arXiv subjects

Richard Craster

Publications and source records attributed to Richard Craster.

At least 19 recordsLinked to original sources

arXiv2026

Nonreciprocal topological kink-wave propagation in mechanical metamaterials

Nonlinear mechanical metamaterials can exhibit emergent transport phenomena that mimic topological protection without relying on linear band topology. Here, we realize a bifurcation-induced nonreciprocal lattice that supports robust propagation of elastic kink waves. Each unit is a prestrained, hinged-beam circulator that develops angular momentum bias during snap-through transitions between buckling states, producing an effective breaking of time reversal symmetry. Coupling such units into a hexagonal array yields a mechanically chiral network where localized soliton-like excitations propagate unidirectionally along interfaces and edges, immune to sharp bends. We demonstrate non-dispersive kink transport governed by a SineGordon type field whose effective bias encodes mechanical chirality. This framework bridges bifurcation dynamics and nonreciprocal transport, establishing a nonlinear route toward topological like mechanical functionality without magnetic or gyroscopic bias.

cond-mat.mtrl-sci↗

arXiv2025

Metamaterials and Fluid Flows

Understanding and controlling the dynamic interactions between fluid flows and solid materials and structures-a field known as fluid-structure interaction -is central not only to established disciplines such as aerospace and naval engineering but also to emerging technologies such as energy harvesting, soft robotics, and biomedical devices. In recent years, the advent of metamaterials-rationally designed composites with properties beyond their constituents, often not found in conventional materials-has provided exciting opportunities for rethinking and redesigning fluid-structure interaction. The premise of engineering the internal structure of materials interfacing with fluid flows is opening a new horizon for precise and effective manipulation and control of coupled fluidic, acoustic, and elastodynamics responses. This review focuses on this relatively unexplored interdisciplinary theme with broad real-world technological significance. Key performance metrics, such as fuel consumption of transport systems, efficiency of renewable energy extraction, mitigation of noise emissions, and resilience to structural fatigue, depend on the control of interactions between flow, acoustic, and vibration mechanisms. Flow control, for example, which spans a wealth of regimes such as laminar, transitional, turbulent, and unsteady separated flows, is highly influenced by the ability to tailor fluid-structure interaction behavior. We survey and discuss theoretical frameworks that describe the interplay between fluids and elastic solids, with a focus on contemporary work and emerging concepts. The paper is organised into three main sections-flow-structure interactions, acoustic-structure interactions, and exotic metamaterial concepts with potential impact on fluid-structure interaction-and concludes with perspectives on current challenges and future directions in this rapidly expanding area of research.

cond-mat.soft↗

arXiv2025

On the Practicability of Ceramic-Tiled Walls for Sound Absorption by Tuning Cavities

We present the practicality of structuring ceramic tiles for enhancing sound absorption on rigid walls. The cornerstone of our methodology is to structure walls with cavities so that walls effectively behave as heterogeneous absorbing surfaces over a large frequency bandwidth. Using this approach, ceramic tiled walls are developed by integrating tuned cavity structures based on Helmholtz resonators. Such a design leverages the empty joints between tiles to form resonator necks, while the space between the ceramic tiles and the wall acts as the resonator chambers. By arranging these resonators in a spatially graded array, we achieve broadband sound absorption which targets low-frequency noise generated by impacts, footsteps and ambient sources. This makes the system highly suitable for practical architectural applications. The study encompasses the entire process, from numerical modeling and analytical formulation to the fabrication and mounting of resonant tiles, followed by experimental validation, clearly demonstrating the effectiveness of the proposed solution in real-world conditions. The findings highlight the strong potential of this approach for practical tiled room acoustic treatment and noise mitigation.

physics.app-ph↗

arXiv2025

Space-Time Elastic Metamaterials for Zero-Frequency and Zero-Wavenumber Bandgaps

We create wave-matter space-time metamaterials using optical trapping forces to manipulate mass-spring chains and create zero-frequency and zero-wavenumber band gaps: the bosonic nature of phonons, and hence this elastodynamic setting, traditionally prohibits either zero-frequency or zero-wavenumber band gaps. Here, we generate zero-frequency gaps using optomechanical interactions within a 3D mass-spring chain by applying an optical trapping force to hold or manipulate a mass in a contactless manner independent of its elastodynamic excitations. Through careful modification of the geometrical parameters in the trapped monoatomic mass-spring chain, we demonstrate the existence of a zero-frequency gap generated by the optical forces on the masses. The precise control we have over the system allows us to drive another set of masses and springs out of phase with its traveling wave thereby creating a zero-wavenumber band gap.

physics.optics↗

arXiv2025

Controlling the Propagation of Flexural Elastic Waves With Ceramic Metatiles

In this work, we examine the application of phononic metamaterials for elastic impact noise insulation in tiled flooring, through the development of an innovative ceramic metatile that incorporates phononic crystals with optimized joint configurations. First, we optimize the geometrical and material parameters of the proposed metatile, which is composed of small ceramic subtiles connected by silicon joints, in order to reduce longitudinal and flexural wave propagation on tiled floors, which are responsible for noise vibrations in tiled environments. A bandgap is achieved that effectively suppresses the transmission of impact noise through the periodic structural configuration. For flexural waves, the ceramic metatile exhibits a pronounced attenuation of wave transmission in the range of $500$-$1900$ Hz along the $[100]$ direction, and $500$-$1400$ Hz along the $[110]$ direction. For longitudinal waves, a broad bandgap is observed, spanning from $400$ Hz to $1950$ Hz in both the $[100]$ and $[110]$ directions. Additionally, the bandgaps shift toward lower frequencies with increasing width of the subtiles and silicon joints, or with a decrease in the Young's modulus of the silicon. In both experimental and numerical tests, it is demonstrated that the integration of silicon joints inside the ceramic metatile improves the acoustic insulation performance, as measured by the reduction of impact noise levels across a wide range of low frequencies. The findings highlight the potential of metamaterials in architectural acoustics, offering innovative solutions for elastic wave control in tiled environments.

physics.app-ph↗

arXiv2024

Predicting band structures for 2D Photonic Crystals via Deep Learning

Photonic crystals (PhCs) are periodic dielectric structures that exhibit unique electromagnetic properties, such as the creation of band gaps where electromagnetic wave propagation is inhibited. Accurately predicting dispersion relations, which describe the frequency and direction of wave propagation, is vital for designing innovative photonic devices. However, traditional numerical methods, like the Finite Element Method (FEM), can encounter significant computational challenges due to the multiple scales present in photonic crystals, especially when calculating band structures across the entire Brillouin zone. To address this, we propose a supervised learning approach utilizing U-Net, along with transfer learning and Super-Resolution techniques, to forecast dispersion relations for 2D PhCs. Our model reduces computational expenses by producing high-resolution band structures from low-resolution data, eliminating the necessity for fine meshes throughout the Brillouin zone. The U-Net architecture enables the simultaneous prediction of multiple band functions, enhancing efficiency and accuracy compared to existing methods that handle each band function independently. Our findings demonstrate that the proposed model achieves high accuracy in predicting the initial band functions of 2D PhCs, while also significantly enhancing computational efficiency. This amalgamation of data-driven and traditional numerical techniques provides a robust framework for expediting the design and optimization of photonic crystals. The approach underscores the potential of integrating deep learning with established computational physics methods to tackle intricate multiscale problems, establishing a new benchmark for future PhC research and applications.

math.NA↗

arXiv2024

Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization

The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization which results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading therefore to a corrective advective term which cancels out non-reciprocity at the leading order but not at the second order.

math.AP↗

arXiv2024

An hp-Adaptive Sampling Algorithm for Dispersion Relation Reconstruction of 3D Photonic Crystals

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 refined at each iteration, construct a conforming element-wise polynomial space on the adaptive mesh such that the distribution of the local polynomial spaces reflects the regularity of the band functions, and define an element-wise Lagrange interpolation operator to approximate the band functions. We rigorously prove the convergence of the algorithm. To illustrate the significant potential of the algorithm, we present two numerical tests with band gap optimization.

math.NA↗

arXiv2023

High-frequency homogenization for periodic dispersive media

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 approximations of the dispersion diagrams, and the wavefields, so obtained are then cross-validated via detailed comparison with finite element method simulations in both one and two dimensions.

physics.class-ph↗

arXiv2020

Elastic Wave Near-Cloaking

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 recognising 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 \rvc{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.

cond-mat.mtrl-sci↗

arXiv2020

The influence of structure geometry and material on seismic metamaterial performance

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 technological hurdles involved in this challenge. Engineering the structure of the SM serves as a basis to tune and enhance its functionality, and inspired by split rings, swiss-rolls, notch-shaped and labyrinthine designs of elementary cells in electromagnetic and mechanical metamaterials, we investigate altering the structure geometries of SMs with the aim of creating large bandgaps \textcolor{black}{in a subwavelength regime}. We show that square stiff inclusions, perform better in comparison to circular ones, whilst keeping the same filling fraction. En route to enhancing the bandgap, we have also studied the performance of SMs with different constituent materials; we find that steel columns, as inclusions, show large bandgaps, however, the columns are too large for steel to be a feasible material in practical or financial terms. Non-reinforced concrete would be preferable for industry level scaling up of the technology because, concrete is cost-effective, easy to cast directly at the construction site and easy to provide arbitrary geometry of the structure. As a part of this study, we show that concrete columns can also be designed to exhibit bandgaps if we cast them within a soft soil coating surrounding the protected area for various civil structures like a bridge, building, oil pipelines etc.

physics.app-ph↗

arXiv2020

Designing Hyper-Thin Acoustic Metasurfaces with Membrane Resonators

We design extremely-thin acoustic metasurfaces, providing a versatile platform for the manipulation of reflected pressure fields, that are constructed from mass loads and stretched membranes fixed to a periodic rigid framework. These metasurfaces demonstrate deeply subwavelength control and can have thicknesses an order of magnitude less than those based around Helmholtz resonators. Each sub-unit of the metasurface is resonant at a frequency tuned geometrically, this tunability provides phase control and using a set of finely tuned membrane resonators we create a phase-grating metasurface. This surface is designed to exhibit all-angle negative reflections with the ratio of wavelength, $λ$, to thickness, $h$, of $λ/h\approx 23.1$, and to create a flat mirror using the phase profile of an elliptic reflecting mirror. A further important acoustic application is to sound diffusers and we proceed to design a deeply subwavelength membrane-based meta-diffuser that can be two orders of magnitude thinner than the operating wavelength, i.e. thickness $\approxλ/102$. This paves the way for developing advanced acoustic metasurfaces with applicability to functional acoustic devices in sound-related industries.

physics.app-ph↗

arXiv2019

Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains

We introduce a new efficient algorithm for Helmholtz problems in perforated domains with the design of the scheme allowing for possibly large wavenumbers. Our method is based upon the Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) as proposed recently in [14]. For a regular coarse mesh with mesh size H, we establish O(H) convergence of this algorithm under the resolution assumption, and with the level parameter being sufficiently large. The performance of the algorithm is demonstrated by extensive 2-dimensional numerical tests including those motivated by photonic crystals.

math.NA↗

arXiv2019

Seismic wave shield using cubic arrays of split-ball resonators

Metre size inertial resonators located in the ground have been theoretically shown to interact with a seismic wave (attenuation, band gaps) to enable protection of surface structures such as buildings. The challenge for Civil Engineering is to both reduce the size of these resonators and to increase their efficiency. Here we explore steel spheres, connected to a concrete bulk medium, either by a coating of rubber, or rubber and steel ligaments, or air and steel ligaments. We show that for a cubic lattice periodicity of 1 metre, we achieve stop bands in the frequency range 14 to 20 Hz; by splitting spheres in 2 and 8 pieces, we tune down the stop bands frequencies and further increase their bandwidth. We thus demonstrate we are able to provide a variety of inertial resonators with stop bands below 10 Hz i.e., in the frequency range of interest for earthquake engineering.

physics.class-ph↗

arXiv2019

On near-cloaking for linear elasticity

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 Cosserat and Willis frameworks are shown to be equivalent to certain high contrast small defect problems for the 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 the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence of the solutions to the transmission problems is investigated, when the Lamé parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

math.AP↗

arXiv2019

Novel topological beam-splitting in photonic crystals

We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric 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 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.

physics.optics↗

arXiv2018

Geometrically navigating topological platonic modes around gentle and sharp bends

Predictive theory to geometrically engineer devices and materials in continuum systems to have desired topological-like effects is developed here by bridging the gap between quantum and continuum mechanical descriptions. A platonic crystal, a bosonic-like system in the language of quantum mechanics, is shown to exhibit topological valley modes despite the system having no direct physical connection to quantum effects. We emphasise a predictive, first-principle, approach, the strength of which is demonstrated by the ability to design well-defined broadband edge states, resistant to backscatter, using geometric differences; the mechanism underlying energy transfer around gentle and sharp corners is described. Using perturbation methods and group theory, several distinct cases of symmetry-induced Dirac cones which when gapped yield non-trivial band-gaps are identified and classified. The propagative behavior of the edge states around gentle or sharp bends depends strongly upon the symmetry class of the bulk media and we illustrate this via numerical simulations.

cond-mat.mes-hall↗

arXiv2018

Designing multi-directional energy-splitters and topological valley supernetworks

Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics literature that has, so far, been limited to 2-directional splitters. Additionally, we describe a design paradigm that gives greater detail, about the relative transmission along outgoing leads, away from a junction; previously only the negligible transmission leads were predictable. We utilise semi-analytic numerical simulations, as opposed to finite element methods, to clearly illustrate all of these features with highly resolved edge states. As a consequence of this theory, novel networks, with directionality tunable by geometry, ideal for applications such as beam-splitters, switches and filters are created. Coupling these novel networks, that contain multi-directional energy-splitters, culminates in the first realization of a topological supernetwork.

cond-mat.mes-hall↗