Publications
354 results found
Maling BJ, Colquitt DJ, Craster RV, 2015, 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.
Wray AW, Matar OK, Craster, et al., 2015, Electrostatic Suppression of the "Coffee-stain Effect", Procedia IUTAM, Vol: 15, Pages: 172-177, ISSN: 2210-9838
The dynamics of a slender, nano-particle laden droplet are examined when it is subjected to an electric field. Under a long-waveassumption, the governing equations are reduced to a coupled pair of nonlinear evolution equations prescribing the dynamics of theinterface and the depth-averaged particle concentration. This incorporates the effects of viscous stress, capillarity, electrostaticallyinducedMaxwell stress, van der Waals forces, evaporation and concentration-dependent rheology. It has previously been shown27that electric fields can be used to suppress the ring effect typically exhibited when such a droplet undergoes evaporation. Wedemonstrate here that the use of electric fields affords many diverse ways of controlling the droplets.
Colquitt DJ, Craster RV, Makwana M, 2015, HIGH FREQUENCY HOMOGENISATION FOR ELASTIC LATTICES, QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, Vol: 68, Pages: 203-230, ISSN: 0033-5614
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- Citations: 16
Quintanilla FH, Lowe MJS, Craster RV, 2015, Modeling guided elastic waves in generally anisotropic media using a spectral collocation method, Journal of the Acoustical Society of America, Vol: 137, Pages: 1180-1194, ISSN: 0001-4966
Guided waves are now well established for some applications in the non-destructive evaluation of structures and offer potential for deployment in a vast array of other cases. For their development, it is important to have reliable and accurate information about the modes that propagate for particular waveguide structures. Essential information that informs choices of mode transducer, operating frequencies, and interpretation of signals, among other issues, is provided by the dispersion curves of different modes within various combinations of geometries and materials. In this paper a spectral collocation method is successfully used to handle the more complicated and realistic waveguide problems that are required in non-destructive evaluation; many pitfalls and limitations found in root-finding routines based on the partial wave method are overcome by using this approach. The general cases presented cover anisotropic homogeneous perfectly elastic materials in flat and cylindrical geometry. Non-destructive evaluation applications include complex waveguide structures, such as single or multi-layered fiber composites, lined, bonded and buried structures. For this reason, arbitrarily multi-layered systems with both solid and fluid layers are also addressed as well as the implementation of interface models of imperfect boundary conditions between layers.
Theodorakis PE, Mueller EA, Craster RV, et al., 2015, Superspreading: Mechanisms and Molecular Design, Langmuir, Vol: 31, Pages: 2304-2309, ISSN: 1520-5827
Joseph LM, Craster RV, 2015, Reflection from a semi-infinite stack of layers using homogenization, Wave Motion, Vol: 54, Pages: 145-156, ISSN: 0165-2125
A canonical scattering problem is that of a plane wave incident upon a periodic layered medium. Our aim here is to replace the periodic medium by a homogenized counterpart and then to investigate whether this captures the reflection and transmission behaviour accurately at potentially high frequencies.We develop a model based upon high frequency homogenization and compare the reflection coefficients and full fields with the exact solution. For some material properties it is shown that the asymptotic behaviour of the dispersion curves are locally linear near critical frequencies and that low frequency behaviour is replicated at these critical, high, frequencies. The homogenization approach accurately replaces the periodic medium and the precise manner in which this is achieved then opens the way to future numerical implementation of this technique to scattering problems.
Balmforth NJ, Craster RV, Hewitt IJ, 2015, The speed of an inclined ruck., Proc Math Phys Eng Sci, Vol: 471, ISSN: 1364-5021
Steady rucks in an elastic beam can roll at constant speed down an inclined plane. We examine the dynamics of these travelling-wave structures and argue that their speed can be dictated by a combination of the physical conditions arising in the vicinity of the 'contact points' where the beam is peeled off the underlying plane and stuck back down. We provide three detailed models for the contact dynamics: viscoelastic fracture, a thermodynamic model for bond formation and detachment and adhesion mediated by a thin liquid film. The results are compared with experiments.
Colquitt DJ, Craster RV, Antonakakis T, et al., 2015, Rayleigh-Bloch waves along elastic diffraction gratings, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 471, ISSN: 1364-5021
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- Citations: 24
Quintanilla FH, Lowe M, Craster R, 2015, Dispersion Curves for Guided Elastic Waves in Multilayered Anisotropic Media Generated with the Spectral Method, 41st Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE), Publisher: AMER INST PHYSICS, Pages: 739-745, ISSN: 0094-243X
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- Citations: 1
Craster RV, 2015, Dynamic Homogenization, 9th International Congress of the International-Society-for-Analysis-its-Applications-and-Computations (ISAAC), Publisher: SPRINGER, Pages: 41-50, ISSN: 2194-1009
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- Citations: 4
Karapetsas G, Craster RV, Matar OK, 2015, Surfactant Enhanced Spreading of Liquid Drops on Solid Surfaces, International Conference of Computational Methods in Sciences and Engineering (ICCMSE), Publisher: AMER INST PHYSICS, Pages: 425-428, ISSN: 0094-243X
Shi F, Choi W, Skelton E, et al., 2015, Investigation of the Validity of the Elastic Kirchhoff Approximation for Rough Cracks Using a Finite Element Approach, 41st Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE), Publisher: AMER INST PHYSICS, Pages: 1722-1729, ISSN: 0094-243X
Shi F, Choi W, Skelton EA, et al., 2014, A Time-Domain Finite Element Boundary Integration Method for Ultrasonic Nondestructive Evaluation, IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL, Vol: 61, Pages: 2054-2066, ISSN: 0885-3010
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- Citations: 6
Antonakakis T, Craster RV, Guenneau S, 2014, Homogenisation for elastic photonic crystals and dynamic anisotropy, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, Vol: 71, Pages: 84-96, ISSN: 0022-5096
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- Citations: 46
Makwana M, Craster RV, 2014, Homogenisation for hexagonal lattices and honeycomb structures, QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, Vol: 67, Pages: 599-630, ISSN: 0033-5614
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- Citations: 6
Kuchin IV, Matar OK, Craster RV, et al., 2014, Influence of the Disjoining Pressure on the Equilibrium Interfacial Profile in Transition Zone Between a Thin Film and a Capillary Meniscus, Colloids and Interface Science Communications, Vol: 1, Pages: 18-22, ISSN: 2215-0382
The behaviour of liquid layers on solid substrates depends on a number of factors, the most important of which is the action of surface forces in the vicinity of the three phase contact line. The equilibrium interfacial (gas/liquid) profile in the transition zone between the thin flat film and the spherical part of a meniscus is determined by the combined action of the disjoining/conjoining and capillary pressures. The disjoining/conjoining pressure is considered to include the electrostatic, van der Waals and structural components. The Poisson–Boltzmann equation is also solved with various boundary conditions to calculate the electrostatic component of the disjoining/conjoining pressure. Wetting conditions are considered and the interfacial profile is determined for various parameters governing the surface interactions, as well as the ratio between the disjoining/conjoining and capillary pressures.
Craster RV, Joseph LM, Kaplunov J, 2014, Long-wave asymptotic theories: The connection between functionally graded waveguides and periodic media, WAVE MOTION, Vol: 51, Pages: 581-588, ISSN: 0165-2125
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- Citations: 53
Wray AW, Papageorgiou DT, Craster RV, et al., 2014, Electrostatic Suppression of the "Coffee Stain Effect", LANGMUIR, Vol: 30, Pages: 5849-5858, ISSN: 0743-7463
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- Citations: 49
Theodorakis PE, Müller EA, Craster RV, et al., 2014, Insights into surfactant-assisted superspreading, Current Opinion in Colloid & Interface Science, ISSN: 1359-0294
Antonakakis T, Craster RV, Guenneau S, 2014, Moulding and shielding flexural waves in elastic plates, EPL, Vol: 105, ISSN: 0295-5075
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- Citations: 23
Antonakakis T, Craster RV, Guenneau S, et al., 2014, An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 470, ISSN: 1364-5021
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- Citations: 10
Kuchin IV, Matar OK, Craster RV, et al., 2014, Modeling the effect of surface forces on the equilibrium liquid profile of a capillary meniscus, SOFT MATTER, Vol: 10, Pages: 6024-6037, ISSN: 1744-683X
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- Citations: 12
Choi W, Skelton EA, Shi F, et al., 2014, Rough Surface Reconstruction for Ultrasonic NDE Simulation, 10th International Conference on Barkhausen and Micro-Magnetics (ICBM), Publisher: AMER INST PHYSICS, Pages: 587-594, ISSN: 0094-243X
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- Citations: 2
Antonakakis T, Craster RV, Guenneau S, et al., 2014, High frequency homogenization: Going from the microscale to the macroscale, 9th International Conference on Structural Dynamics (EURODYN), Publisher: EUROPEAN ASSOC STRUCTURAL DYNAMICS, Pages: 3413-3416, ISSN: 2311-9020
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- Citations: 1
Antonakakis T, Craster RV, Guenneau S, 2013, High-frequency homogenization of zero-frequency stop band photonic and phononic crystals, NEW JOURNAL OF PHYSICS, Vol: 15, ISSN: 1367-2630
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- Citations: 32
Makwana M, Craster RV, 2013, Localised point defect states in asymptotic models of discrete lattices, QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, Vol: 66, Pages: 289-316, ISSN: 0033-5614
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- Citations: 18
Antonakakis T, Craster RV, Guenneau S, et al., 2013, Asymptotic theory of microstructured surfaces: An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces
An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which also go under other names such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identified and compared to full numerical simulations. We also investigate non-periodic situations where a long-scale geometric variation in the structure is introduced and show that localised defect states emerge which the asymptotic theory explains.
Antonakakis T, Craster RV, Guenneau S, 2013, Asymptotics for metamaterials and photonic crystals, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 469, ISSN: 1364-5021
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- Citations: 35
Bhattacharya S, Craster RV, Flynn MR, 2013, Buckling of a thin, viscous film in an axisymmetric geometry, PHYSICS OF FLUIDS, Vol: 25, ISSN: 1070-6631
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- Citations: 3
Craster RV, Makwana M, 2013, Modelling microstructured media: periodic systems and effective media, CISM International Centre for Mechanical Sciences, Courses and Lectures, Pages: 1-17
My aim in these lectures is to give a broad overview of the Mathematics and Physics of perfectly periodic systems, drawing heavily upon the literature of solid-state physics: it is essential to understand how structure on a micro-scale affects longer scale macro-scale behaviour and periodic systems are a naturally place to begin. Periodic systems are, on one hand, quite special and the constructive interference created by periodicity leads to strong effects that we shall see later, but on the other hand many natural and man-made structures exhibit, at least some, general periodic structure. After developing the language of periodic systems we will turn our attention to the development of asymptotic “effective” media that are posed entirely upon the macro-scale. Importantly we will develop asymptotic theories valid at high frequencies. A general approach valid for continua, semi-discrete (frame) and fully discrete (mass-spring) systems will be developed. If time allows we will then look further into some of the remarkable physics that can be seen when waves move through structured media: defect states, all-angle negative refraction and ultra-refraction.
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