Papers submitted
2. Charlton, C. and Parnell, W.J.
"Elastic Invisibility in Three Dimensions: Neutral Inclusions and Low Frequency Transparency"
Submitted to Q. J. Mech Appl. Math.
1. Cotterill, P.A., Nigro, D. and Parnell, W.J.
"An elastodynamic Willis meta-layer with directional-dependent attenuation."
In preparation for submission to Proc Roy Soc A.
See the arxiv version here.
Papers in the pipeline for imminent submission
1. Charlton, C., Assier, R. and Cotterill, P.A. and Parnell, W.J.
"Multiple Scattering Effects on the elastodynamic giant monopole resonance of spherical voids
Books
Parnell, W.J. "An introduction to homogenization, micromechanics and effective medium theory". Cambridge University Press. Due out 2027.
Book chapters
Norris, A.N. and Parnell, W.J."Hyperelastic cloaking theory". A handbook of metamaterials and nanophotonics. Editors: Maier, S., Shamonina, K., Guenneau, S., Hess, O. and Aizpurua, J. World Scientific (2017).
Berger, J.R., Geer, S.R. and Parnell, W.J. "Homogenization approaches for the elastic properties of porous materials". Pore scale phenomena. Frontiers in energy and environment. Editors: Poate, J.M., Kazemi, H., Illinagasekare, T. and Kee, R.J. World Scientific (2015).
Books
Parnell, W.J. "An introduction to homogenization, micromechanics and effective medium theory". Cambridge University Press. Due out 2027.
Book chapters
Norris, A.N. and Parnell, W.J."Hyperelastic cloaking theory". A handbook of metamaterials and nanophotonics. Editors: Maier, S., Shamonina, K., Guenneau, S., Hess, O. and Aizpurua, J. World Scientific (2017).
Berger, J.R., Geer, S.R. and Parnell, W.J. "Homogenization approaches for the elastic properties of porous materials". Pore scale phenomena. Frontiers in energy and environment. Editors: Poate, J.M., Kazemi, H., Illinagasekare, T. and Kee, R.J. World Scientific (2015).
Papers published
2025
84. Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition
G Núñez, WJ Parnell, RC Assier
Proceedings of the Royal Society A 481 (2318), 20250162
83. Reflection and transmission of elastic waves from an immersed Willis slab at oblique incidence
M Gattin, N Bochud, G Rosi, PA Cotterill, WJ Parnell, S Naili
International Journal of Solids and Structures 318, 15
82. All-polymer syntactic foams: Linking large strain cyclic experiments to Quasilinear Viscoelastic modelling for materials characterisation
SN Nguyen, R De Pascalis, Z Yousaf, WJ Parnell
Composites Part B: Engineering 288, 111866
2024
81. Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
EG Neefjes, D Nigro, RC Assier, WJ Parnell
Journal of Fluids and Structures 131, 104219
80. Tensor decomposition for modified quasi-linear viscoelastic models: Towards a fully non-linear theory
V Balbi, T Shearer, WJ Parnell
Mathematics and Mechanics of Solids 29 (6), 1064-1088
79. Enhancing the fire-resistance performance of composite laminates via multi-scale hybridisation: A review
HK Dalfi, K Jan, A Al-Badri, M Peerzada, Z Yousaf, W Parnell, N Morrison, ...
Journal of Industrial Textiles 54, 15280837241226988
2023
78. A three-dimensional active cloaking strategy for the Helmholtz equation that exploits the symmetry of the platonic solids
CH Yeung, WJ Parnell, T Shearer
JASA Express Letters 3 (6)
2022
77. Transition from equatorial to whole-shell buckling in embedded spherical shells under axisymmetric far-field loading
GW Jones, MJA Smith, M Thorpe, ID Abrahams, WJ Parnell
International Journal of Solids and Structures 256, 111957
76. Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator
MJA Smith, PA Cotterill, D Nigro, WJ Parnell, ID Abrahams
Philosophical Transactions of the Royal Society A 380 (2237), 20210383
75. Garcia Neefjes, E., Nigro, D., Gower, A.L., Assier, R.C., Pinfield, V.J. and Parnell, W.J.
"A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress relaxation."
Proc. Roy. Soc. A 478 (2265), 20220193 (https://doi.org/10.1098/rspa.2022.0193)
74. Touboul, M., Cotterill, P.A., Nigro, D. and Parnell, W.J.
"Enhanced elastodynamic resonance via co-dipole metaclusters."
Applied Physics Letters 121 (10) (https://doi.org/10.1063/5.0100487)
73. Cotterill, P.A., Nigro, D. and Parnell, W.J.
"Deeply subwavelength giant monopole elastodynamic metacluster resonators."
Proc. Roy. Soc. A. 478 (2263), 20220026 (https://doi.org/10.1098/rspa.2022.0026)
72. Russell, E., Assier, R.C. and Parnell, W.J.
"Manipulating thermal fields with inhomogeneous heat spreaders."
Applied Mathematical Modelling 106, 225-240 (https://doi.org/10.1016/j.apm.2022.01.026)
See also Arxiv version available here.
71. Haughton, J., Cotter, S., Parnell, W.J. and Shearer, T.
"Bayesian inference on a microstructural, hyperelastic model of tendon deformation."
J. Roy. Soc. Interface 19 (190), 20220031. (https://doi.org/10.1098/rsif.2022.0031)
70. Yousaf, Z., Morrison, N.F. and Parnell, W.J.
"Tensile properties of all-polymeric syntactic foam composites: experimental characterisation and mathematical modelling."
Composites B 231, 109556. (https://doi.org/10.1016/j.compositesb.2021.109556)
See also Arxiv version available here.
2021
69. Parnell, W.J., Rowley, W.D. and Curati, N.R.M.
"Tackling Noise Pollution with Slow Sound."
Frontiers for Young Minds, A World of Sound Collection. December 2021. (link here)
68. Curd, M.E., Morrison, N.F., Smith M.J.A., Gajjar, P., Yousaf, Z. and Parnell, W.J. (2021) (open access)
"Geometrical and Mechanical Characterisation of Hollow Thermoplastic microspheres for syntactic foam applications"
Composites B. 223, 108952. (https://doi.org/10.1016/j.compositesb.2021.108952)
See also arxiv: arXiv:2005.12862.
67. Smith M.J.A., Yousaf, Z., Potluri, P. and Parnell, W.J. (2021) (open access)
"Modelling hollow thermoplastic syntactic foams under high-strain compressive loading"
Comp. Sci. Tech. 231, 108882 (doi.org/10.1016/j.compscitech.2021.108882)
66. Berjamin, H., Destrade, M. and Parnell, W.J. (2021) (open access)
"On the thermodynamic consistency of Quasi-linear Viscoelastic Models for soft solids"
Mechanics Research Communications 111, 103648 (doi.org/10.1016/j.mechrescom.2020.103648)
2020
65. Norris, A.N. and Parnell, W.J. (2020) (open access)
"Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions "
Proc. Roy. Soc. A 476, 20190725 (doi.org/10.1098/rspa.2019.0725)
64. De Pascalis and Parnell, W.J. (2020) (open access)
"Optimal design of antiplane wave band gaps in phononic media through genetic algorithm-informed pre-stress"
Extreme Mechanics Letters 40, 100896 (doi.org/10.1016/j.eml.2020.100896)
63. Shrimali, B., Parnell, W.J. and Lopez-Pamies, O. (2020) (open access)
"A simple explicit model constructed from a homogenisation solution for the large strain mechanical response of elastomeric syntactic foams"
Int. J. Nonlinear Mechanics 125, 103548 (doi.org/10.1016/j.ijnonlinmec.2020.103548)
62. Yousaf, Z., Smith, M.J.A., Potluri, P. and Parnell, W.J. (2020) (open access)
"Compression properties of polymeric syntactic foams under cyclic loading."
Composites B 186, 107764, (doi.org/10.1016/j.compositesb.2020.107764).
61. Shearer, T., Parnell, W.J., Lynch, B., Screen, H.R.C. and Abrahams, I.D. (2020) (open access)
"A recruitment model of tendon viscoelasticity that incorporates fibril creep and explains strain-dependent relaxation."
ASME J. Biomech. Eng. 142(7), 071003, (doi.org/10.1115/1.4045662).
60. Calvo-Jurado, C. and Parnell, W.J. (2020)
"Induced fields in isolated elliptical inhomogeneities due to imposed polynomial fields at infinity"I
Int. J. Computer Math. 97 (18-29) (doi.org/10.1080/00207160.2018.1455972)
2019
59. Gower, A., Abrahams, I.D. and Parnell, W.J. (2019) (open access)
"A proof that multiple waves can propagate in ensemble-averaged particulate materials"
Proc. Roy. Soc. A. (doi.org/10.1098rspa.2019.0344)
58. Gower, A., Parnell, W.J. and Abrahams, I.D. (2019) (open access)
"Multiple waves can propagate in random particulate materials"
SIAM J. Appl. Mathematics 79(6), 2569-2592. (doi.org/10.1137/18M122306X)
57. Parnell, W.J. and De Pascalis, R. (2019) (open access)
"Soft metamaterials with dynamic functionality tuned by pre-deformation."
Phil. Trans. A 377, 2144. (doi.org/10.1098/rsta.2018.0072)
Special issue commemorating the work of Ronald Rivlin.
56. Lynott, G, Andrew, V., Parnell, W.J., Simon, M., Abrahams, I.D. and Assier, R. (2019) (open access)
"Acoustic scattering from a two-dimensional array; tail end asymptotics for efficient evaluation of the periodic Green's function."
Wave Motion 89, 232-244. (doi.org/10.1016/j.wavemoti.2019.01.012)
55. Gorbushin, N., Naili, S, Assier, R.C., Nguyen, C-H. and Parnell, W.J. (2019) (open access)
"Transient thermal boundary value problems in the half-space with mixed convective boundary conditions."
J. Eng. Mathematics 114, 141-158. (doi.org/10.1007/s10665-019-09986-6)
54. Rus, G., Melchor, J., Bochud, N., Peralta, L and Parnell, W.J. (2019) (open access)
"Damage prediction via nonlinear ultrasound: a micromechanical approach."
Ultrasonics 93, 145-155. (doi.org/10.1016/j.ultras.2018.10.009)
2018
53. Cotterill, P.A., Nigro, D., Abrahams, I.D., Garcia-Neefjes, E. and Parnell, W.J. (2018) (open access)
"Thermo-viscous damping of acoustic waves in narrow channels: a comparison of effects in air and water."
J. Acoust. Soc. America 144, 3421. (doi.org/10.1121/1.5078528)
52. De Pascalis, R., Parnell, W.J., Abrahams, I.D., Shearer, T., Daly, D.M. and Grundy, D. (2018) (open access)
"The inflation of viscoelastic balloons and hollow viscera."
Proc. Roy. Soc. A. 474, 20180101 (doi.org/10.1098/rspa.2018.0102)
51. Balbi, V., Shearer, T. and Parnell, W.J. (2018) (open access)
"A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation."
Proc. Roy. Soc. A 474, 20180231 (doi.org/10.1098/rspa.2018.0231) and available now on Arxiv.
50. Gower, A.L, Gower, R.M., Deakin, J., Parnell, W.J. and Abrahams, I.D. (2018)
"Characterising random media with near-surface backscattering: a machine learning approach for the measurement of particle size and concentration"
EuroPhysics letters 122 (5), 54001, (doi.org/10.1209/0295-5075/122/54001) and available now on Arxiv.
49. Rowley, W.D., Parnell, W.J., Abrahams, I.D., Voisey, S.R., Lamb, J. and Etaix, N. (2018) (open access)
"Deepening subwavelength acoustic resonance via metamaterials with universal broadband elliptical microstructure"
Applied Physics Letters 112, 251902 (doi.org/10.1063/1.5022197) and available now on Arxiv.
48. Zhang, P. and Parnell, W.J. (2018) (open access)
"Hyperelastic antiplane ground cloaking."
J Acoust. Soc. America 143 (5) (doi.org/10.1121/1.5036629) and available now on Arxiv
47. Gower, A., Smith, M.J.A., Parnell, W.J. and Abrahams, I.D. (2018) (open access)
"Reflection from a multi-species material and its transmitted effective wavenumber."
Proc. Roy. Soc. A. 474, 20170864. (doi.org/10.1098/rspa.2017.0864) and available now on Arxiv.
46. Torrent, D., Parnell, W.J. and Norris, A.N. (2018) (open access)
"Loss compensation in time-dependent elastic metamaterials"
Phys. Rev. B 97, 014105 (doi.10.1103/PhysRevB.97.014105) and available now on Arxiv
2017
45. Joyce, D. and Parnell, W.J. (2017) (open access)
"The Newtonian potential inhomogeneity problem: non-uniform eigenstrains in cylinders of non-uniform cross section"
J. Eng. Mathematics (50 years special issue). 107(1), 283-303. (doi.10.1007/s10665-017-9923-9)
44. Zhang, P. and Parnell, W.J. (2017)
"Band gap formation and tunability in stretchable serpentine interconnects."
ASME J. Applied Mechanics 84(9), 091007. (doi.10.1115/1.4037314).
43. Joyce, D., Parnell, W.J, Abrahams, I.D. and Assier, R. (2017) (open access)
"An integral equation method for the homogenization of unidirectional fibre reinforced media; antiplane elasticity and other potential problems."
Proc. Roy. Soc. A 473, 20170080. (doi.10.1098/rspa.2017.0080)
42. Zhang, P. and Parnell, W.J. (2017) (open access)
"Soft phononic crystals with deformation-independent band gaps."
Proc. Roy. Soc. A 473, 20160865. (doi.10.1098/rspa.2016.0865)
41. Geer, S., Berger, J.R., Parnell, W.J. and Mustoe, G.G.W. (2017)
"A Comparison of Discrete Element and Micromechanical Methods for Determining the Effective Elastic Properties of Geomaterials"
Computers and Geotechnics. 87, 1-9. (doi.10.1016/j.compgeo.2017.01.018)
40. Calvo-Jurado, C. and Parnell, W.J. (2017) (open access)
" The influence of two-point statistics on the Hashin-Shtrikman bounds for three-phase composites"
J. Comp. Applied Math. 318, 354-365. (doi.10.1016/j.cam.2016.08.046)
39. Barnwell, E.G., Parnell, W.J. and Abrahams, I.D. (2017) (open access)
"Tunable elastodynamic band gaps"
Extreme Mechanics Letters 12, 23-29. (doi.10.1016/j.eml.2016.10.009)
38. Song, Y., Gitman, I., Parnell, W.J. and Askes, H. (2017) (open access)
"The influence of random microstructure on wave propagation through random media"
Int J Fracture 204(1), 115-120. (doi.10.1007/s10704-016-0170-2)
2016
37. Parnell, W.J. (2016) (open access)
"The Eshelby, Hill, Moment and Concentration tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostatics"
J. Elasticity 125(2), 231-294. (doi:10.1007/s10659-016-9573-6)
36. Parnell, W.J., Nguyen, V.-H., Assier, R., Naili, S. and Abrahams, I.D. (2016) (open access)
"Transient thermal mixed boundary value problems in the half-space"
SIAM J. Appl. Mathematics 76 (3), 845-866. (doi:10.1137/15M1021076)
35. Barnwell, E.G., Parnell, W.J. and Abrahams, I.D. (2016) (open access)
"Anti-plane elastic wave propagation in pre-stressed periodic structures; tuning, band gap switching and invariance"
Wave Motion 63, 98-110. (doi:10.1016/j.wavemoti.2016.02.001)
2015
34. Parnell, W.J. and Calvo-Jurado, C. (2015) (open access)
"On the construction of the Hashin-Shtrikman bounds for transversely isotropic two-phase linear elastic fibre reinforced composites"
J. Eng. Mathematics 95, 295-323. (doi:10.1007/s10665-014-9777-3)
33. Shearer, T., Parnell, W.J. and Abrahams, I.D. (2015) (open access)
"Antiplane wave scattering from a cylindrical cavity in pre-stressed non-linear elastic media"
Proc. Roy. Soc. A. 471, 20150450. (doi:10.1098/rspa.2015.0450)
32. Martin, P.A., Abrahams, I.D. and Parnell, W.J. (2015) (open access)
"One dimensional reflection by a semi-infinite periodic row of scatterers"
Wave Motion 58, 1-12. (doi:10.1016/j.wavemoti.2015.06.005)
31. Futhazar, G., Parnell, W.J. and Norris, A.N. (2015) (open access)
"Active cloaking for flexural waves in thin plates"
J. Sound Vibration 356, 1-19. (doi:10.1016/j.jsv.2015.06.023)
30. Cotterill, P.A, Parnell, W.J., Abrahams, I.D., Miller, R. and Thorpe, M. (2015)
"The time-harmonic antiplane response of a constrained layer"
J. Sound Vibration 348, 167-184. (doi:10.1016/j.jsv.2015.03.014)
29. De Pascalis, R., Abrahams, I.D. and Parnell, W.J. (2015) (open access)
"Simple shear of a compressible viscoelastic material"
Int. J. Eng. Science 88, 64-72. (doi:10.1016/j.ijengsci.2014.11.011)
28. Calvo-Jurado, C. and Parnell, W.J. (2015)
"Hashin-Shtrikman bounds on the effective thermal conductivity of a transversely isotropic two-phase composite material"
J. Math. Chemistry 53, 828-843. (doi:10.1007/s10910-014-0452-87)
27. Granke, M., Grimal, Q., Parnell, W.J., Raum, K., Gerisch, A., Peyrin, F., Saied, A. and Laugier, P. (2015)
"To what extent can cortical bone millimeter scale elasticity be predicted by a two phase composite model with variable porosity?"
Acta Biomaterialia 12, 207-215. (doi:10.1016/j.actbio.2014.10.011)
2014
26. Gilchrist, M., Murphy, J.G., Parnell, W.J. and Pierrat, B. (2014)
"Modelling the slight compressibility of anisotropic soft tissue"
Int. J. Solids Structures 51, 3857-3865. (doi:10.1016/j.ijsolstr.2014.06.018)
25. Norris, A.N., Amirkulova, F.A. and Parnell, W.J. (2014)
"Active elastodynamic cloaking"
Math. Mech. Solids 19, 603-625. (doi.org/10.1177/1081286513479962)
24. De Pascalis, R., Abrahams, I.D. and Parnell, W.J. (2014) (open access)
"On nonlinear viscoelastic deformations - a reappraisal of Fung's quasilinear viscoelastic model"
Proceedings of the Royal Society A 470 (2166), 20140058 (doi:10.1098/rspa.2014.0058)
23. Williams, T.D. and Parnell, W.J. (2014) (open access)
"Effective antiplane elastic properties of an orthotropic solid weakened by a periodic distribution of cracks"
Quart. J. Mech. Applied Mathematics, 67, 311-342 (doi.org/10.1093/qjmam/hbu008)
2013
22. Shearer, T., Parnell, W.J., Abrahams, I.D. and Daros, C.H. (2013)
"Torsional wave propagation in an incompressible pre-stressed nonlinear elastic cylindrical annulus"
Quart. J. Mech. Applied Mathematics 66, 465-487. (doi.org/10.1093/qjmam/hbt014)
21. Parnell, W.J. and Shearer, T. (2013)
"Antiplane elastic wave cloaking using metamaterials, homogenization and nonlinear hyperelasticity"
Wave Motion 50, 1140-1152. (doi.org/10.1016/j.wavemoti.2013.06.006)
20. De Pascalis, R., Parnell, W.J. and Abrahams, I.D. (2013)
"Predicting the nonlinear pressure-volume curve of an elastic microsphere composite"
. Journal of the Mechanics and Physics of Solids 61, 1106-1123 (doi.org/10.1016/j.jmps.2012.11.005)
2012
19. Norris, A.N., Amirkulova, F.A. and Parnell, W.J. (2012)
"Source amplitudes for active exterior cloaking"
Inverse problems 28, 105002 (doi:10.1088/0266-5611/28/10/105002)
18. Norris, A.N. and Parnell, W.J. (2012)
"Hyperelastic cloaking theory: Transformation elasticity with prestressed solids"
Proceedings of the Royal Society A, 468, 2881-2903. (doi:10.1098/rspa.2012.0123)
17. Willoughby, N., Parnell, W.J., Hazel, A., Abrahams, I.D. (2012)
"Homogenization methods to approximate the effective response of random inhomogeneous fibre reinforced media"
International Journal of Solids and Structures, 49, 1421–1433. (doi:10.1016/j.ijsolstr.2012.02.010)
16. Parnell, W.J., Vu, M.-B., Grimal, Q. and Naili, S. (2012)
"Analytical methods to determine the effective mesoscopic and macrosopic elastic properties of cortical bone"
Journal of Biomechanics and Modelling in Mechanobiology 11, 883-901. (doi:10.1007/s10237-011-0359-2)
15. Parnell, W.J., Norris, A.N. and Shearer, T. (2012)
"Employing pre-stress to generate finite cloaks for antiplane elastic waves"
Applied Physics Letters 100, 171907, (doi:10.1063/1.4704566)
14. Parnell, W.J. (2012)
"Nonlinear pre-stress for cloaking from antiplane elastic waves"
Proceedings of the Royal Society A 468, 563-580, (doi:10.1098/rspa.2011.0477)
13. Parnell, W.J. and Abrahams, I.D. (2012)
"Scattering from a cylindrical void in a pre-stressed incompressible neo-Hookean material"
Communications in Computational Physics 11, 367-382 (doi:10.4208/cicp.111209.160610s)
2011
12. Grimal, Q., Rus, G., Parnell, W.J. and Laugier, P. (2011)
"A two-parameter model of the effective elastic modulus tensor for cortical bone"
Journal of Biomechanics 44, 1621-1625 (doi:10.1016/j.jbiomech.2011.03.006 )
11. Parnell, W.J. and Abrahams, I.D. (2011)
"The effective wavenumber of a pre-stressed nonlinear microvoided composite"
Journal of Physics: Conference Series 269, 012007 (doi:10.1088/1742-6596/269/1/012007)
10. Parnell, W.J. and Martin, P.A. (2011)
"Multiple scattering of flexural waves by random configurations of inclusions in thin plates"
Wave Motion 48, 161-175 (doi:10.1016/j.wavemoti.2010.10.004)
2010
9. Parnell, W.J. and Abrahams, I.D. (2010)
"Multiple point scattering to determine the effective wavenumber and effective properties of an inhomogeneous slab region"
Waves in Random and Complex Media 20, 678-701 (doi:10.1080/17455030.2010.510858)
8. Martin, P.A., Maurel, A. and Parnell, W.J. (2010)
"Estimating the dynamic effective mass density of random composites"
Journal of the Acoustical Society of America 128, 571-577 (doi:10.1121/1.3458849)
7. Parnell, W.J., Abrahams, I.D. and Brazier-Smith, P.R. (2010)
"Effective properties of a composite half-space: exploring the relationship between homogenization and multiple scattering theories"
Quarterly Journal of Mechanics and Applied Mathematics 63, 145-175 (doi:10.1093/qjmam/hbq002)
2009
6. Parnell, W.J. and Grimal, Q. (2009)
"The influence of mesoscopic porosity on cortical bone anisotropy. Investigations via asymptotic homogenization"
Journal of the Royal Society Interface 6, 97-109 (doi:10.1098/rsif.2008.0255)
2008
5. Parnell, W.J. and Abrahams, I.D. (2008)
"Homogenization for wave propagation in periodic fibre reinforced media with complex microstructure. I - Theory"
Journal of the Mechanics and Physics of Solids 56, 2521-2540 (doi:10.1016/j.jmps.2008.02.003)
4. Parnell, W.J. and Abrahams, I.D. (2008)
"A new integral equation approach to elastodynamic homogenization"
Proceedings of the Royal Society A 464, 1461-1482, (doi:10.1098/rspa.2007.0254)
2007
3. Parnell, W.J. (2007)
"Effective wave propagation in a pre-stressed nonlinear elastic composite bar"
IMA Journal of Applied Mathematics 72, 223-244 (doi:10.1093/imamat/hxl033)
2006
2. Parnell, W.J. (2006)
"Coupled thermoelasticity in a composite half-space"
Journal of Engineering Mathematics 56, 1-21. (doi:10.1007/s10665-006-9038-1)
1. Parnell, W.J. and Abrahams, I.D. (2006)
"Dynamic Homogenization in Periodic Fibre Reinforced Media. Quasi-static limit for SH Waves"
Wave Motion 43, 474-498. (doi:10.1016/j.wavemoti.2006.03.003)
