arXiv subjects

R. V. Craster

Publications and source records attributed to R. V. Craster.

17 recordsLinked to original sources

arXiv2024

Tunable topological edge modes in Su-Schrieffer-Heeger arrays

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.

physics.app-ph↗

arXiv2023

Robust collimated beaming in 3D acoustic sonic crystals

We demonstrate strongly collimated beaming, 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-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beaming phenomenon and use a crystal consisting of a finite rectangular cuboid array of $4\times 10\times 10$ polymer spheres $1.38$~cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as $1.5$~cm. Collimation effects are observed in the time domain for chirps with central frequencies at $14.2$~kHz and $18$~kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer (SMI) -- a recently proposed technique to observe complex acoustic fields -- that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.

physics.app-ph↗

arXiv2022

Elastic Orbital Angular Momentum

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.

cond-mat.soft↗

arXiv2019

Fresnel drag in space-time modulated metamaterials

A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actual material motion. We discuss how both the permittivity and permeability need to be modulated in order to achieve these effects, and we present an equivalent transmission line model.

physics.optics↗

arXiv2019

Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.

math-ph↗

arXiv2018

Rayleigh-Bloch, topological edge and interface waves for structured elastic plates

Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal arrangements. We model array and interface waves for structured thin elastic plates, so-called platonic crystals, that share many analogies with their electromagnetic and acoustic counterparts, photonic and phononic crystals, and much of what we present carries across to those systems. These crystals support several forms of edge or array-guided modes, that decay perpendicular to their direction of propagation. To rapidly, and accurately, characterise these modes and their decay we develop a spectral Galerkin method, using a Fourier--Hermite basis, to provide highly accurate dispersion diagrams and mode-shapes, that are confirmed with full scattering simulations. We illustrate this approach using Rayleigh Bloch modes, and generalise high frequency homogenisation, along a line array, to extract the envelope wavelength along the array. Rayleigh-Bloch modes along graded arrays of rings of point masses are investigated and novel forms of the rainbow trapping effect and wave hybridisation are demonstrated. Finally, the method is used to investigate the dispersion curves and mode-shapes of interfacial waves created by geometrical differences in adjoining media.

physics.class-ph↗

arXiv2018

Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling

Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.

cond-mat.soft↗

arXiv2018

Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes

The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a starting-point, and extending to a general mean-reverting process, we investigate the long- and short-time asymptotics using a combination of Hopf-Cole and Laplace transform techniques. As a result we are able to give a single formula that is correct in both limits, as well as being exact in certain special cases. We demonstrate the results using a variety of other models.

math-ph↗

arXiv2018

Acoustic flat lensing using an indefinite medium

Acoustic flat lensing is achieved here by tuning a phononic array to have indefinite medium behaviour in a narrow frequency spectral region along the acoustic branch. This is confirmed by the occurrence of a flat band along an unusual path in the Brillouin zone and by interpreting the intersection point of isofrequency contours on the corresponding isofrequency surface; coherent directive beams are formed whose reflection from the array surfaces create lensing. Theoretical predictions are corroborated by time-domain experiments, airborne acoustic waves generated by a source with a frequency centered about $10.6$ kHz, placed at three different distances from one side of a finite phononic crystal slab, constructed from polymeric spheres, yield distinctive focal spots on the other side. These experiments evaluate the pressure field using optical feedback interferometry and demonstrate precise control of the three-dimensional wave trajectory through a sonic crystal.

physics.class-ph↗

arXiv2018

Platonic Localisation: One Ring to Bind Them

In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring-mass resonators can be tuned to produce a "negative inertia" input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes.

physics.class-ph↗

arXiv2017

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.

physics.class-ph↗

arXiv2017

Clamped seismic metamaterials: Ultra-low broad frequency stop-bands

The regularity of earthquakes, their destructive power, and the nuisance of ground vibration in urban environments, all motivate designs of defence structures to lessen the impact of seismic and ground vibration waves on buildings. Low frequency waves, in the range $1$ to $10$ Hz for earthquakes and up to a few tens of Hz for vibrations generated by human activities, cause a large amount of damage, or inconvenience, depending on the geological conditions they can travel considerable distances and may match the resonant fundamental frequency of buildings. The ultimate aim of any seismic metamaterial, or any other seismic shield, is to protect over this entire range of frequencies, the long wavelengths involved, and low frequency, have meant this has been unachievable to date. Elastic flexural waves, applicable in the mechanical vibrations of thin elastic plates, can be designed to have a broad zero-frequency stop-band using a periodic array of very small clamped circles. Inspired by this experimental and theoretical observation, all be it in a situation far removed from seismic waves, we demonstrate that it is possible to achieve elastic surface (Rayleigh) and body (pressure P and shear S) wave reflectors at very large wavelengths in structured soils modelled as a fully elastic layer periodically clamped to bedrock. We identify zero frequency stop-bands that only exist in the limit of columns of concrete clamped at their base to the bedrock. In a realistic configuration of a sedimentary basin 15 meters deep we observe a zero frequency stop-band covering a broad frequency range of $0$ to $30$ Hz.

physics.class-ph↗

arXiv2016

Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials, and metasurfaces, in the bulk and at the surface respectively. Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in displacement from surface to bulk waves.

physics.geo-ph↗

arXiv2016

Radiation from structured-ring resonators

We investigate the scalar-wave resonances of systems composed of identical Neumann-type inclusions arranged periodically around a circular ring. Drawing on natural similarities with the undamped Rayleigh-Bloch waves supported by infinite linear arrays, we deduce asymptotically the exponentially small radiative damping in the limit where the ring radius is large relative to the periodicity. In our asymptotic approach, locally linear Rayleigh-Bloch waves that attenuate exponentially away from the ring are matched to a ring-scale WKB-type wave field. The latter provides a descriptive physical picture of how the mode energy is transferred via tunnelling to a circular evanescent-to-propagating transition region a finite distance away from the ring, from where radiative grazing rays emanate to the far field. Excluding the zeroth-order standing-wave modes, the position of the transition circle bifurcates with respect to clockwise and anti-clockwise contributions, resulting in striking spiral wavefronts.

physics.class-ph↗

arXiv2015

Modulation of diffusion rate of therapeutic peptide drugs using graphene oxide membranes

We investigate diffusion of a peptide drug through Graphene Oxide (GO) membranes that are modeled as a porous layered laminate constructed from aligned flakes of GO. Our experiments using a peptide drug show a tunable non-linear dependence of the peptide concentration upon time. This is confirmed using numerical simulations with a diffusion equation accounting for the photothermal degradation of fluorophores and an effective percolation model. This modeling yields an interpretation of the control and delay of drug diffusion through GO membranes. The ability to modulate the density of hydrogel-like GO membranes to control drug release rates could be a step forwards in tailoring drug release properties of the hydrogels for therapeutic applications.

cond-mat.mtrl-sci↗

arXiv2015

The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms

An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The theory we develop is then applied to two topical examples, the first being the case of aligned dielectric cylinders, which has great importance in the modelling of photonic crystal fibres. We then consider the propagation of waves in a structured metafilm, here chosen to be a planar array of dielectric spheres. At certain frequencies strongly directional dynamic anisotropy is observed, and the asymptotic theory is shown to capture the effect, giving highly accurate qualitative and quantitative results as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour.

math-ph↗

arXiv2014

High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.

physics.class-ph↗