresses in the film are transmitted to the plate and drive bending. Mathematical...

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 nume...

Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength...

Precise manipulation of the direction and re-direction of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite frame-like structure and the requirement to channel energy away from critical regions, leaving them vibration-free, and redirect energy along edges towards energy concentrators for d...

Introducing an axis of reflection symmetry in a quasicrystal leads to the creation of localised edge modes that can be used to build waveguides. We develop theory that characterises reflection-induced localised modes in materials that are formed by recursive tiling rules. This general theory treats a one-dimensional continuous differential model an...

Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems and metam...

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions fo...

Introducing an axis of reflectional symmetry in a quasicrystal leads to the creation of localised edge modes that can be used to build waveguides. We develop theory that characterises reflection-induced localised modes in materials that are formed by recursive tiling rules. This general theory treats a one-dimensional continuous differential model...

This corrects the article DOI: 10.1103/PhysRevLett.128.064301.

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions fo...

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 elasti...

This work establishes a general method for studying localised eigenmodes in periodic media with defects. Our approach can be used to describe two broad classes of perturbations to periodic differential problems, both compact and non-compact: those caused by inserting a finite-sized piece of arbitrary material and those caused by creating an interfa...

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...

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...

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 co...

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 elasti...

Motivated by the importance of lattice structures in multiple fields, we investigate the propagation of flexural waves in a thin woven 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 metade...

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...

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 focussing of underwater sound across a broad range of frequencies. The diffracted beams, that form a c...

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 network...

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 a...

We use square and rectangular phononic crystals to create experimental realizations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure that must belong to either a square or rectangular lattice system and not to any hexagonal-based structure. The phononic system we use...

Diverting and controlling the impact of elastic vibrations upon an infrastructure is a major challenge for seismic hazard mitigation and for the reduction of machine noise and vehicle vibration in the urban environment. Seismic metamaterials (SMs), with their inherent ability to manipulate wave propagation, provide a key route for overcoming the te...

We investigate structured arrays and rings in elasticity to design elastic platonic circuits that utilise resonant phenomena. Creating ring resonators, and understanding their coupling to input and output arrays, allows for the development of platonic circuits including add-drop filters (ADFs) and coupled resonator elastic arrays (CREAs), and hence...

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 ov...

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 g...

We combine two different fields, topological physics and graded metamaterials, to design a topological metasurface to control and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic plate, using a square lattice, that hosts symmetry-induced topological edge states. By concurrently allowing the elastic su...

We systematically engineer a series of square and rectangular phononic crystals to create experimental realisations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure which must belong to either a square or rectangular lattice system and not to any hexagonal-based stru...

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 po...

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 c...

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 grat...

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...

We consider the mixing of a viscous fluid by the rotation of a pitched blade turbine inside an open, cylindrical tank, with air as the lighter fluid above. To examine the flow and interfacial dynamics, we utilise a highly-parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation stra...

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 ov...

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 propagat...

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilise...

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe the...

The effect of surfactants on the tail and film dynamics of elongated gas bubbles propagating through circular capillary tubes is investigated by means of an extensive three-dimensional numerical study using a hybrid front-tracking/level-set method. The focus is on the visco-inertial regime, which occurs when the Reynolds number of the flow is much...

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states which emerge at the interface between trivial and non-trivial regions can be used for directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these sta...

Diverting, and controlling, elastic vibrations impacting upon infrastructure is a major challenge for seismic hazard mitigation, and for the reduction of machine noise and vehicle vibration in the urban environment. Seismic metamaterials (SMs), with their inherent ability to manipulate wave propagation, provide a key route for overcoming the techno...