Publications
354 results found
Maling B, Craster RV, 2016, Asymptotic analysis of a Bragg fiber: a multiple scales approach, IMA Journal of Applied Mathematics, Vol: 81, Pages: 1191-1208, ISSN: 0272-4960
We develop an asymptotic approach to find the guided modes, and their frequencies, within a Bragg fiberconsisting of a cylindrical dielectric core surrounded by concentric cylindrical cladding layers; thesefibers have the aim of transporting electromagnetic waves over long distances with minimal transmissionlosses. We derive a scalar ordinary differential equation eigenvalue problem on a dynamic long-scale thathas the details of the short-scale field built into its coefficients, which is then straightforward to solve. Theresulting asymptotic results are compared against full numerical solutions and their accuracy verified.
Maling B, Colquitt D, Craster RV, 2016, Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings, Wave Motion, Vol: 69, Pages: 35-49, ISSN: 0165-2125
A two-scale asymptotic theory is developed to generate continuum equations that model the macroscopic be-haviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily longrelative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated throughintegrated quantities. The resulting equations include tensors that represent effective refractive indices near bandedge frequencies along all principal axes directions, and these govern scalar functions providing long-scale mod-ulation of short-scale Bloch eigenstates, which can be used to predict the propagation of waves at frequenciesoutside of the long wavelength regime; these results are outside of the remit of typical homogenisation schemes.The theory we develop is applied to two topical examples, the first being the case of aligned dielectric cylin-ders, which has great importance in modelling photonic crystal fibres. Results of the asymptotic theory are veri-fied against numerical simulations by comparing photonic band diagrams and evanescent decay rates for guidedmodes. The second example is the propagation of electromagnetic waves localised within a planar array of di-electric spheres; at certain frequencies strongly directional propagation is observed, commonly described as dy-namic anisotropy. Computationally this is a challenging three-dimensional calculation, which we perform, andthen demonstrate that the asymptotic theory captures the effect, giving highly accurate qualitative and quantitativecomparisons as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour.
Shi F, Lowe MJS, Craster RV, 2016, Recovery of correlation function of internal random rough surfaces from diffusely scattered elastic waves, Journal of the Mechanics and Physics of Solids, Vol: 99, Pages: 483-494, ISSN: 0022-5096
We propose an ultrasonic methodology to reconstruct the height correlation function of remotely inaccessible random rough surfaces in solids. The inverse method is based on the Kirchhoff approximation(KA), and it requires measuring the angular distribution of diffuse scattering intensities by sending in a narrow band incident pulse. Near field scattering effects are also included by considering the Fresnel assumption. The proposed approach is successfully verified by simulating the scattering from multiple realizations of rough surfaces whose correlation function is known, calculating the mean scattering intensities from these received signals, and then deploying the inverse method on these to reconstruct the original correlation function. Very good agreement between the reconstructed correlation function and the original is found, for a wide range of roughness parameters. In addition, the effect of reducing the number of realizations to approximate the mean intensity are investigated, providing confidence bounds for the experiment. An experiment on a corrugated rough surface is performed with a limited number of scans using a phased array, which further validates the proposed inversion algorithm.
Sasihithlu K, Pendry JB, Craster RV, 2016, Van der Waals force assisted heat transfer for vacuum gap spacings
Phonons (collective atomic vibrations in solids) are more effective intransporting heat than photons. This is the reason why the conduction mode ofheat transport in nonmetals (mediated by phonons) is dominant compared to theradiation mode of heat transport (mediated by photons). However, since phononsare unable to traverse a vacuum gap (unlike photons) it is commonly believedthat two bodies separated by a gap cannot exchange heat via phonons. Recently,a mechanism was proposed by which phonons can transport heat across a vacuumgap - through Van der Waals interaction between two bodies with gap less thanwavelength of light. Such heat transfer mechanisms are highly relevant forheating (and cooling) of nanostructures; the heating of the flying heads inmagnetic storage disks is a case in point. Here, the theoretical derivation formodeling phonon transmission is revisited and extended to the case of twobodies made of different materials separated by a vacuum gap. Magnitudes ofphonon transmission, and hence the heat transfer, for commonly used materialsin the micro and nano-electromechanical industry are calculated and comparedwith the calculation of conduction heat transfer through air for small gaps.
Haslinger SG, Movchan NV, Movchan AB, et al., 2016, Controlling flexural waves in semi-infinite platonic crystals
We address the problem of scattering and transmission of a plane flexuralwave through a semi-infinite array of point scatterers/resonators, which take avariety of physically interesting forms. The mathematical model accounts forseveral classes of point defects, including mass-spring resonators attached tothe top surface of the flexural plate and their limiting case of concentratedpoint masses. We also analyse the special case of resonators attached toopposite faces of the plate. The problem is reduced to a functional equation ofthe Wiener-Hopf type, whose kernel varies with the type of scattererconsidered. A novel approach, which stems from the direct connection betweenthe kernel function of the semi-infinite system and the quasi-periodic Green'sfunctions for corresponding infinite systems, is used to identify specialfrequency regimes. We thereby demonstrate dynamically anisotropic wave effectsin semi-infinite platonic crystals, with particular attention paid to designingsystems to exhibit dynamic neutrality (perfect transmission) and localisationclose to the structured interface.
Pendry JB, Sasihithlu K, Craster RV, 2016, Phonon-assisted heat transfer between vacuum-separated surfaces, Physical Review B - Condensed Matter and Materials Physics, Vol: 94, ISSN: 1098-0121
With increasing interest in nanotechnology, the question arises of how heat is exchanged between materials separated by only a few nanometers of vacuum. Here, we present calculations of the contribution of phonons to heat transfer mediated by van der Waals forces and compare the results to other mechanisms such as coupling through near field fluctuations. Our results show a more dramatic decay with separation than previous work.
Fitzgerald JM, Narang P, Craster RV, et al., 2016, Quantum Plasmonics, Proceedings of the IEEE, Vol: 104, Pages: 2307-2322, ISSN: 0018-9219
Quantum plasmonics is an exciting subbranch of nanoplasmonics where the laws of quantum theory are used to describe light–matter interactions on the nanoscale. Plasmonic materials allow extreme subdiffraction confinement of (quantum or classical) light to regions so small that the quantization of both light and matter may be necessary for an accurate description. State-of-the-art experiments now allow us to probe these regimes and push existing theories to the limits which opens up the possibilities of exploring the nature of many-body collective oscillations as well as developing new plasmonic devices, which use the particle quality of light and the wave quality of matter, and have a wealth of potential applications in sensing, lasing, and quantum computing. This merging of fundamental condensed matter theory with application-rich electromagnetism (and a splash of quantum optics thrown in) gives rise to a fascinating area of modern physics that is still very much in its infancy. In this review, we discuss and compare the key models and experiments used to explore how the quantum nature of electrons impacts plasmonics in the context of quantum size corrections of localized plasmons and quantum tunneling between nanoparticle dimers. We also look at some of the remarkable experiments that are revealing the quantum nature of surface plasmon polaritons.
Maling B, Craster RV, 2016, Whispering Bloch modes, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1364-5021
We investigate eigenvalue problems for the planar Helmholtz equation in open systems with a high order of rotational symmetry. The resulting solutions have similarities with the whispering gallery modes exploited in photonic micro-resonators and elsewhere, but unlike these do not necessarily require a surrounding material boundary, with confinement instead resulting from the geometry of a series of inclusions arranged in a ring. The corresponding fields exhibit angular quasi-periodicity reminiscent of Bloch waves, and hence we refer to them as whispering Bloch modes (WBMs). We show that if the geometry of the system is slightly perturbed such that the rotational symmetry is broken, modes with asymmetric field patterns can be observed, resulting in field enhancement and other potentially desirable effects. We investigate the WBMs of two specific geometries first using expansion methods and then by applying a two-scale asymptotic scheme.
Harutyunyan D, Milton GW, Craster RV, 2016, High-frequency homogenization for travelling waves in periodic media, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1364-5021
We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1=ω 2 and [Formula: see text] where Λ=(λ1λ2…λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a⊙b is defined to be the vector (a 1 b 1,a 2 b 2,…,a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.
Schnitzer O, Giannini V, Maier SA, et al., 2016, Surface-plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1364-5021
According to the hydrodynamic Drude model, surface plasmon resonances of metallic nanostructures blueshift owing to the non-local response of the metal’s electron gas. The screening length characterizing the non-local effect is often small relative to the overall dimensions of the metallic structure, which enables us to derive a coarse-grained non-local description using matched asymptotic expansions; a perturbation theory for the blueshifts of arbitrary-shaped nanometallic structures is then developed. The effect of non-locality is not always a perturbation and we present a detailed analysis of the ‘bonding’ modes of a dimer of nearly touching nanowires where the leading-order eigenfrequencies and eigenmode distributions are shown to be a renormalization of those predicted assuming a local metal permittivity.
Craster RV, Lowe M, Shi F, et al., 2016, Diffuse scattered field of elastic waves from randomly rough surfaces using an analytical Kirchhoff theory, Journal of the Mechanics and Physics of Solids, Vol: 92, Pages: 260-277, ISSN: 0022-5096
We develop an elastodynamic theory to predict the diffuse scattered field of elastic waves by randomly rough surfaces, for the first time, with the aid of the Kirchhoff approximation (KA). Analytical expressions are derived incorporating surface statistics, to represent the expectation of the angular distribution of the diffuse intensity for different modes. The analytical solutions are successfully verified with numerical Monte Carlo simulations, and also validated by comparison with experiments. We then apply the theory to quantitatively investigate the effects of the roughness and the shear-to-compressional wave speed ratio on the mode conversion and the scattering intensity, from low to high roughness within the valid region of KA. Both the direct and the mode converted intensities are significantly affected by the roughness, which leads to distinct scattering patterns for different wave modes. The mode conversion effect is very strong around the specular angle and it is found to increase as the surface appears to be more rough. In addition, the 3D roughness induced coupling between the out-of-plane shear horizontal (SH) mode and the in-plane modes is studied. The intensity of the SH mode is shown to be very sensitive to the out-of-plane correlation length, being influenced more by this than by the RMS value of the roughness. However, it is found that the depolarization pattern for the diffuse field is independent of the actual value of the roughness.
Vanel AL, Craster RV, Colquitt DJ, et al., 2016, Asymptotics of dynamic lattice Green’s functions, Wave Motion, Vol: 67, Pages: 15-31, ISSN: 0165-2125
In the study of periodic problems it is natural and commonplace to use Fourier transforms to obtain explicit lattice Green’s functions in the form of multidimensional integrals. Considerable physical information is encapsulated within the Green’s function and our aim is to extract the behaviour near critical frequencies by creating connections with multiple-scale homogenisation methods recently applied to partial differential equations. We show that the integrals naturally contain two-scales, a short-scale on the scale of the lattice and a long-scale envelope. For pedagogic purposes we first consider the well-known two dimensional square lattice, followed by the three dimensional cubic lattice. The features we uncover, and the asymptotics, are generic for many lattice structures. Finally we consider a topical three dimensional example from structural mechanics showing dynamic anisotropy, that is, at specific frequencies all the energy is directed along specific characteristic directions.
Colombi A, Colquitt D, Roux P, et al., 2016, A seismic metamaterial: the resonant metawedge, Scientific Reports, Vol: 6, ISSN: 2045-2322
Critical concepts from three different fields, elasticity, plasmonics and metamaterials, are brought together to design a metasurface at the geophysical scale, the resonant metawedge, to control seismic Rayleigh waves. Made of spatially graded vertical subwavelength resonators on an elastic substrate, the metawedge can either mode convert incident surface Rayleigh waves into bulk elastic shear waves or reflect the Rayleigh waves creating a "seismic rainbow" effect analogous to the optical rainbow for electromagnetic metasurfaces. Time-domain spectral element simulations demonstrate the broadband efficacy of the metawedge in mode conversion while an analytical model is developed to accurately describe and predict the seismic rainbow effect; allowing the metawedge to be designed without the need for extensive parametric studies and simulations. The efficiency of the resonant metawedge shows that large-scale mechanical metamaterials are feasible, will have application, and that the time is ripe for considering many optical devices in the seismic and geophysical context.
Choi W, Skelton EA, Pettit J, et al., 2016, A generic hybrid model for the simulation of three-dimensional bulk elastodynamics for use in nondestructive evaluation, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol: 63, Pages: 726-736, ISSN: 0885-3010
A three-dimensional (3-D) generic hybrid model is developed for the simulation of elastic waves in applications in nondestructive evaluation (NDE) that efficiently links different solution strategies but, crucially, is independent of the particular schemes employed. This is an important step forward in facilitating rapid and accurate large-scale simulations, and this advances the two-dimensional (2-D) generic hybrid methodology recently developed by the authors. The hybrid model provides an efficient and effective tool for creating highly accurate simulations that model the wave propagation and scattering, enabling the interpretation of inspection data; the new methodology is verified against other numerical simulations. Furthermore, its deployment to simulate wave reflection from side-drilled holes (SDHs), comparing the results with experimental measurements, provides a realistic demonstration as well as further validation.
Colombi A, Guenneau S, Roux P, et al., 2016, Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves., Scientific Reports, Vol: 6, ISSN: 2045-2322
Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3-10 Hz, and for low-speed sedimentary soil (vs: 300-500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency.
Haslinger SG, Craster RV, Movchan AB, et al., 2016, Dynamic interfacial trapping of flexural waves in structured plates, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1364-5021
The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.
Kovalchuk NM, Matar OK, Craster RV, et al., 2016, The effect of adsorption kinetics on the rate of surfactant-enhanced spreading, Soft Matter, Vol: 12, Pages: 1009-1013, ISSN: 1744-6848
A comparison of the kinetics of spreading of aqueous solutions of two different surfactants on an identical substrate and their short time adsorption kinetics at the water/air interface has shown that the surfactant which adsorbs slower provides a higher spreading rate. This observation indicates that Marangoni flow should be an important part of the spreading mechanism enabling surfactant solutions to spread much faster than pure liquids with comparable viscosities and surface tensions.
Schnitzer O, Giannini V, Craster RV, et al., 2016, Asymptotics of surface-plasmon redshift saturation at subnanometric separations, Physical Review B, Vol: 93, ISSN: 2469-9950
Many promising nanophotonics endeavors hinge upon the unique plasmonic properties of nanometallic structures with narrow nonmetallic gaps, which support superconcentrated bonding modes that singularly redshift with decreasing separations. In this Rapid Communication, we present a descriptive physical picture, complemented by elementary asymptotic formulas, of a nonlocal mechanism for plasmon redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalization of the corresponding local ones. Specifically, the renormalization furnishes an asymptotic plasmon-frequency lower bound that scales with the 1/4 power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.
Colombi A, Roux P, Guenneau S, et al., 2016, Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances, Scientific Reports, Vol: 6, ISSN: 2045-2322
We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.
Makwana M, Antonakakis T, Maling B, et al., 2016, Wave mechanics in media pinned at bravais lattice points, SIAM Journal on Applied Mathematics, Vol: 76, Pages: 1-26, ISSN: 1095-712X
The propagation of waves through microstructured media with periodically arrangedinclusions has applications in many areas of physics and engineering, stretching from photonic crystalsthrough to seismic metamaterials. In the high-frequency regime, modeling such behavior iscomplicated by multiple scattering of the resulting short waves between the inclusions. Our aimis to develop an asymptotic theory for modeling systems with arbitrarily shaped inclusions locatedon general Bravais lattices. We then consider the limit of pointlike inclusions, the advantage beingthat exact solutions can be obtained using Fourier methods, and go on to derive effective mediumequations using asymptotic analysis. This approach allows us to explore the underlying reasons fordynamic anisotropy, localization of waves, and other properties typical of such systems, and in particulartheir dependence upon geometry. Solutions of the effective medium equations are comparedwith the exact solutions, shedding further light on the underlying physics. We focus on examplesthat exhibit dynamic anisotropy as these demonstrate the capability of the asymptotic theory to pickup detailed qualitative and quantitative features.
Colombi A, Roux P, Colquitt D, et al., 2016, Conversion and reflection of Rayleigh waves with the seismic metawedge, 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), Publisher: IEEE, Pages: 313-315
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Theodorakis PE, Müller EA, Craster RV, et al., 2015, Modelling the superspreading of surfactant-laden droplets with computer simulation, Soft Matter, Vol: 11, Pages: 9254-9261, ISSN: 1744-683X
The surfactant-driven superspreading of droplets on hydrophobic substrates is considered. A key element of the superspreading mechanism is the adsorption of surfactant molecules from the liquid-vapour interface onto the substrate through the contact line, which must be coordinated with the replenishment of interfaces with surfactant from the interior of the droplet. We use molecular dynamics simulations with coarse-grained force fields to provide a detailed structural description of the droplet shape and surfactant dynamics during the superspreading process. We also provide a simple method for accurate estimation of the contact angle subtended by the droplets at the contact line.
Puvirajesinghe TM, Zhi ZL, Craster RV, et al., 2015, 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.
Ceresoli L, Abdeddaim R, Antonakakis T, et al., 2015, Dynamic effective anisotropy: Asymptotics, simulations, and microwave experiments with dielectric fibers, PHYSICAL REVIEW B, Vol: 92, ISSN: 1098-0121
We investigate dynamic effective anisotropy in photonic crystals (PCs) through a combination of an effective medium theory, which is a high-frequency homogenization (HFH) method explicitly developed to operate for short waves, as well as through numerical simulations and microwave experiments. The HFH yields accurate predictions of the effective anisotropic properties of periodic structures when the wavelength is of comparable order to the pitch of the array; specifically, we investigate a square array of pitch 2 cm consisting of dielectric rods of radius 0.5 cm and refractive index n=6√ within an air matrix. This behaves as an effective medium, with strong artificial anisotropy, at a frequency corresponding to a flat band emerging from a Dirac-like point in transverse magnetic (TM) polarization. At this frequency, highly directive emission is predicted for an electric source placed inside this PC, and this artificial anisotropy can be shown to coincide with a change of character of the underlying effective equation from isotropic to unidirective, with coefficients of markedly different magnitudes appearing in the effective equation tensor. In transverse electric (TE) polarization, we note a second radical change of character of the underlying effective equation, this time from elliptic to hyperbolic, near a frequency at which a saddle point occurs in the corresponding dispersion curves. Delicate microwave experiments are performed in both polarizations for such a PC consisting of 80 rods, and we demonstrate that a directive emission in the form of a + (respectively, an X) is indeed seen experimentally at the predicted frequency 9.5 GHz in TM polarization (respectively, 5.9 GHz in TE polarization). These are clearly dynamic effects since in the quasistatic regime the PC just behaves as an isotropic medium.
Hernando Quintanilla F, Lowe MJS, Craster RV, 2015, Full 3D dispersion curve solutions for guided waves in generally anisotropic media, Journal of Sound and Vibration, Vol: 363, Pages: 545-559, ISSN: 1095-8568
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials.These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
Quintanilla FH, Fan Z, Lowe MJS, et al., 2015, Guided waves' dispersion curves in anisotropic viscoelastic single- and multi-layered media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 471, Pages: 1-23, ISSN: 1364-5021
Guided waves propagating in lossy media are encountered in many problems across different areas of physics such as electromagnetism, elasticity and solid-state physics. They also constitute essential tools in several branches of engineering, aerospace and aircraft engineering, and structural health monitoring for instance. Waveguides also play a central role in many non-destructive evaluation applications. It is of paramount importance to accurately represent the material of the waveguide to obtain reliable and robust information about the guided waves that might be excited in the structure. A reasonable approximation to real solids is the perfectly elastic approach where the frictional losses within the solid are ignored. However, a more realistic approach is to represent the solid as a viscoelastic medium with attenuation for which the dispersion curves of the modes are, in general, different from their elastic counterparts. Existing methods are capable of calculating dispersion curves for attenuated modes but they can be troublesome to find and the solutions are not as reliable as in the perfectly elastic case. In this paper, in order to achieve robust and accurate results for viscoelasticity a spectral collocation method is developed to compute the dispersion curves in generally anisotropic viscoelastic media in flat and cylindrical geometry. Two of the most popular models to account for material damping, Kelvin–Voigt and Hysteretic, are used in various cases of interest. These include orthorhombic and triclinic materials in single- or multi-layered arrays. Also, and due to its importance in industry, a section is devoted to pipes filled with viscous fluids. The results are validated by comparison with those from semi-analytical finite-element simulations.
Quintanilla FH, Fan Z, Lowe MJS, et al., 2015, Dispersion Loci of Guided Waves in Viscoelastic Composites of General Anisotropy, 42nd Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE), Publisher: American Institute of Physics (AIP), ISSN: 1551-7616
Guided waves play an important role in many applications of NDE to structures of flat and cylindrical geometry. In order to develop and optimise the inspection, it is essential to have a good understanding of the wave modes that can propagate in the target structure. These can be complicated, especially in structures composed of multiple layers, anisotropic properties or materials that exhibit damping that absorbs the energy of the waves. Dispersion curves in anisotropic viscoelastic media are presented here. They have been computed by using a pseudospectral collo-cation method, details of its implementation are briefly outlined and references to the relevant literature given.
Martin RJ, Craster RV, Kearney MJ, 2015, Infinite product expansion of the Fokker-Planck equation with steady-state solution, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 471, ISSN: 1471-2946
We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.
Theodorakis P, Kovalchuk NM, Starov VM, et al., 2015, Superspreading: Mechanisms and Molecular Design, Mainz Material Simulation Days 2015, Pages: 29-29
Shi F, Choi W, Lowe MJS, et al., 2015, The validity of Kirchhoff theory for scattering of elastic waves from rough surfaces, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 471, ISSN: 1364-5021
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