Imperial College London

ProfessorRichardCraster

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8554r.craster Website

 
 
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Location

 

6M24Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

283 results found

Makwana M, Craster R, Guenneau S, 2019, Topological beam-splitting in photonic crystals., Opt Express, Vol: 27, Pages: 16088-16102

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

Journal article

Makwana M, Craster R, Guenneau S, 2019, Topological beam-splitting in photonic crystals, Publisher: OPTICAL SOC AMER

Working paper

Palmer S, Xiao X, Pazos-Perez N, Guerrini L, Correa-Duarte M, Maier S, Craster R, Alvarez-Puebla R, Giannini Vet al., 2019, Extraordinarily transparent compact metallic metamaterials, Nature Communications, Vol: 10, ISSN: 2041-1723

The design of achromatic optical components requires materials with high transparency and low dispersion. We show that although metals are highly opaque, densely packed arrays of metallic nanoparticles can be more transparent to infrared radiation than dielectrics such as germanium, even when the arrays are over 75% metal by volume. Such arrays form effective dielectrics that are virtually dispersion-free over ultra-broadband ranges of wavelengths from microns up to millimeters or more. Furthermore, the local refractive indices may be tuned by altering the size, shape, and spacing of the nanoparticles, allowing the design of gradient-index lenses that guide and focus light on the microscale. The electric field is also strongly concentrated in the gaps between the metallic nanoparticles, and the simultaneous focusing and squeezing of the electric field produces strong ‘doubly-enhanced’ hotspots which could boost measurements made using infrared spectroscopy and other non-linear processes over a broad range of frequencies.

Journal article

Martin RJ, Kearney MJ, Craster R, 2019, Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes, Journal of Physics A: Mathematical and Theoretical, Vol: 52, ISSN: 1751-8113

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.

Journal article

Dubois M, Perchoux J, Vanel AL, Tronche C, Achaoui Y, Dupont G, Bertling K, Rakic AD, Antonakakis T, Enoch S, Abdeddaim R, Craster RV, Guenneau Set al., 2019, Acoustic flat lensing using an indefinite medium, PHYSICAL REVIEW B, Vol: 99, ISSN: 2469-9950

Journal article

Vanel AL, Craster RV, Schnitzer O, Asymptotic modelling of phononic box crystals, SIAM Journal on Applied Mathematics, ISSN: 0036-1399

We introduce phononic box crystals, namely arrays of adjoined perforated boxes, as a three-dimensional prototype for an unusual class of subwavelength metamaterials based on directly coupling resonating elements. In this case, when the holes coupling the boxes are small, we create networks of Helmholtz resonators with nearest-neighbour interactions. We use matched asymptotic expansions, in the small hole limit, to derive simple, yet asymptotically accurate, discrete wave equations governing the pressure field. These network equations readily furnish analytical dispersion relations for box arrays, slabs and crystals, that agree favourably with finite-element simulations of the physical problem. Our results reveal that the entire acoustic branch is uniformly squeezed into a subwavelength regime; consequently, phononic box crystals exhibit nonlinear-dispersion effects (such as dynamic anisotropy) in a relatively wide band, as well as a high effective refractive index in the long-wavelength limit. We also study the sound field produced by sources placed within one of the boxes by comparing and contrasting monopole- with dipole-type forcing; for the former the pressure field is asymptotically enhanced whilst for the latter there is no asymptotic enhancement and the translation from the microscale to the discrete description entails evaluating singular limits, using a regularized and efficient scheme, of the Neumann's Green's function for a cube. We conclude with an example of using our asymptotic framework to calculate localized modes trapped within a defected box array.

Journal article

Chaplain GJ, Makwana MP, Craster R, 2019, Rayleigh-Bloch, topological edge and interface waves for structured elastic plates, WAVE MOTION, Vol: 86, Pages: 162-174, ISSN: 0165-2125

Journal article

Martin R, Craster RV, Pannier A, Kearney MJet al., 2019, Analytical approximation to the multidimensional Fokker--Planck equation with steady state, Journal of Physics A: Mathematical and Theoretical, Vol: 52, ISSN: 1751-8113

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.

Journal article

Berte R, Della Picca F, Poblet M, Li Y, Cortes E, Craster RV, Maier SA, Bragas AVet al., 2018, Acoustic far-field hypersonic surface wave detection with single plasmonic nanoantennas, Physical Review Letters, Vol: 121, ISSN: 0031-9007

The optical properties of small metallic particles allow us to bridge the gap between the myriad of subdiffraction local phenomena and macroscopic optical elements. The optomechanical coupling between mechanical vibrations of Au nanoparticles and their optical response due to collective electronic oscillations leads to the emission and the detection of surface acoustic waves (SAWs) by single metallic nanoantennas. We take two Au nanoparticles, one acting as a source and the other as a receptor of SAWs and, even though these antennas are separated by distances orders of magnitude larger than the characteristic subnanometric displacements of vibrations, we probe the frequency content, wave speed, and amplitude decay of SAWs originating from the damping of coherent mechanical modes of the source. Two-color pump-probe experiments and numerical methods reveal the characteristic Rayleigh wave behavior of emitted SAWs, and show that the SAW-induced optical modulation of the receptor antenna allows us to accurately probe the frequency of the source, even when the eigenmodes of source and receptor are detuned.

Journal article

Makwana MP, Craster R, 2018, Designing multidirectional energy splitters and topological valley supernetworks, PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950

Journal article

Makwana MP, Craster R, 2018, Geometrically navigating topological plate modes around gentle and sharp bends, PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950

Journal article

Guenneau S, Brule S, Enoch S, Diatta A, Achaoui Y, Ungureanu B, Hutridurga H, Craster RVet al., 2018, Some challenges regarding cloaking and earthquake protection, Pages: 158-160

© 2018 IEEE. Building upon analogies with cloaking of elastic waves in plates, a large scale experiment has demonstrated unprecedented control of surface seismic waves in structured soils. Here, we would like to review recent research advances and remaining challenges in the theory and applications of seismic metamaterials for cloaking and earthquake protection. We recall some results on transformation elastodynamics and introduce mathematical theory of near cloaking for elastic equations. The former is a natural framework for scattering problems in unbounded domains, while the latter addresses boundary measurements in bounded domains. These two fields of investigation bring complementary information on cloaking efficiency. Intimate links between cloaking and wave protection will be also discussed.

Conference paper

Bennetts LG, Peter MA, Craster R, 2018, Graded resonator arrays for spatial frequency separation and amplification of water waves, Journal of Fluid Mechanics, Vol: 854, ISSN: 0022-1120

A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.

Journal article

Kahouadji L, Nowak E, Kovalchuk N, Chergui J, Juric D, Shin S, Simmons MJH, Craster RV, Matar OKet al., 2018, Simulation of immiscible liquid-liquid flows in complex microchannel geometries using a front-tracking scheme, MICROFLUIDICS AND NANOFLUIDICS, Vol: 22, ISSN: 1613-4982

The three-dimensional two-phase flow dynamics inside a microfluidic device of complex geometry is simulated using a parallel, hybrid front-tracking/level-set solver. The numerical framework employed circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The device considered in the present work is constructed via a module that defines solid objects by means of a static distance function. The construction combines primitive objects, such as a cylinder, a plane, and a torus, for instance, using simple geometrical operations. The numerical solutions predicted encompass dripping and jetting, and transitions in flow patterns are observed featuring the formation of drops, ‘pancakes’, plugs, and jets, over a wide range of flow rate ratios. We demonstrate the fact that vortex formation accompanies the development of certain flow patterns, and elucidate its role in their underlying mechanisms. Experimental visualisation with a high-speed imaging are also carried out. The numerical predictions are in excellent agreement with the experimental data.

Journal article

Craster RV, Sassi R, 2018, Spectral algorithms for reaction-diffusion equations, Publisher: arXiv

A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches. The examples are chosen from the literature to illustrate points and queries that naturally arise.

Working paper

Movchan AB, McPhedran RC, Carta G, Craster RVet al., 2018, Platonic localisation: one ring to bind them, Archive of Applied Mechanics, ISSN: 0939-1533

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.

Journal article

Choi W, Shi F, Lowe MJS, Skelton EA, Craster RV, Daniels WLet al., 2018, Rough surface reconstruction of real surfaces for numerical simulations of ultrasonic wave scattering, NDT and E International, Vol: 98, Pages: 27-36, ISSN: 0963-8695

The scattering of waves by rough surfaces plays a significant role in many fields of physical sciences including ultrasonics where failure surfaces are often rough and their accurate identification is critical. The prediction of the strength of scattering can be hampered when the roughness is not adequately characterised and this is a particular issue when the surface roughness is within an order of the incident wavelength. Here we develop a methodology to reconstruct, and accurately represent, rough surfaces using an AutoRegressive (AR) process that then allows for rapid numerical simulations of ultrasonic wave rough surface scattering in three dimensions. Gaussian, exponential and AR surfaces are reconstructed based on real surface data and the statistics of the surfaces are compared with each other. The statistics from the AR surfaces agree well with those from actual rough surfaces, taken from experimental samples, in terms of the heights as well as the gradients, which are the two main factors in accurately predicting the wave scattering intensities. Ultrasonic rough surface scattering is simulated numerically using the Kirchhoff approximation, and comparisons with Gaussian, exponential, AR and real sample surfaces are performed; scattering intensities found using AR surfaces show the best agreement with the real sample surfaces.

Journal article

Craster R, Guenneau S, Hutridurga Ramaiah H, Pavliotis Get al., 2018, Cloaking via mapping for the heat equation, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Vol: 16, Pages: 1146-1174, ISSN: 1540-3459

This paper explores the concept of near-cloaking in the context of time-dependentheat propagation. We show that after the lapse of a certain threshold time, the boundary measure-ments for the homogeneous heat equation are close to the cloaked heat problem in a certain Sobolevspace norm irrespective of the density-conductivity pair in the cloaked region. A regularised trans-formation media theory is employed to arrive at our results. Our proof relies on the study of the longtime behaviour of solutions to the parabolic problems with high contrast in density and conductivitycoefficients. It further relies on the study of boundary measurement estimates in the presence of smalldefects in the context of steady conduction problem. We then present some numerical examples to illustrate our theoretical results.

Journal article

Smith ER, Theodorakis PE, Craster RV, Matar OKet al., 2018, Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling., Langmuir, ISSN: 0743-7463

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.

Journal article

Skelton E, Craster RV, Colombi A, Colquitt Det al., 2018, The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion, New Journal of Physics, Vol: 20, ISSN: 1367-2630

We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.

Journal article

Puvirajesinghe TM, Zhi ZL, Craster RV, Guenneau Set al., 2018, Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide, Journal of the Royal Society Interface, Vol: 15, ISSN: 1742-5662

Graphene oxide (GO) is increasingly used for controlling mass diffusion in hydrogel-based drug delivery applications. On the macro-scale, the density of GO in the hydrogel is a critical parameter for modulating drug release. Here, we investigate the diffusion of a peptide drug through a network of GO membranes and GO-embedded hydrogels, modelled as porous matrices resembling both laminated and 'house of cards' structures. Our experiments use a therapeutic peptide and show a tunable nonlinear dependence of the peptide concentration upon time. We establish models using numerical simulations with a diffusion equation accounting for the photo-thermal degradation of fluorophores and an effective percolation model to simulate the experimental data. The modelling yields an interpretation of the control of drug diffusion through GO membranes, which is extended to the diffusion of the peptide in GO-embedded agarose hydrogels. Varying the density of micron-sized GO flakes allows for fine control of the drug diffusion. We further show that both GO density and size influence the drug release rate. The ability to tune the density of hydrogel-like GO membranes to control drug release rates has exciting implications to offer guidelines for tailoring drug release rates in hydrogel-based therapeutic delivery applications.

Journal article

Seungwon S, Chergui J, Juric D, Kahouadji L, Matar OK, Craster Ret al., 2018, A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant, Journal of Computational Physics, Vol: 359, ISSN: 0021-9991

A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737–757) is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.

Journal article

Berte R, Picca FD, Poblet M, Li Y, Cortés E, Craster RV, Maier SA, Bragas AVet al., 2018, Generation and detection of surface acoustic waves using single plasmonic nanoresonators

© 2018 The Author (s). We show in this work that coherent phonons generated after the decay of optically-excited plasmons in isolated metallic nanoantennas, are transmitted through the substrate as surface acoustic waves (SAWs) which can be detected by other nanoantennas used as receptors and positioned at distances up to 3μm away from the source. Two color sub-ps pump-probe technique and numerical methods suggest wave speed and amplitude decay characteristic of Rayleigh waves, the former within 3.2% of the predicted for fused silica. It is also shown that the mechanical excitation of the receptors via SAW modulates the optical response of the probe transmission and that its spectral content shows that the detection is feasible, even when the vibrational modes of the receptor are detuned from those of the source.

Conference paper

Brule S, Ungureanu B, Achaoui Y, Diatta A, Aznavourian R, Antonakakis T, Craster R, Enoch S, Guenneau Set al., 2017, Metamaterial-like transformed urbanism, INNOVATIVE INFRASTRUCTURE SOLUTIONS, Vol: 2, ISSN: 2364-4176

Journal article

Schnitzer O, Craster RV, 2017, Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers, SIAM Journal on Applied Mathematics, Vol: 77, Pages: 2119-2135, ISSN: 0036-1399

We study waves governed by the planar Helmholtz equation, propagating in aninfinite lattice of subwavelength Dirichlet scatterers, the periodicity beingcomparable to the wavelength. Applying the method of matched asymptoticexpansions, the scatterers are effectively replaced by asymptotic pointconstraints. The resulting coarse-grained Bloch-wave dispersion problem issolved by a generalised Fourier series, whose singular asymptotics in thevicinities of scatterers yield the dispersion relation governing modes that arestrongly perturbed from plane-wave solutions existing in the absence of thescatterers; there are also empty-lattice waves that are only weakly perturbed.Characterising the latter is useful in interpreting and potentially designingthe dispersion diagrams of such lattices. The method presented, that simplifiesand expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could beapplied in the future to study more sophisticated designs entailing resonantsubwavelength elements distributed over a lattice with periodicity on the orderof the operating wavelength.

Journal article

Vanel AL, Schnitzer O, Craster RV, 2017, Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals, Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 119, ISSN: 1286-4854

We demonstrate that photonic and phononic crystals consisting of closely spaced inclusions constitute a versatile class of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystal form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous photonic (phononic) crystals are in fact asymptotically equivalent, at low frequencies, to discrete capacitor-inductor (mass-spring) networks whose lumped parameters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch, or branches when the discrete analogue is polyatomic, is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power $1/4$ ; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals. The insight gained from the network approach is used to show that, surprisingly, the continuum created by a closely packed hexagonal lattice of cylinders is represented by a discrete honeycomb lattice. The analogy is utilised to show that the hexagonal continuum lattice has a Dirac-point degeneracy that is lifted in a controlled manner by specifying the area of a symmetry-breaking defect.

Journal article

Craster R, Guenneau S, Hutridurga H, Pavliotis Get al., 2017, Regularized transformation optics for transient heat transfer, 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 127-129

Conference paper

Colombi A, Craster R, Clark M, Colquitt Det al., 2017, Slow waves, elastic rainbow and dynamic anisotropy with a cluster of resonant rods on an elastic halfspace, 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 409-410

Conference paper

Shi F, Lowe M, Skelton EA, Craster RVet al., 2017, A time-domain finite element boundary integral approach for elastic wave scattering, Computational Mechanics, Pages: 1-13, ISSN: 0178-7675

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Journal article

Colombi A, Roux P, Miniaci M, Craster R, Guenneau S, Gueguen Pet al., 2017, The role of large scale computing behind the development of seismic (and elastic) metamaterials., 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 406-408

Conference paper

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