## Refereed Articles

[1] P.A. Cotterill, W.P. Parnell, I.D. Abrahams, R. Miller, and M. Thorpe. The time-harmoinc antiplane

elastic response of a constrained layer. Journal of Sound and Vibration, 348:167–184, 2015. (pdf)

[2] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. Simple shear of a compressible quasilinear viscoelastic

material. International Journal of Engineering Science, 88(SI):64–72, 2015.

[3] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. On nonlinear viscoelastic deformations: a reappraisal

of fung’s quasi-linear viscoelastic model. Proceedings of the Royal Society, A 470(2166):20140058,

2014.

[4] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. Predicting the pressure-volume curve of an elastic

microsphere composite. Journal of the Mechanics and Physics of Solids, 61(4):1106–1123, 2013.

[5] T. Shearer, I.D. Abrahams, and W.J. Parnell. Torsional wave propagation in a pre-stressed hyperelastic

annular circular cylinder. Quarterly Journal of Mechanics and Applied Mathematics, 66(4):465–487,

2013.

[6] I.D. Abrahams and J.B. Lawrie. Scattering of flexural waves by a semi-infinite crack in an elastic plate

carrying an electric current. Mathematics and Mechanics of Solids, 17(1):43–58, 2012.

[7] M. Heil, T. Kharrat, P.A. Cotterill, and I.D. Abrahams. Quasi-resonances in sound-insulating coatings.

Journal of Sound and Vibration, 331(21):4774–4784, 2012.

[8] W.J. Parnell and I.D. Abrahams. Antiplane wave scattering from a cylindrical void in a pre-stressed

incompressible neo-Hookean material. Communications in Computational Physics, 11(2):367–382, 2012.

[9] E. Perrey-Debain and I.D. Abrahams. TE mode mixing dynamics in curved multimode optical waveguides.

Communications in Computational Physics, 11(2):525–540, 2012.

[10] N. Willoughby, W.J. Parnell, A.L. Hazel, and I.D. Abrahams. Homogenization methods to approximate

the effective response of random fibre-reinforced composites. International Journal of solids and

structures, 49(13):1421–1433, 2012.

[11] W.J. Parnell and I.D. Abrahams. The effective wavenumber of a pre-stressed nonlinear microvoided

composite. Journal of Physics Conference Series, 269(012007):1–10, 2011.

[12] R. Green, G. Fusai, and I.D. Abrahams. The Wiener-Hopf technique and discretely monitored pathdependent

option pricing. Mathematical Finance, 20(2):259–288, 2010.

[13] W.J. Parnell and I.D. Abrahams. Multiple point scattering to determine the effective wavenumber

and effective material properties of an inhomogeneous slab. Waves in Random and Complex Media,

20(4):678–701, 2010.

[14] W.J. Parnell, I.D. Abrahams, and P.R. Brazier-Smith. Effective properties of a composite half-space:

exploring the relationship between homogenization and multiple-scattering theories. Quarterly Journal

of Mechanics and Applied Mathematics, 63(2):145–175, 2010.

[15] E. Perrey-Debain and I.D. Abrahams. A general asymptotic expansion formula for integrals involving

high-order orthogonal polynomials. SIAM Journal on Scientific Computing, 31(5):3884–3904, 2009.

[16] I.D. Abrahams, A.M.J. Davis, and S.G. Llewellyn Smith. Asymmetric channel divider in stokes flow.

SIAM Journal on Applied Mathematics, 68(5):1439–1463, 2008.

[17] I.D. Abrahams, A.M.J. Davis, and S.G. Llewellyn Smith. Matrix Wiener-Hopf approximation for a

partially clamped plate. Quarterly Journal of Mechanics and Applied Mathematics, 61:241–265, 2008. [18] R. Harter, M.J. Simon, and I.D. Abrahams. The effect of surface tension on localized free-surface

oscillations about surface-piercing bodies. Proceedings of the Royal Society, A 464(2099):3039–3054,

2008.

[19] W.J. Parnell and I.D. Abrahams. Homogenization for wave propagation in periodic fibre-reinforced media

with complex microstructure. I - theory. Journal of the Mechanics and Physics of Solids, 56(7):2521–

2540, 2008.

[20] W.J. Parnell and I.D. Abrahams. A new integral equation approach to elastodynamic homogenization.

Proceedings of the Royal Society, A 464(2094):1461–1482, 2008.

[21] E. Perrey-Debain, I.D. Abrahams, and J.D. Love. A continuous model for mode mixing in graded-index

multimode fibres with random imperfections. Proceedings of the Royal Society, A 464(2092):987–1007,

2008.

[22] B. Erbas and I.D. Abrahams. Scattering of sound waves by an infinite grating composed of rigid plates.

Wave Motion, 44(4):282–303, 2007.

[23] R. Green, I.D. Abrahams, and G. Fusai. Pricing financial claims contingent upon an underlying asset

monitored at discrete times. Journal of Engineering Mathematics, 59(4):373–384, 2007.

[24] R. Harter, I.D. Abrahams, and M.J. Simon. The effect of surface tension on trapped modes in water-wave

problems. Proceedings of the Royal Society, A 463(2088):3131–3149, 2007.

[25] J.B. Lawrie and I.D. Abrahams. A brief historical perspective of the Wiener-Hopf technique. Journal of

Engineering Mathematics, 59(4):351–358, 2007.

[26] A.N. Norris and I.D. Abrahams. A multiple-scales approach to crack-front waves. Journal of Engineering

Mathematics, 59(4):399–417, 2007.

[27] W.J. Parnell and I.D. Abrahams. Multiple scattering in periodic and random media: an overview.

Proceedings of 4th Conference of Groupement de Recherche GDR 2501: ‘etude de la propagation

ultrasonore en milieux non homogènes en vue du contrôle non destructif’, eds. M. Deschamps & A.

Leger, 2007.

[28] E. Perrey-Debain and I.D. Abrahams. A diffusion analysis approach to TE mode propagation in randomly

perturbed optical waveguides. SIAM Journal on Applied Mathematics, 68(2):523–543, 2007.

[29] I. Thompson and I.D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.

II - far field analysis. Proceedings of the Royal Society, A 463(2082):1615–1638, 2007.

[30] B.H. Veitch and I.D. Abrahams. On the commutative factorization of n ×n matrix Wiener-Hopf kernels

with distinct eigenvalues. Proceedings of the Royal Society, A 463(2078):613–639, 2007.

[31] G. Fusai, I.D. Abrahams, and C. Sgarra. An exact analytical solution for discrete barrier options. Finance

and Stochastics, 10(1):1–26, 2006.

[32] G.W. Owen and I.D. Abrahams. Elastic wave radiation from a high frequency finite-length transducer.

Journal of Sound and Vibration, 298(1-2):108–131, 2006.

[33] G.W. Owen, A.J. Willmott, and I.D. Abrahams. Scattering of barotropic rossby waves by the antarctic

circumpolar current. Journal of Geophysical Research - Oceans, 111(C12):C12024, 2006.

[34] W.J. Parnell and I.D. Abrahams. Dynamic homogenization in periodic fibre reinforced media. Quasistatic

limit for SH waves. Wave Motion, 43(6):474–498, 2006.

[35] E. Perrey-Debain and I.D. Abrahams. A band factorization technique for transition matrix element

asymptotics. Computer Physics Communications, 175(5):315–322, 2006.

[36] G.W. Owen, A.J. Willmott, I.D. Abrahams, and H. Mansley. The scattering of rossby waves from finite

abrupt topography. Geophysical and Astrophysical Fluid Dynamics, 99(3):219–239, 2005.

[37] I. Thompson and I.D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.

I - formal solution. Proceedings of the Royal Society, A 461(2063):3413–3436, 2005.

[38] I.D. Abrahams. On the application of the Wiener-Hopf technique to problems in dynamic elasticity.

Wave Motion, 36(4):311–333, 2002.

[39] I.D. Abrahams and A.M.J. Davis. Deflection of a partially clamped elastic plate. Proceedings of IUTAM

Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, eds. I.D. Abrahams, P.A.

Martin & M.J. Simon, 68:303–312, 2002.

[40] I.D. Abrahams, G.W. Owen, and A.J. Willmott. The scattering of Rossby waves by ocean ridges.

Proceedings of IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, eds.

I.D. Abrahams, P.A. Martin & M.J. Simon, 68:3–12, 2002.

[41] J.B. Lawrie and I.D. Abrahams. On the propagation and scattering of fluid-structural waves in a threedimensional

duct bounded by thin elastic walls. Proceedings of IUTAM Symposium on Diffraction and

Scattering in Fluid Mechanics and Elasticity, eds. I.D. Abrahams, P.A. Martin & M.J. Simon, 68:279–

288, 2002.

[42] G.W. Owen, I.D. Abrahams, A.J. Willmott, and C.W. Hughes. On the scattering of baroclinic Rossby

waves by a ridge in a continuously stratified ocean. Journal of Fluid Mechanics, 465:131–155, 2002.

[43] I. Thompson, I.D. Abrahams, and A.N. Norris. On the existence of flexural edge waves on thin orthotropic

plates. Journal of the Acoustical Society of America, 112(5):1756–1765, 2002.

[44] I.D. Abrahams and G.R. Wickham. On transient oscillations of plates in moving fluids. Wave Motion,

33(1):7–23, 2001.

[45] G.W. Owen and I.D. Abrahams. Radiation from a transducer into an elastic half-space. Proceedings

of IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media, eds. R.C.

McPhedran, L.C. Botten & N.A. Nicorovici, pages 73–88, 2001.

[46] I.D. Abrahams. The application of Padé approximants to Wiener-Hopf factorization. IMA Journal of

Applied Mathematics, 65(3):257–281, 2000.

[47] I.D. Abrahams and A.N. Norris. On the existence of flexural edge waves on submerged elastic plates.

Proceedings of the Royal Society, A 456(1999):1559–1582, 2000.

[48] M.A. Heckl and I.D. Abrahams. Curve squeal of train wheels. I - mathematical model for its generation.

Journal of Sound and Vibration, 229(3):669–693, 2000.

[49] A.N. Norris, V.V. Krylov, and I.D. Abrahams. Flexural edge waves and comments on "a new bending

wave solution for the classical plate equation". Journal of the Acoustical Society of America,

107(3):1781–1784, 2000.

[50] I.D. Abrahams. Sound radiation from a line forced perforated elastic sandwich panel. Journal of the

Acoustical Society of America, 105(6):3009–3020, 1999.

[51] J.B. Lawrie and I.D. Abrahams. An orthogonality relation for a class of problems with high-order

boundary conditions; applications in sound-structure interaction. Quarterly Journal of Mechanics and

Applied Mathematics, 52(2):161–181, 1999.

[52] I.D. Abrahams. On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type. Proceedings

of the Royal Society, A 454(1974):1719–1743, 1998.

[53] J.B. Lawrie and I.D. Abrahams. Applications of a general orthogonality relation to acoustic scattering

in ducts with high order boundary conditions. Proceedings of Days on Diffraction, pages 6–19, 1998.

[54] I.D. Abrahams. On the solution of Wiener-Hopf problems involving noncommutative matrix kernel

decompositions. SIAM Journal on Applied Mathematics, 57(2):541–567, 1997.

[55] J.B. Lawrie and I.D. Abrahams. Scattering of fluid loaded elastic plate waves at the vertex of a wedge

of arbitrary angle. I - analytic solution. IMA Journal of Applied Mathematics, 59(1):1–23, 1997.

[56] I.D. Abrahams. On explicit approximate non-commutative factorization of matrix wiener-hopf kernels.

in Pitman Research Notes in Mathematics, eds. H. Sebest & S. Cloude, 361:41–55, 1996.

[57] I.D. Abrahams. Radiation and scattering of waves on an elastic half-space; a non-commutative matrix

Wiener-Hopf problem. Journal of the Mechanics and Physics of Solids, 44(12):2125–2154, 1996.

[58] M.A. Heckl and I.D. Abrahams. Active control of friction-driven oscillations. Journal of Sound and

Vibration, 193(1):417–426, 1996.

[59] J.B. Lawrie and I.D. Abrahams. Travelling waves on a membrane: reflection and transmission at a

corner of arbitrary angle. II. Proceedings of the Royal Society, A 452(1950):1649–1677, 1996.

[60] I.D. Abrahams. Chaotic scattering of sound waves by buckled elastic plates. Proceedings of IUTAM

Symposium on Nonlinear Waves in Solids, eds. J. Wegner & F. Norwood, ASME Book No. AMR137:41–

46, 1995.

[61] I.D. Abrahams and J.B. Lawrie. On the factorization of a class of Wiener-Hopf kernels. IMA Journal of

Applied Mathematics, 55(1):35–47, 1995.

[62] I.D. Abrahams and J.B. Lawrie. Travelling waves on a membrane: reflection and transmission at a

corner of arbitrary angle. I. Proceedings of the Royal Society, A 451(1943):657–683, 1995.

[63] B. Zhang and I.D. Abrahams. The radiation of sound from a finite ring-forced cylindrical elastic shell. I

- Wiener-Hopf analysis. Proceedings of the Royal Society, A 450(1938):89–108, 1995.

[64] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. Caustic formation from a point source in a shear layer

over an elastic surface; a model for the suppression of coherent fluid structures? in Structural Acoustics,

Scattering and Propagation, eds. J.E. Ffowcs Williams, D. Lee & A.D. Pierce, pages 221–236, 1994.

[65] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. Sound radiation and caustic formation from a pointsource

in a wall shear-layer. AIAA Journal, 32(6):1135–1144, 1994.

[66] J.C. Engineer and I.D. Abrahams. The radiation of sound-waves from a lightly loaded finite elastic shell.

II - nonlinear shell resonances. Journal of Sound and Vibration, 174(3):353–377, 1994.

[67] J.B. Lawrie and I.D. Abrahams. Acoustic radiation from two opposed semiinfinite coaxial cylindrical

wave-guides. II - separated ducts. Wave Motion, 19(1):83–109, 1994.

[68] J.B. Lawrie and I.D. Abrahams. Radiation of sound from two coaxial cylindrical waveguides; a matrix

wiener-hopf formulation. in Structural Acoustics, Scattering and Propagation, eds. J.E. Ffowcs Williams,

D. Lee & A.D. Pierce, pages 177–190, 1994.

[69] B. Zhang and I.D. Abrahams. A numerical evaluation of the sound field scattered by a finite fluid-loaded

elastic shell. in Structural Acoustics, Scattering and Propagation, eds. J.E. Ffowcs Williams, D. Lee &

A.D. Pierce, pages 191–206, 1994.

[70] I.D. Abrahams. The effect of nonlinearity on the scattering of sound by lightly loaded thin elastic

structures. in Pitman Research Notes in Mathematics 4th ed., eds. B.D. Sleeman & R. Jarvis, 1993.

[71] J.B. Lawrie, I.D. Abrahams, and C.M. Linton. Acoustic radiation from two opposed semiinfinite coaxial

cylindrical wave-guides. I - overlapping edges. Wave Motion, 18(2):121–142, 1993.

[72] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. On the development of caustics in shear flows over

rigid walls. Journal of the Acoustical Society of America, 92(1):428–434, 1992.

[73] I.D. Abrahams and G.R. Wickham. Scattering of elastic-waves by a small inclined surface-breaking

crack. Journal of the Mechanics and Physics of Solids, 40(8):1707–1733, 1992.

[74] I.D. Abrahams and G.R. Wickham. Scattering of elastic-waves by an arbitrary small imperfection in the

surface of a half-space. Journal of the Mechanics and Physics of Solids, 40(8):1683–1706, 1992.

[75] I.D. Abrahams and G.R. Wickham. The propagation of elastic-waves in a certain class of inhomogeneous

anisotropic materials. I - the refraction of a horizontally polarized shear-wave source. Proceedings of the

Royal Society, A 436(1898):449–478, 1992.

[76] J.C. Engineer and I.D. Abrahams. The radiation of sound-waves from a lightly loaded finite elastic shell.

I - duct and shell resonances for linear-motions. Journal of Sound and Vibration, 153(2):291–310, 1992.

[77] I.D. Abrahams and J.C. Engineer. A secularity condition for systems of linear partial-differential equations.

Journal of Sound and Vibration, 150(2):338–341, 1991.

[78] I.D. Abrahams and G.R. Wickham. The scattering of ultrasound by a small surface imperfection.

Proceedings of the Institute of Acoustics, 13(2):103–110, 1991.

[79] I.D. Abrahams and G.R. Wickham. The scattering of water-waves by two semi-infinite opposed vertical

walls. Wave Motion, 14(2):145–168, 1991.

[80] G.R. Wickham and I.D. Abrahams. The refraction of ultrasound in grainy and inhomogeneous fibrereinforced

materials. Proceedings of the Institute of Acoustics, 13(2):125–136, 1991.

[81] I.D. Abrahams. Complex motions of a fluid-loaded nonlinear elastic plate; periodic, subharmonic and

chaotic vibrations. Proceedings of the Institute of Acoustics, 12(1):501–510, 1990.

[82] I.D. Abrahams and G.R. Wickham. Acoustic scattering by two parallel slightly staggered rigid plates.

Wave Motion, 12(3):281–297, 1990.

[83] I.D. Abrahams and G.R. Wickham. General Wiener-Hopf factorization of matrix kernels with exponential

phase-factors. SIAM Journal on Applied Mathematics, 50(3):819–838, 1990.

[84] I.D. Abrahams and G.R. Wickham. Lacunas in welds. Proceedings of IUTAM Conference on Elastic

Wave Propagation and Nondestructive Testing, eds. S.K. Datta & J.D. Achenbach, pages 385–386,

1990.

[85] I.D. Abrahams and G.R. Wickham. On the scattering of sound by two semi-infinite parallel staggered

plates. II - evaluation of the velocity potential for an incident plane-wave and an incident duct mode.

Proceedings of the Royal Society, A 427(1872):139–171, 1990.

[86] I.D. Abrahams and G.R. Wickham. Scattering by a small surface breaking crack. Proceedings of

IUTAM Conference on Elastic Wave Propagation and Nondestructive Testing, eds. S.K. Datta & J.D.

Achenbach, pages 387–389, 1990.

[87] I.D. Abrahams. Scattering of sound by a finite non-linear elastic plate bounding a nearly resonant cavity.

Journal of Sound and Vibration, 130(3):387–404, 1989.

[88] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. On the development of caustics in shear flows over

rigid walls. SIAM Journal on Applied Mathematics, 49(6):1652–1664, 1989.

[89] T.A. Shepard, G.F. Lockwood, L.J. Aarons, and I.D. Abrahams. Mean residence time for drugs subject

to enterohepatic cycling. Journal of Pharmacokinetics and Biopharmaceutics, 17(3):327–345, 1989.

[90] I.D. Abrahams. Acoustic scattering by a finite nonlinear elastic plate. II - coupled primary and secondary

resonances. Proceedings of the Royal Society, A 418(1854):247–260, 1988.

[91] I.D. Abrahams. Matrix Wiener-Hopf problems - Author’s reply. Journal of Sound and Vibration,

124(3):584–585, 1988.

[92] I.D. Abrahams and G.R. Wickham. On the scattering of sound by two semi-infinite parallel staggered

plates. I - explicit matrix Wiener-Hopf factorization. Proceedings of the Royal Society, A 420(1858):131–

156, 1988.

[93] I.D. Abrahams. Acoustic scattering by a finite nonlinear elastic plate. I - primary, secondary and combination

resonances. Proceedings of the Royal Society, A 414(1846):237–253, 1987.

[94] I.D. Abrahams. On the sound field generated by membrane-surface waves on a wedge-shaped boundary.

Proceedings of the Royal Society, A 411(1840):239–250, 1987.

[95] I.D. Abrahams. Scattering of sound by three semi-infinite planes. Journal of Sound and Vibration,

112(2):396–398, 1987.

[96] I.D. Abrahams. Scattering of sound by two parallel semi-infinite screens. Wave Motion, 9(4):289–300,

1987.

[97] I.D. Abrahams. Diffraction by a semi-infinite membrane in the presence of a vertical barrier. Journal of

Sound and Vibration, 111(2):191–207, 1986.

[98] I.D. Abrahams. Scattering of sound by a semi-infinite elastic plate with a soft backing - a matrix

Wiener-Hopf problem. IMA Journal of Applied Mathematics, 37(3):227–245, 1986.

[99] I.D. Abrahams. Scattering of sound by an elastic plate with flow. Journal of Sound and Vibration,

89(2):213–231, 1983.

[100] I.D. Abrahams. Scattering of sound by finite elastic surfaces bounding ducts or cavities near resonance.

Quarterly Journal of Mechanics and Applied Mathematics, 35(Feb):91–101, 1982.

[101] I.D. Abrahams. Scattering of sound by large finite geometries. IMA Journal of Applied Mathematics,

29(1):79–97, 1982.

[102] I.D. Abrahams. Scattering of sound by a heavily loaded finite elastic plate. Proceedings of the Royal

Society, A 378(1772):89–117, 1981.

elastic response of a constrained layer. Journal of Sound and Vibration, 348:167–184, 2015. (pdf)

[2] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. Simple shear of a compressible quasilinear viscoelastic

material. International Journal of Engineering Science, 88(SI):64–72, 2015.

[3] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. On nonlinear viscoelastic deformations: a reappraisal

of fung’s quasi-linear viscoelastic model. Proceedings of the Royal Society, A 470(2166):20140058,

2014.

[4] R. De Pascalis, I.D. Abrahams, and W.J. Parnell. Predicting the pressure-volume curve of an elastic

microsphere composite. Journal of the Mechanics and Physics of Solids, 61(4):1106–1123, 2013.

[5] T. Shearer, I.D. Abrahams, and W.J. Parnell. Torsional wave propagation in a pre-stressed hyperelastic

annular circular cylinder. Quarterly Journal of Mechanics and Applied Mathematics, 66(4):465–487,

2013.

[6] I.D. Abrahams and J.B. Lawrie. Scattering of flexural waves by a semi-infinite crack in an elastic plate

carrying an electric current. Mathematics and Mechanics of Solids, 17(1):43–58, 2012.

[7] M. Heil, T. Kharrat, P.A. Cotterill, and I.D. Abrahams. Quasi-resonances in sound-insulating coatings.

Journal of Sound and Vibration, 331(21):4774–4784, 2012.

[8] W.J. Parnell and I.D. Abrahams. Antiplane wave scattering from a cylindrical void in a pre-stressed

incompressible neo-Hookean material. Communications in Computational Physics, 11(2):367–382, 2012.

[9] E. Perrey-Debain and I.D. Abrahams. TE mode mixing dynamics in curved multimode optical waveguides.

Communications in Computational Physics, 11(2):525–540, 2012.

[10] N. Willoughby, W.J. Parnell, A.L. Hazel, and I.D. Abrahams. Homogenization methods to approximate

the effective response of random fibre-reinforced composites. International Journal of solids and

structures, 49(13):1421–1433, 2012.

[11] W.J. Parnell and I.D. Abrahams. The effective wavenumber of a pre-stressed nonlinear microvoided

composite. Journal of Physics Conference Series, 269(012007):1–10, 2011.

[12] R. Green, G. Fusai, and I.D. Abrahams. The Wiener-Hopf technique and discretely monitored pathdependent

option pricing. Mathematical Finance, 20(2):259–288, 2010.

[13] W.J. Parnell and I.D. Abrahams. Multiple point scattering to determine the effective wavenumber

and effective material properties of an inhomogeneous slab. Waves in Random and Complex Media,

20(4):678–701, 2010.

[14] W.J. Parnell, I.D. Abrahams, and P.R. Brazier-Smith. Effective properties of a composite half-space:

exploring the relationship between homogenization and multiple-scattering theories. Quarterly Journal

of Mechanics and Applied Mathematics, 63(2):145–175, 2010.

[15] E. Perrey-Debain and I.D. Abrahams. A general asymptotic expansion formula for integrals involving

high-order orthogonal polynomials. SIAM Journal on Scientific Computing, 31(5):3884–3904, 2009.

[16] I.D. Abrahams, A.M.J. Davis, and S.G. Llewellyn Smith. Asymmetric channel divider in stokes flow.

SIAM Journal on Applied Mathematics, 68(5):1439–1463, 2008.

[17] I.D. Abrahams, A.M.J. Davis, and S.G. Llewellyn Smith. Matrix Wiener-Hopf approximation for a

partially clamped plate. Quarterly Journal of Mechanics and Applied Mathematics, 61:241–265, 2008. [18] R. Harter, M.J. Simon, and I.D. Abrahams. The effect of surface tension on localized free-surface

oscillations about surface-piercing bodies. Proceedings of the Royal Society, A 464(2099):3039–3054,

2008.

[19] W.J. Parnell and I.D. Abrahams. Homogenization for wave propagation in periodic fibre-reinforced media

with complex microstructure. I - theory. Journal of the Mechanics and Physics of Solids, 56(7):2521–

2540, 2008.

[20] W.J. Parnell and I.D. Abrahams. A new integral equation approach to elastodynamic homogenization.

Proceedings of the Royal Society, A 464(2094):1461–1482, 2008.

[21] E. Perrey-Debain, I.D. Abrahams, and J.D. Love. A continuous model for mode mixing in graded-index

multimode fibres with random imperfections. Proceedings of the Royal Society, A 464(2092):987–1007,

2008.

[22] B. Erbas and I.D. Abrahams. Scattering of sound waves by an infinite grating composed of rigid plates.

Wave Motion, 44(4):282–303, 2007.

[23] R. Green, I.D. Abrahams, and G. Fusai. Pricing financial claims contingent upon an underlying asset

monitored at discrete times. Journal of Engineering Mathematics, 59(4):373–384, 2007.

[24] R. Harter, I.D. Abrahams, and M.J. Simon. The effect of surface tension on trapped modes in water-wave

problems. Proceedings of the Royal Society, A 463(2088):3131–3149, 2007.

[25] J.B. Lawrie and I.D. Abrahams. A brief historical perspective of the Wiener-Hopf technique. Journal of

Engineering Mathematics, 59(4):351–358, 2007.

[26] A.N. Norris and I.D. Abrahams. A multiple-scales approach to crack-front waves. Journal of Engineering

Mathematics, 59(4):399–417, 2007.

[27] W.J. Parnell and I.D. Abrahams. Multiple scattering in periodic and random media: an overview.

Proceedings of 4th Conference of Groupement de Recherche GDR 2501: ‘etude de la propagation

ultrasonore en milieux non homogènes en vue du contrôle non destructif’, eds. M. Deschamps & A.

Leger, 2007.

[28] E. Perrey-Debain and I.D. Abrahams. A diffusion analysis approach to TE mode propagation in randomly

perturbed optical waveguides. SIAM Journal on Applied Mathematics, 68(2):523–543, 2007.

[29] I. Thompson and I.D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.

II - far field analysis. Proceedings of the Royal Society, A 463(2082):1615–1638, 2007.

[30] B.H. Veitch and I.D. Abrahams. On the commutative factorization of n ×n matrix Wiener-Hopf kernels

with distinct eigenvalues. Proceedings of the Royal Society, A 463(2078):613–639, 2007.

[31] G. Fusai, I.D. Abrahams, and C. Sgarra. An exact analytical solution for discrete barrier options. Finance

and Stochastics, 10(1):1–26, 2006.

[32] G.W. Owen and I.D. Abrahams. Elastic wave radiation from a high frequency finite-length transducer.

Journal of Sound and Vibration, 298(1-2):108–131, 2006.

[33] G.W. Owen, A.J. Willmott, and I.D. Abrahams. Scattering of barotropic rossby waves by the antarctic

circumpolar current. Journal of Geophysical Research - Oceans, 111(C12):C12024, 2006.

[34] W.J. Parnell and I.D. Abrahams. Dynamic homogenization in periodic fibre reinforced media. Quasistatic

limit for SH waves. Wave Motion, 43(6):474–498, 2006.

[35] E. Perrey-Debain and I.D. Abrahams. A band factorization technique for transition matrix element

asymptotics. Computer Physics Communications, 175(5):315–322, 2006.

[36] G.W. Owen, A.J. Willmott, I.D. Abrahams, and H. Mansley. The scattering of rossby waves from finite

abrupt topography. Geophysical and Astrophysical Fluid Dynamics, 99(3):219–239, 2005.

[37] I. Thompson and I.D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.

I - formal solution. Proceedings of the Royal Society, A 461(2063):3413–3436, 2005.

[38] I.D. Abrahams. On the application of the Wiener-Hopf technique to problems in dynamic elasticity.

Wave Motion, 36(4):311–333, 2002.

[39] I.D. Abrahams and A.M.J. Davis. Deflection of a partially clamped elastic plate. Proceedings of IUTAM

Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, eds. I.D. Abrahams, P.A.

Martin & M.J. Simon, 68:303–312, 2002.

[40] I.D. Abrahams, G.W. Owen, and A.J. Willmott. The scattering of Rossby waves by ocean ridges.

Proceedings of IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, eds.

I.D. Abrahams, P.A. Martin & M.J. Simon, 68:3–12, 2002.

[41] J.B. Lawrie and I.D. Abrahams. On the propagation and scattering of fluid-structural waves in a threedimensional

duct bounded by thin elastic walls. Proceedings of IUTAM Symposium on Diffraction and

Scattering in Fluid Mechanics and Elasticity, eds. I.D. Abrahams, P.A. Martin & M.J. Simon, 68:279–

288, 2002.

[42] G.W. Owen, I.D. Abrahams, A.J. Willmott, and C.W. Hughes. On the scattering of baroclinic Rossby

waves by a ridge in a continuously stratified ocean. Journal of Fluid Mechanics, 465:131–155, 2002.

[43] I. Thompson, I.D. Abrahams, and A.N. Norris. On the existence of flexural edge waves on thin orthotropic

plates. Journal of the Acoustical Society of America, 112(5):1756–1765, 2002.

[44] I.D. Abrahams and G.R. Wickham. On transient oscillations of plates in moving fluids. Wave Motion,

33(1):7–23, 2001.

[45] G.W. Owen and I.D. Abrahams. Radiation from a transducer into an elastic half-space. Proceedings

of IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media, eds. R.C.

McPhedran, L.C. Botten & N.A. Nicorovici, pages 73–88, 2001.

[46] I.D. Abrahams. The application of Padé approximants to Wiener-Hopf factorization. IMA Journal of

Applied Mathematics, 65(3):257–281, 2000.

[47] I.D. Abrahams and A.N. Norris. On the existence of flexural edge waves on submerged elastic plates.

Proceedings of the Royal Society, A 456(1999):1559–1582, 2000.

[48] M.A. Heckl and I.D. Abrahams. Curve squeal of train wheels. I - mathematical model for its generation.

Journal of Sound and Vibration, 229(3):669–693, 2000.

[49] A.N. Norris, V.V. Krylov, and I.D. Abrahams. Flexural edge waves and comments on "a new bending

wave solution for the classical plate equation". Journal of the Acoustical Society of America,

107(3):1781–1784, 2000.

[50] I.D. Abrahams. Sound radiation from a line forced perforated elastic sandwich panel. Journal of the

Acoustical Society of America, 105(6):3009–3020, 1999.

[51] J.B. Lawrie and I.D. Abrahams. An orthogonality relation for a class of problems with high-order

boundary conditions; applications in sound-structure interaction. Quarterly Journal of Mechanics and

Applied Mathematics, 52(2):161–181, 1999.

[52] I.D. Abrahams. On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type. Proceedings

of the Royal Society, A 454(1974):1719–1743, 1998.

[53] J.B. Lawrie and I.D. Abrahams. Applications of a general orthogonality relation to acoustic scattering

in ducts with high order boundary conditions. Proceedings of Days on Diffraction, pages 6–19, 1998.

[54] I.D. Abrahams. On the solution of Wiener-Hopf problems involving noncommutative matrix kernel

decompositions. SIAM Journal on Applied Mathematics, 57(2):541–567, 1997.

[55] J.B. Lawrie and I.D. Abrahams. Scattering of fluid loaded elastic plate waves at the vertex of a wedge

of arbitrary angle. I - analytic solution. IMA Journal of Applied Mathematics, 59(1):1–23, 1997.

[56] I.D. Abrahams. On explicit approximate non-commutative factorization of matrix wiener-hopf kernels.

in Pitman Research Notes in Mathematics, eds. H. Sebest & S. Cloude, 361:41–55, 1996.

[57] I.D. Abrahams. Radiation and scattering of waves on an elastic half-space; a non-commutative matrix

Wiener-Hopf problem. Journal of the Mechanics and Physics of Solids, 44(12):2125–2154, 1996.

[58] M.A. Heckl and I.D. Abrahams. Active control of friction-driven oscillations. Journal of Sound and

Vibration, 193(1):417–426, 1996.

[59] J.B. Lawrie and I.D. Abrahams. Travelling waves on a membrane: reflection and transmission at a

corner of arbitrary angle. II. Proceedings of the Royal Society, A 452(1950):1649–1677, 1996.

[60] I.D. Abrahams. Chaotic scattering of sound waves by buckled elastic plates. Proceedings of IUTAM

Symposium on Nonlinear Waves in Solids, eds. J. Wegner & F. Norwood, ASME Book No. AMR137:41–

46, 1995.

[61] I.D. Abrahams and J.B. Lawrie. On the factorization of a class of Wiener-Hopf kernels. IMA Journal of

Applied Mathematics, 55(1):35–47, 1995.

[62] I.D. Abrahams and J.B. Lawrie. Travelling waves on a membrane: reflection and transmission at a

corner of arbitrary angle. I. Proceedings of the Royal Society, A 451(1943):657–683, 1995.

[63] B. Zhang and I.D. Abrahams. The radiation of sound from a finite ring-forced cylindrical elastic shell. I

- Wiener-Hopf analysis. Proceedings of the Royal Society, A 450(1938):89–108, 1995.

[64] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. Caustic formation from a point source in a shear layer

over an elastic surface; a model for the suppression of coherent fluid structures? in Structural Acoustics,

Scattering and Propagation, eds. J.E. Ffowcs Williams, D. Lee & A.D. Pierce, pages 221–236, 1994.

[65] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. Sound radiation and caustic formation from a pointsource

in a wall shear-layer. AIAA Journal, 32(6):1135–1144, 1994.

[66] J.C. Engineer and I.D. Abrahams. The radiation of sound-waves from a lightly loaded finite elastic shell.

II - nonlinear shell resonances. Journal of Sound and Vibration, 174(3):353–377, 1994.

[67] J.B. Lawrie and I.D. Abrahams. Acoustic radiation from two opposed semiinfinite coaxial cylindrical

wave-guides. II - separated ducts. Wave Motion, 19(1):83–109, 1994.

[68] J.B. Lawrie and I.D. Abrahams. Radiation of sound from two coaxial cylindrical waveguides; a matrix

wiener-hopf formulation. in Structural Acoustics, Scattering and Propagation, eds. J.E. Ffowcs Williams,

D. Lee & A.D. Pierce, pages 177–190, 1994.

[69] B. Zhang and I.D. Abrahams. A numerical evaluation of the sound field scattered by a finite fluid-loaded

elastic shell. in Structural Acoustics, Scattering and Propagation, eds. J.E. Ffowcs Williams, D. Lee &

A.D. Pierce, pages 191–206, 1994.

[70] I.D. Abrahams. The effect of nonlinearity on the scattering of sound by lightly loaded thin elastic

structures. in Pitman Research Notes in Mathematics 4th ed., eds. B.D. Sleeman & R. Jarvis, 1993.

[71] J.B. Lawrie, I.D. Abrahams, and C.M. Linton. Acoustic radiation from two opposed semiinfinite coaxial

cylindrical wave-guides. I - overlapping edges. Wave Motion, 18(2):121–142, 1993.

[72] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. On the development of caustics in shear flows over

rigid walls. Journal of the Acoustical Society of America, 92(1):428–434, 1992.

[73] I.D. Abrahams and G.R. Wickham. Scattering of elastic-waves by a small inclined surface-breaking

crack. Journal of the Mechanics and Physics of Solids, 40(8):1707–1733, 1992.

[74] I.D. Abrahams and G.R. Wickham. Scattering of elastic-waves by an arbitrary small imperfection in the

surface of a half-space. Journal of the Mechanics and Physics of Solids, 40(8):1683–1706, 1992.

[75] I.D. Abrahams and G.R. Wickham. The propagation of elastic-waves in a certain class of inhomogeneous

anisotropic materials. I - the refraction of a horizontally polarized shear-wave source. Proceedings of the

Royal Society, A 436(1898):449–478, 1992.

[76] J.C. Engineer and I.D. Abrahams. The radiation of sound-waves from a lightly loaded finite elastic shell.

I - duct and shell resonances for linear-motions. Journal of Sound and Vibration, 153(2):291–310, 1992.

[77] I.D. Abrahams and J.C. Engineer. A secularity condition for systems of linear partial-differential equations.

Journal of Sound and Vibration, 150(2):338–341, 1991.

[78] I.D. Abrahams and G.R. Wickham. The scattering of ultrasound by a small surface imperfection.

Proceedings of the Institute of Acoustics, 13(2):103–110, 1991.

[79] I.D. Abrahams and G.R. Wickham. The scattering of water-waves by two semi-infinite opposed vertical

walls. Wave Motion, 14(2):145–168, 1991.

[80] G.R. Wickham and I.D. Abrahams. The refraction of ultrasound in grainy and inhomogeneous fibrereinforced

materials. Proceedings of the Institute of Acoustics, 13(2):125–136, 1991.

[81] I.D. Abrahams. Complex motions of a fluid-loaded nonlinear elastic plate; periodic, subharmonic and

chaotic vibrations. Proceedings of the Institute of Acoustics, 12(1):501–510, 1990.

[82] I.D. Abrahams and G.R. Wickham. Acoustic scattering by two parallel slightly staggered rigid plates.

Wave Motion, 12(3):281–297, 1990.

[83] I.D. Abrahams and G.R. Wickham. General Wiener-Hopf factorization of matrix kernels with exponential

phase-factors. SIAM Journal on Applied Mathematics, 50(3):819–838, 1990.

[84] I.D. Abrahams and G.R. Wickham. Lacunas in welds. Proceedings of IUTAM Conference on Elastic

Wave Propagation and Nondestructive Testing, eds. S.K. Datta & J.D. Achenbach, pages 385–386,

1990.

[85] I.D. Abrahams and G.R. Wickham. On the scattering of sound by two semi-infinite parallel staggered

plates. II - evaluation of the velocity potential for an incident plane-wave and an incident duct mode.

Proceedings of the Royal Society, A 427(1872):139–171, 1990.

[86] I.D. Abrahams and G.R. Wickham. Scattering by a small surface breaking crack. Proceedings of

IUTAM Conference on Elastic Wave Propagation and Nondestructive Testing, eds. S.K. Datta & J.D.

Achenbach, pages 387–389, 1990.

[87] I.D. Abrahams. Scattering of sound by a finite non-linear elastic plate bounding a nearly resonant cavity.

Journal of Sound and Vibration, 130(3):387–404, 1989.

[88] I.D. Abrahams, G.A. Kriegsmann, and E.L. Reiss. On the development of caustics in shear flows over

rigid walls. SIAM Journal on Applied Mathematics, 49(6):1652–1664, 1989.

[89] T.A. Shepard, G.F. Lockwood, L.J. Aarons, and I.D. Abrahams. Mean residence time for drugs subject

to enterohepatic cycling. Journal of Pharmacokinetics and Biopharmaceutics, 17(3):327–345, 1989.

[90] I.D. Abrahams. Acoustic scattering by a finite nonlinear elastic plate. II - coupled primary and secondary

resonances. Proceedings of the Royal Society, A 418(1854):247–260, 1988.

[91] I.D. Abrahams. Matrix Wiener-Hopf problems - Author’s reply. Journal of Sound and Vibration,

124(3):584–585, 1988.

[92] I.D. Abrahams and G.R. Wickham. On the scattering of sound by two semi-infinite parallel staggered

plates. I - explicit matrix Wiener-Hopf factorization. Proceedings of the Royal Society, A 420(1858):131–

156, 1988.

[93] I.D. Abrahams. Acoustic scattering by a finite nonlinear elastic plate. I - primary, secondary and combination

resonances. Proceedings of the Royal Society, A 414(1846):237–253, 1987.

[94] I.D. Abrahams. On the sound field generated by membrane-surface waves on a wedge-shaped boundary.

Proceedings of the Royal Society, A 411(1840):239–250, 1987.

[95] I.D. Abrahams. Scattering of sound by three semi-infinite planes. Journal of Sound and Vibration,

112(2):396–398, 1987.

[96] I.D. Abrahams. Scattering of sound by two parallel semi-infinite screens. Wave Motion, 9(4):289–300,

1987.

[97] I.D. Abrahams. Diffraction by a semi-infinite membrane in the presence of a vertical barrier. Journal of

Sound and Vibration, 111(2):191–207, 1986.

[98] I.D. Abrahams. Scattering of sound by a semi-infinite elastic plate with a soft backing - a matrix

Wiener-Hopf problem. IMA Journal of Applied Mathematics, 37(3):227–245, 1986.

[99] I.D. Abrahams. Scattering of sound by an elastic plate with flow. Journal of Sound and Vibration,

89(2):213–231, 1983.

[100] I.D. Abrahams. Scattering of sound by finite elastic surfaces bounding ducts or cavities near resonance.

Quarterly Journal of Mechanics and Applied Mathematics, 35(Feb):91–101, 1982.

[101] I.D. Abrahams. Scattering of sound by large finite geometries. IMA Journal of Applied Mathematics,

29(1):79–97, 1982.

[102] I.D. Abrahams. Scattering of sound by a heavily loaded finite elastic plate. Proceedings of the Royal

Society, A 378(1772):89–117, 1981.

## Books and Edited Works

[B1] W.J. Parnell, and I.D. Abrahams. Introduction to Homogenization Methods in Continuum Mechanics.

Cambridge University Press, _240pp, to appear, 2016.

[B2] M. Lowe, N. Saffari, A. Lhemery, M. Deschamps, A. Leger, and I.D. Abrahams. Proceedings of 6th Groupe

De Recherche (GDR) 2501 and 9th Anglo-French Physical Acoustics Joint Conference (AFPAC), January

2010. IOP Journal of Physics Conference Series, 269:250 pages, 2011.

[B3] J.B. Lawrie, and I.D. Abrahams. Special Issue entitled “The Wiener-Hopf Technique: Modern Applications

and Developments”. Journal of Engineering Mathematics, 59(4):351–475, 2007.

[B4] I.D. Abrahams, P.A. Martin, and M.J. Simon. Proceedings of IUTAM Symposium on Diffraction and

Scattering in Fluid Mechanics and Elasticity, Kluwer Press. 366 pages, 2002.

[B5] I.D. Abrahams, P.A. Martin and A.N. Norris. Special Issue. Wave Motion, 33(1):1-116, 2001.

Cambridge University Press, _240pp, to appear, 2016.

[B2] M. Lowe, N. Saffari, A. Lhemery, M. Deschamps, A. Leger, and I.D. Abrahams. Proceedings of 6th Groupe

De Recherche (GDR) 2501 and 9th Anglo-French Physical Acoustics Joint Conference (AFPAC), January

2010. IOP Journal of Physics Conference Series, 269:250 pages, 2011.

[B3] J.B. Lawrie, and I.D. Abrahams. Special Issue entitled “The Wiener-Hopf Technique: Modern Applications

and Developments”. Journal of Engineering Mathematics, 59(4):351–475, 2007.

[B4] I.D. Abrahams, P.A. Martin, and M.J. Simon. Proceedings of IUTAM Symposium on Diffraction and

Scattering in Fluid Mechanics and Elasticity, Kluwer Press. 366 pages, 2002.

[B5] I.D. Abrahams, P.A. Martin and A.N. Norris. Special Issue. Wave Motion, 33(1):1-116, 2001.

## Other Publications

[S1] B.D Sleeman, I.D. Abrahams. Douglas Samuel Jones MBE. 10 January 1922 U 26 November 2013, BiographicalMemoirs

of Fellows of the Royal Society, Published online before print, doi: 10.1098/rsbm.2015.0005,

24 June 2015.

[S2] I.D. Abrahams, P.A. Martin. Fritz Joseph Ursell. 28 April 1923 U 11 May 2012, Biographical Memoirs of

Fellows of the Royal Society, 59:407-421, 2013.

[S3] D. Yumashev, I.D. Abrahams, C.J. Chapman, P. Joseph, N. Peake, C.P. Walker, P.A. Cotterill. Broadband

Hydroacoustics Research Report (Unclassified), Phase 2, Thales Underwater Systems UK, Contract Number

Dstlx 1000062650 BHAR, Document Number: 0026K7626,62921576,575, December 2012.

[S4] D. Yumashev, I.D. Abrahams, C.J. Chapman, P. Joseph, N. Peake, C.P. Walker, P.A. Cotterill. Broadband

Hydroacoustics Research Report (Unclassified), Phase 1, Thales Underwater Systems UK, Contract Number

Dstlx 1000062650 BHAR, Document Number: 0026K7626,62461037,179, March 2012.

[S5] I.D. Abrahams, P.A. Martin, and A.N. Norris. G.R. Wickham: An appreciation. Wave Motion, 33(1):1-6,

2001.

[S4] Publication by postdoctoral assistant: A. McMillan. A non-linear friction model for self-excited vibrations.

Journal of Sound and Vibration, 205(3):323-335, 1997.

[S6] I.D. Abrahams. Interaction of Sound Waves with Finite Plates and Cavities. AUWE internal report

(unclassified), 65382, 1983.

[S7] I.D. Abrahams. Scattering of Sound by Finite Thin Elastic Plates and Cavities. PhD Thesis, Imperial

College London, 1982.

of Fellows of the Royal Society, Published online before print, doi: 10.1098/rsbm.2015.0005,

24 June 2015.

[S2] I.D. Abrahams, P.A. Martin. Fritz Joseph Ursell. 28 April 1923 U 11 May 2012, Biographical Memoirs of

Fellows of the Royal Society, 59:407-421, 2013.

[S3] D. Yumashev, I.D. Abrahams, C.J. Chapman, P. Joseph, N. Peake, C.P. Walker, P.A. Cotterill. Broadband

Hydroacoustics Research Report (Unclassified), Phase 2, Thales Underwater Systems UK, Contract Number

Dstlx 1000062650 BHAR, Document Number: 0026K7626,62921576,575, December 2012.

[S4] D. Yumashev, I.D. Abrahams, C.J. Chapman, P. Joseph, N. Peake, C.P. Walker, P.A. Cotterill. Broadband

Hydroacoustics Research Report (Unclassified), Phase 1, Thales Underwater Systems UK, Contract Number

Dstlx 1000062650 BHAR, Document Number: 0026K7626,62461037,179, March 2012.

[S5] I.D. Abrahams, P.A. Martin, and A.N. Norris. G.R. Wickham: An appreciation. Wave Motion, 33(1):1-6,

2001.

[S4] Publication by postdoctoral assistant: A. McMillan. A non-linear friction model for self-excited vibrations.

Journal of Sound and Vibration, 205(3):323-335, 1997.

[S6] I.D. Abrahams. Interaction of Sound Waves with Finite Plates and Cavities. AUWE internal report

(unclassified), 65382, 1983.

[S7] I.D. Abrahams. Scattering of Sound by Finite Thin Elastic Plates and Cavities. PhD Thesis, Imperial

College London, 1982.