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David Abrahams - publications

List of publications

2017

  • Joyce, D., Parnell, W., Assier, R., & Abrahams, I. (2017). An integral equation method for the homogenization of unidirectional fibre reinforced media; antiplane elasticity and other potential problems.Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. . Publication link: 50e2af13-d17c-453f-ab9a-e936e52eae09

2016

2015

2014

  • De Pascalis, R., Abrahams, I. D., & Parnell, W. (2014). On nonlinear viscoelastic deformations - a reappraisal of Fung's quasilinear viscoelastic model. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. . Publication link: 17b33757-4acf-450d-b433-ff0d696a33af
  • De Pascalis, R., Abrahams, I. D., & Parnell, W. (2014). On nonlinear viscoelastic deformations: a reappraisal of Fung's quasi-linear viscoelastic model. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, 470(2166), [20140058]. DOI: 10.1098/rspa.2014.0058. Publication link: efe65d41-f383-474c-87b6-e275d3a18bf0

2013

  • Shearer, T., Abrahams, I. D., Parnell, W. J., & Daros, C. H. (2013). Torsional wave propagation in a pre-stressed hyperelastic annular circular cylinder. Quarterly Journal of Mechanics and Applied Mathematics, 66(4), 465-487. DOI: 10.1093/qjmam/hbt014. Publication link: f661039e-8c85-44cf-9cf7-42bb0a29917c
  • De Pascalis, R., David Abrahams, I., & Parnell, W. J. (2013). Predicting the pressure-volume curve of an elastic microsphere composite. Journal of the Mechanics and Physics of Solids, 61(4), 1106-1123. DOI: 10.1016/j.jmps.2012.11.005. Publication link: 70bc4cf1-ca5c-48fc-9279-a5b1a2ad957c

2012

2011

2010

2009

  • Perrey-Debain, E., & Abrahams, I. D. (2009). A general asymptotic expansion formula for integrals involving high-order orthogonal polynomials. SIAM Journal on Scientific Computing, 31(5), 3884-3904. DOI: 10.1137/080736740. Publication link: b1ec2f87-718d-4863-adcd-e135bdb72e87

2008

  • Abrahamst, I. D., David, A. M. J., & Smith, S. G. L. (2008). Asymmetric channel divider in stokes flow. SIAM Journal on Applied Mathematics, 68(5), 1439-1463. DOI: 10.1137/070703211. Publication link: bac71856-c527-44a4-8fc4-a1f9004cd97e
  • Perrey-Debain, E., Abrahams, I. D., & Love, J. D. (2008). A continuous model for mode mixing in graded-index multimode fibres with random imperfections. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2092), 987-1007. DOI: 10.1098/rspa.2007.0023. Publication link: 4abc295d-fede-47e0-a1e8-bfbff8cd3c8e
  • Abrahams, I. D., Davis, A. M. J., & Smith, S. G. L. (2008). Matrix Wiener-Hopf approximation for a partially clamped plate. Quarterly Journal of Mechanics and Applied Mathematics, 61(2), 241-265. DOI: 10.1093/qjmam/hbn004. Publication link: 421ff202-ca18-4cda-b1db-117b69e27220
  • Parnell, W. J., & 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(7), 2521-2540. DOI: 10.1016/j.jmps.2008.02.003. Publication link: 1913c896-c09a-47d3-ae00-393cf5b85aef
  • Parnell, W. J., & Abrahams, I. D. (2008). A new integral equation approach to elastodynamic homogenization. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2094), 1461-1482. DOI: 10.1098/rspa.2007.0254. Publication link: 678ffd2a-d14c-4415-a6e5-f9bb3fc0af75
  • Harter, R., Simon, M. J., & Abrahams, I. D. (2008). The effect of surface tension on localized free-surface oscillations about surface-piercing bodies. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2099), 3039-3054. DOI: 10.1098/rspa.2008.0059. Publication link: 78303af1-d035-481e-b605-dab7d5c5252f

2007

2006

2005

  • Owen, G. W., Willmott, A. J., Abrahams, I. D., & Mansley, H. (2005). The scattering of Rossby waves from finite abrupt topography. Geophysical and Astrophysical Fluid Dynamics, 99(3), 219-239. DOI: 10.1080/03091920500087690. Publication link: 68b5e3a7-3beb-4475-af69-8f556888b430
  • Thompson, I., & Abrahams, I. D. (2005). Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I formal solution. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2063), 3413-3436. DOI: 10.1098/rspa.2004.1418. Publication link: 473cefec-4a55-477c-8554-cf7a614da3cc

2002

  • Owen, G. W., Abrahams, I. D., Willmott, A. J., & Hughes, C. W. (2002). On the scattering of baroclinic Rossby waves by a ridge in a continuously stratified ocean. Journal of Fluid Mechanics, 465, 131-155. DOI: 10.1017/S0022112002001027. Publication link: e85c565d-e2ba-41bf-9f4d-df0401447834
  • Lawrie, J. B., & Abrahams, I. D. (2002). On the propagation and scattering of fluid-structural waves in a three-dimensional duct bounded by thin elastic walls. In IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING IN FLUID MECHANICS AND ELASTICITY, PROCEEDINGS. (Vol. 68, pp. 279-288). Publication link: b46da278-4867-42b6-8f9f-4c3ffa24e9ae
  • Abrahams, I. D., Owen, G. W., & Willmott, A. J. (2002). The scattering of Rossby waves by ocean ridges. In IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING IN FLUID MECHANICS AND ELASTICITY, PROCEEDINGS. (Vol. 68, pp. 3-12). Publication link: 6d041134-c75f-4612-95fa-ac42f89e0661
  • Abrahams, I. D., & Davis, A. M. J. (2002). Deflection of a partially clamped elastic plate. In IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING IN FLUID MECHANICS AND ELASTICITY, PROCEEDINGS. (Vol. 68, pp. 303-312). Publication link: 4f4fb7ad-e917-40ae-968a-aaaf2fb70006
  • Thompson, I., Abrahams, I. D., & Norris, A. N. (2002). On the existence of flexural edge waves on thin orthotropic plates. Journal of the Acoustical Society of America, 112(5 I), 1756-1765. DOI: 10.1121/1.1506686. Publication link: 7dc84c34-b4ae-4dcd-aa52-01e517b1f598
  • Abrahams, I. D. (2002). On the application of the Wiener-Hopf technique to problems in dynamic elasticity. WAVE MOTION, 36(4), 311-333. DOI: 10.1016/S0165-2125(02)00027-6. Publication link: 957281bb-3c68-4e67-8701-563f47486235

2001

2000

  • Abrahams, I. D., Martin, P. A., & Simon, M. J. (2000). DIFFRACTION AND SCATTERING IN FLUID MECHANICS AND ELASTICITY. In Fluid Mechanics and its Applications. (Vol. 68). (Fluid Mechanics and its Applications). Dordrect, The Netherlands: Kluwer Academic Publishers. . Publication link: f78a3a92-fd26-4d66-93ad-1f8fbee0b3cc
  • David Abrahams, I., & Norris, A. N. (2000). On the existence of flexural edge waves on submerged elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 456(1999), 1559-1582. DOI: 10.1098/rspa.2000.0576. Publication link: d5705623-5fd9-4f9c-b9fe-eef473bbf24d
  • Heckl, M. A., & Abrahams, I. D. (2000). Curve squeal of train wheels, Part 1: mathematical model for its generation. Journal of Sound and Vibration, 229(3), 669-693. DOI: 10.1006/jsvi.1999.2510. Publication link: da891879-8f98-4809-8df6-72c1e1508ff1
  • Abrahams, I. D. (2000). Application of Pade approximants to Wiener-Hopf factorization. IMA Journal of Applied Mathematics , 65(3), 257-281. DOI: 10.1093/imamat/65.3.257. Publication link: d404f59e-5aee-4682-9db8-2470d10bbddf
  • Norris, A. N., Krylov, V. V., & Abrahams, I. D. (2000). Flexural edge waves and comments on 'a new bending wave solution for the classical plate equation' [J. Acoust. Soc. Am. 104, 2220-2222 (1998)]. Journal of the Acoustical Society of America, 107(3), 1781-1785. DOI: 10.1121/1.428457. Publication link: 0be68ecc-4668-4811-99e0-c4d59481bcd0

1999

  • Lawrie, J. B., & Abrahams, I. D. (1999). 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. DOI: 10.1093/qjmam/52.2.161. Publication link: 29387018-dbab-472e-89a6-928cbaeac889
  • Abrahams, I. D. (1999). Sound radiation from a line forced perforated elastic sandwich panel. Journal of the Acoustical Society of America, 105(6), 3009-3020. DOI: 10.1121/1.424627. Publication link: 671210bc-de43-4b44-acd9-b7b21d50d9c5

1998

  • David Abrahams, I. (1998). On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1974), 1719-1743. DOI: 10.1098/rspa.1998.0229. Publication link: b33afccc-e65f-4b0b-9aed-4cbc3c8fd23c

1997

  • Lawrie, J. B., & Abrahams, I. D. (1997). Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle .1. Analytic solution. IMA JOURNAL OF APPLIED MATHEMATICS, 59(1), 1-23. . Publication link: b7017709-0509-4ad0-99e5-17d004869f49
  • Abrahams, I. D. (1997). On the solution of Wiener-Hopf problems involving noncommutative matrix kernel decompositions. SIAM Journal on Applied Mathematics, 57(2), 541-567. DOI: 10.1137/S0036139995287673. Publication link: f9b9bd07-e6ff-4282-8979-bde689878fdd

1996

  • Lawrie, J. B., & Abrahams, I. D. (1996). Travelling waves on a membrane: Reflection and transmission at a corner of arbitrary angle .2. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 452(1950), 1649-1677. . Publication link: 27a147ac-9786-497a-b6aa-43975fb033f8
  • Abrahams, I. D. (1996). 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. DOI: 10.1016/S0022-5096(96)00064-6. Publication link: 4d1c0716-0a35-4877-89c1-e706e6abcbdc
  • Heckl, M. A., & Abrahams, I. D. (1996). Active control of friction-driven oscillations. Journal of Sound and Vibration, 193(1), 417-426. DOI: 10.1006/jsvi.1996.0285. Publication link: b1b495aa-c236-4386-b213-a5099b52921c

1995

  • Zhang, B., & Abrahams, I. D. (1995). THE RADIATION OF SOUND FROM A FINITE RING-FORCED CYLINDRICAL ELASTIC SHELL .1. WIENER-HOPF ANALYSIS. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, 450(1938), 89-108. . Publication link: 823fb97f-a6a1-4000-ad40-a99c4e618bd7
  • Abrahams, I. D., & Lawrie, J. B. (1995). On the factorization of a class of wiener-hopf kernels. IMA Journal of Applied Mathematics , 55(1), 35-47. DOI: 10.1093/imamat/55.1.35. Publication link: 616a4441-7775-4d7e-9a5d-7ee5b1420a87
  • Abrahams, I. D., & Lawrie, J. B. (1995). Travelling waves on a membrane: Reflection and transmission at a corner of arbitrary angle .1. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 451(1943), 657-683. . Publication link: 2f7bc267-0737-4f25-86fb-71fbee1688cb

1994

  • Lawrie, J. B., & Abrahams, I. D. (1994). ACOUSTIC RADIATION FROM 2 OPPOSED SEMIINFINITE COAXIAL CYLINDRICAL WAVE-GUIDES .2. SEPARATED DUCTS. Wave Motion, 19(1), 83-109. . Publication link: e22ab259-0b29-4ac3-9fed-1db68ba4cdb9
  • Abrahams, I. D., Kriegsmann, G. A., & Reiss, E. L. (1994). SOUND RADIATION AND CAUSTIC FORMATION FROM A POINT-SOURCE IN A WALL SHEAR-LAYER. AIAA Journal, 32(6), 1135-1144. . Publication link: 68c79021-fdf6-4431-ae9c-fe3ee0116283
  • Engineer, J. C., & Abrahams, I. D. (1994). THE RADIATION OF SOUND-WAVES FROM A LIGHTLY LOADED FINITE ELASTIC SHELL, .2. NONLINEAR SHELL RESONANCES. Journal of Sound and Vibration, 174(3), 353-377. . Publication link: 138eba96-1d15-46ca-9f90-8967a9abdd9f

1993

  • Lawrie, J. B., Abrahams, I. D., & Linton, C. M. (1993). ACOUSTIC RADIATION FROM 2 OPPOSED SEMIINFINITE COAXIAL CYLINDRICAL WAVE-GUIDES .1. OVERLAPPING EDGES. Wave Motion, 18(2), 121-142. . Publication link: 39f6f9db-5c29-43b6-aa09-956205a8a4cc

1992

  • Abrahams, I. D., & Wickham, G. R. (1992). 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. . Publication link: 1fdb0002-0626-4318-8d67-1277bd1cd31c
  • Abrahams, I. D., Kriegsmann, G. A., & Reiss, E. L. (1992). On the development and control of caustics in shear flows over elastic surfaces. Journal of the Acoustical Society of America, 92(1), 428-434. . Publication link: 27f1c061-f2b6-4819-a780-821530ae5f80
  • Abrahams, I. D., & Wickham, G. R. (1992). Scattering of elastic waves by a small inclined surface-breaking crack. Journal of the Mechanics and Physics of Solids, 40(8), 1707-1733. . Publication link: 5dfb6d1c-ecad-48c4-a9f1-8e5681d8b4eb
  • Abrahams, I. D., & Wickham, G. R. (1992). THE PROPAGATION OF ELASTIC-WAVES IN A CERTAIN CLASS OF INHOMOGENEOUS ANISOTROPIC MATERIALS .1. THE REFRACTION OF A HORIZONTALLY POLARIZED SHEAR-WAVE SOURCE. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 436(1898), 449-478. . Publication link: 6bf695ad-de39-4d3b-b1e8-9ea42e3e4481
  • Engineer, J. C., & Abrahams, I. D. (1992). THE RADIATION OF SOUND-WAVES FROM A LIGHTLY LOADED FINITE ELASTIC SHELL .1. DUCT AND SHELL RESONANCES FOR LINEAR-MOTIONS. Journal of Sound and Vibration, 153(2), 291-310. . Publication link: f4e5a8e5-1dc1-4502-b62c-3bfa6156b06d

1991

  • Abrahams, I. D., & Wickham, G. R. (1991). THE SCATTERING OF WATER-WAVES BY 2 SEMI-INFINITE OPPOSED VERTICAL WALLS. Wave Motion, 14(2), 145-168. . Publication link: 8ad62598-3949-449c-bcc6-6d0e9edab41b
  • Abrahams, I. D., & Engineer, J. C. (1991). A secularity condition for systems of linear partial differential equations. Journal of Sound and Vibration, 150(2), 338-341. . Publication link: 1cd3ea6b-7d65-4973-abe3-59be9cc5e40e

1990

  • Abrahams, I. D., & Wickham, G. R. (1990). General Wiener-Hopf factorization of matrix kernels with exponential phase factors. SIAM Journal on Applied Mathematics, 50(3), 819-838. . Publication link: be1739fb-69f1-4b89-9564-5f2134b9c6ec
  • Abrahams, I. D., & Wickham, G. R. (1990). THE SCATTERING OF SOUND BY 2 SEMI-INFINITE PARALLEL STAGGERED PLATES .2. EVALUATION OF THE VELOCITY POTENTIAL FOR AN INCIDENT PLANE-WAVE AND AN INCIDENT DUCT MODE. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 427(1872), 139-171. . Publication link: d11031dd-7557-4c46-b2b2-e778db01d267
  • Abrahams, I. D., & Wickham, G. R. (1990). ACOUSTIC SCATTERING BY 2 PARALLEL SLIGHTLY STAGGERED RIGID PLATES. Wave Motion, 12(3), 281-297. . Publication link: 9d96cf3d-2e8b-4062-a11a-ad4afa4ac8df

1989

  • Shepard, T. A., Lockwood, G. F., Aarons, L. J., & Abrahams, I. D. (1989). Mean residence time for drugs subject to enterohepatic cycling. Journal of Pharmacokinetics and Biopharmaceutics, 17(3), 327-345. DOI: 10.1007/BF01061900. Publication link: ec2c5691-a0e6-4890-a03a-198fe5b49660
  • Abrahams, I. D. (1989). Scattering of sound by a finite non-linear elastic plate bounding a nearly resonant cavity. Journal of Sound and Vibration, 130(3), 387-404. . Publication link: a70ec548-697f-4ac4-ab62-da7bf7b1df0c
  • Abrahams, I. D., Kriegsmann, G. A., & Reiss, E. L. (1989). ON THE DEVELOPMENT OF CAUSTICS IN SHEAR FLOWS OVER RIGID WALLS. SIAM Journal on Applied Mathematics, 49(6), 1652-1664. . Publication link: f8f52c6d-1f4e-45da-922e-88749b4dbf17

1988

  • Abrahams, I. D. (1988). MATRIX WIENER-HOPF PROBLEMS - REPLY. Journal of Sound and Vibration, 124(3), 584-585. . Publication link: 61db7d71-b973-448a-a145-c0b6a1693eda
  • Abrahams, I. D. (1988). ACOUSTIC SCATTERING BY A FINITE NONLINEAR ELASTIC PLATE .2. COUPLED PRIMARY AND SECONDARY RESONANCES. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 418(1854), 247-260. . Publication link: 7f80c5f7-339d-4563-8331-60516999dc4a
  • Abrahams, I. D., & Wickham, G. R. (1988). ON THE SCATTERING OF SOUND BY 2 SEMI-INFINITE PARALLEL STAGGERED PLATES .1. EXPLICIT MATRIX WIENER-HOPF FACTORIZATION. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 420(1858), 131-156. . Publication link: d0f39ce3-dde6-44c1-8f16-04eee97240f8

1987

  • Abrahams, I. D. (1987). SCATTERING OF SOUND BY 3 SEMI-INFINITE PLANES. Journal of Sound and Vibration, 112(2), 396-398. . Publication link: 1e84768a-1a8a-466b-8bd5-19b4ae176806
  • Abrahams, I. D. (1987). ON THE SOUND FIELD GENERATED BY MEMBRANE SURFACE WAVES ON A WEDGE-SHAPED BOUNDARY.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 411(1840), 239-250. . Publication link: 68d1878c-36c7-4166-8498-52d880430da2
  • Abrahams, I. D. (1987). ACOUSTIC SCATTERING BY A FINITE NONLINEAR ELASTIC PLATE .1. PRIMARY, SECONDARY AND COMBINATION RESONANCES. Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 414(1846), 237-253. . Publication link: 50f7066c-eb96-4e14-b876-0002797c2190
  • Abrahams, I. D. (1987). SCATTERING OF SOUND BY 2 PARALLEL SEMI-INFINITE SCREENS. Wave Motion, 9(4), 289-300. . Publication link: fc528a76-09a3-450c-9287-f81dc6a7beab

1986

  • Abrahams, I. D. (1986). 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. DOI: 10.1093/imamat/37.3.227. Publication link: 95490042-15af-4f30-bc0b-a5365257d4a7
  • Abrahams, I. D. (1986). Diffraction by a semi-infinite membrane in the presence of a vertical barrier. Journal of Sound and Vibration, 111(2), 191-207. . Publication link: 85dff329-585a-4a14-b876-310329e7dccc

1983

  • Abrahams, I. D. (1983). Scattering of sound by an elastic plate with flow. Journal of Sound and Vibration, 89(2), 213-231. . Publication link: 673e3dbd-af70-483f-a4cb-452a125855d4

1982

1981

  • Abrahams, I. D. (1981). SCATTERING OF SOUND BY A HEAVILY LOADED FINITE ELASTIC PLATE.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 378(1772), 89-117. . Publication link: 8fc07e78-d793-489e-9984-dcd29d646695