Publications
354 results found
Hennessy MG, Craster RV, Matar OK, 2024, Time-dependent modelling of thin poroelastic films drying on deformable plates, European Journal of Applied Mathematics, Vol: 35, Pages: 62-95, ISSN: 0956-7925
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 film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from t to t1/2 , in agreement with experiments.
Georgiades E, Lowe MJS, Craster RV, 2024, Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation., J Acoust Soc Am, Vol: 155, Pages: 629-639
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 calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.
Rosafalco L, De Ponti JM, Iorio L, et al., 2023, Reinforcement learning optimisation for graded metamaterial design using a physical-based constraint on the state representation and action space., Sci Rep, Vol: 13
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 lumped parameters determined via a general impedance analysis. Realistic conditions are mimicked by considering either magnetic loading or random excitations, the latter scenario requiring the enhancement of the harvesting capability for a class of forcing terms with similar but different frequency content. The RL-based optimisation is empowered by using the physical understanding of wave propagation in a such local resonance system to constrain the state representation and the action space. The procedure outcomes are compared against grading rules optimised through genetic algorithms. While genetic algorithms are more effective in the deterministic setting featuring the application of magnetic loading, the proposed RL-based proves superior in the inherently stochastic setting of the random excitation scenario.
Putley HJ, Guenneau S, Craster RV, et al., 2023, Effective properties of periodic plate-array metacylinders, Physical Review B, Vol: 108, ISSN: 2469-9950
We use semianalytic methods to model a periodic structure of plate-array cylinders (metacylinders), and derive several of the medium's effective material properties in the quasistatic limit. Subject to s-polarized [transverse-electric (TE)] light, the anisotropic dispersion of the crystal manifests as a Maxwell Garnett equation for the effective permittivity at leading order. This is performed both for the case of no material contrast between interior and exterior regions, and a nonunity normalized refractive index. In each case, the leading order effective permittivity is a function of the difference between Bloch wave and plate-array angles. As such, we envisage the metamaterial as being mechanically tunable through uniform mechanical rotation of the constituent metacylinders.
Davies B, Chaplain GJ, Starkey TA, et al., 2023, Graded quasiperiodic metamaterials perform fractal rainbow trapping, Physical Review Letters, Vol: 131, ISSN: 0031-9007
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 geometry for which the effective projection angle is graded along its length. As a result, the fractal structure of local band gaps varies with position, leading to broadband "fractal" rainbow trapping. We demonstrate this principle by designing an acoustic waveguide, which is characterised using theory, simulation and experiments.
Craster RV, Davies B, 2023, Asymptotic characterisation of localised defect modes: Su-Schrieffer-Heeger and related models, SIAM: Multiscale Modeling and Simulation, Vol: 21, Pages: 827-848, ISSN: 1540-3459
Motivated by topologically protected states in wave physics, we study localized eigenmodes in one-dimensional periodic media with defects. The Su–Schrieffer–Heeger model (the canonical example of a one-dimensional system with topologically protected localized defect states) is used to demonstrate the method. Our approach can be used to describe two broad classes of perturbations to periodic differential problems: those caused by inserting a finite-sized piece of arbitrary material and those caused by creating an interface between two different periodic media. The results presented here characterize the existence of localized eigenmodes in each case and, when they exist, determine their eigenfrequencies and provide concise analytic results that quantify the decay rate of these modes. These results are obtained using both high-frequency homogenization and transfer matrix analysis, with good agreement between the two methods.
Craster R, Guenneau S, Kadic M, et al., 2023, Mechanical metamaterials, REPORTS ON PROGRESS IN PHYSICS, Vol: 86, ISSN: 0034-4885
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Lenz SV, Guenneau S, Drinkwater BW, et al., 2023, Transformation twinning to create isospectral cavities, Physical Review B, Vol: 108, ISSN: 2469-9950
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 metamaterial cloaking. We twin a hexagonal drum with a deformed hexagonal drum using a nonsingular coordinate transform that adjusts the deformed shape by mapping a near boundary domain to a zone of heterogeneous anisotropic medium. Splines define the mapping zone for twinning these two drums and we verify isospectrality by a finite-element analysis.
Wiltshaw R, De Ponti JM, Craster RV, 2023, Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states, The Quarterly Journal of Mechanics and Applied Mathematics, Vol: 76, Pages: 163-209, ISSN: 0033-5614
We derive analytical solutions based on singular Green’s functions, which enable efficient computations of scattering simulations or Floquet–Bloch dispersion relations for waves propagating through an elastic plate, whose surface is patterned by periodic arrays of elastic beams. Our methodology is versatile and allows us to solve a range of problems regarding arrangements of multiple beams per primitive cell, over Bragg to deep-subwavelength scales; we cross-verify against finite element numerical simulations to gain further confidence in our approach, which relies upon the hypothesis of Euler–Bernoulli beam theory considerably simplifying continuity conditions such that each beam can be replaced by point forces and moments applied to the neutral plane of the plate. The representations of Green’s functions by Fourier series or Fourier transforms readily follows, yielding rapid and accurate analytical schemes. The accuracy and flexibility of our solutions are demonstrated by engineering topologically non-trivial states, from primitive cells with broken spatial symmetries, following the phononic analogue of the Quantum Valley Hall Effect. Topologically protected states are produced and coexist along: interfaces between adjoining chiral-mirrored bulk media, and edges between one such chiral bulk and the surrounding bare elastic plate, allowing topological circuits to be designed with robust waveguiding. Our topologically protected interfacial states correspond to zero-line modes, and our topological edgestates are produced in accordance with the bulk-edge correspondence. These topologically non-trivial states exist within near flexural resonances of the constituent beams of the phononic crystal and hence can be tuned into a deep-subwavelength regime.
Chaplain GJ, Gliozzi AS, Davies B, et al., 2023, Tunable topological edge modes in Su–Schrieffer–Heeger arrays, Applied Physics Letters, Vol: 122, Pages: 1-6, ISSN: 0003-6951
A potential weakness of topological waveguides is that they act on a fixed narrow band of frequencies. However, by 3D printing samples from a photo-responsive polymer, we can obtain a device whose operating frequency can be fine-tuned dynamically using laser excitation. This greatly enhances existing static tunability strategies, typically based on modifying the geometry. We use a version of the classical Su–Schrieffer–Heeger model to demonstrate our approach.
De Ponti JM, Iorio L, Chaplain GJ, et al., 2023, Tailored topological edge waves via chiral hierarchical metamaterials, Physical Review Applied, Vol: 19, Pages: 1-9, ISSN: 2331-7019
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 damping or energy harvesting. We design an exemplar frame metamaterial, combining two distinct areas of wave physics. First, we consider topological edge states, taking an unconventional tetrachiral lattice. We control these highly localized protected edge states leveraging a hierarchy of scales through the addition of microresonators that impose tunable symmetry breaking and reconfigurable mass. This allows us to achieve precise positional control in the macroscale frame lattice, thereby opening up opportunities for robust signal transport and vibration control. Experiments, theory, and simulation are all utilized to provide a comprehensive analysis and interpretation of the physics.
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, Pages: 1-22, ISSN: 1364-5021
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.
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
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 in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance.
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
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 extensive numerical analyses based on 3D solid elements. Drawing from the underlying dynamic properties of the octet cell, we numerically propose a tailorable design with enhanced filtering capabilities. We transform the geometry of the original unit cell by applying a uniaxial scaling factor that, by breaking the in-plane symmetry of the structure, yields independently tuned struts and consequently multiple tunable bandgaps within the same cell. Our findings expand the spectrum of available numerical analyses on the octet lattice, taking it a significant step closer to its physical implementation. The ability of the octet lattice to control the propagation of flexural vibrations is significant within various applications in the mechanical and civil engineering domains, and we note such frame-like designs could lead to advancements in energy harvesting and vibration protection devices (e.g., lightweight and resonance-tunable absorbers).
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, Erratum: Elastic orbital angular momentum [Phys. Rev. Lett. 128, 064301 (2022)], Physical Review Letters, Vol: 128, ISSN: 0031-9007
Corrected 13 July 2022.
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.
Ungureanu B, Makwana MP, Craster RV, et al., 2022, Elastic body waves control via the Topological Rainbow Effect, Pages: 599-600
We propose a form of topological guidance for flexural waves in thin perforated elastic plates [1], which can be viewed as an approximate model for surface Rayleigh waves propagating through an array of boreholes drilled in soft soil atop bedrock. We do so by considering a square perforation within a square unit cell that is then extended periodically upon a square lattice, as illustrated in figure 1, when combined with the rainbow effect, offers a pragmatic route to energy harvesting.
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.
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