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	School of Mathematics University of Manchester I. David Abrahams Beyer Professor of Applied Mathematics

Room 1.15, Lamb Building, tel: +44 (0)161-275-5901, fax: +44 (0)161-275-5819 e-mail: i.d.abrahams@manchester.ac.uk.


Here are some wind-generated nearly planar periodic water waves on the canal in Saltaire. Note the wave pattern caused by water flowing past an inhomogeneity on the canal wall. More piccies: 1 2 3 4 5	Index Research Activity Conferences Publications Other Publications External Activity Academic Links Other Interests Motorcycles	My 1977 Triumph Bonneville T140 V

David Abrahams' principal duties in 2008:

Chair of the 50th British Applied Mathematics Colloquium (University of Manchester)

President of the Institute of Mathematics and its Applications (2008-2009)
(for anyone with plenty of time on his/her hands, here is an interview I gave in IMA's Mathematics Today in December 2007)

Sub-panel Member of Unit of Assessment F21 (Applied Mathematics) for the Research Assessment Exercise

Research Activity

David Abrahams has devoted research effort to the broad area of applied mathematics, and specifically to the theoretical understanding of wave processes, since graduating in 1982 with a PhD in theoretical acoustics. He has published some 90 articles in this period. Abrahams holds the Beyer Chair of Applied Mathematics at the University of Manchester, a position first occupied by Sir Horace Lamb. He has published extensively in the areas of fluid/structural interactions, nondestructive evaluation, fracture mechanics, electromagnetism, water waves and seismology. He has been particularly concerned over the years with the development of existing or new mathematical techniques, and has had a number of successes in this direction, for example with matrix Wiener-Hopf systems. He is also interested in the application of such methods, for example to problems in physics and engineering, including acoustics, Stokes’ flows in ducts, electromagnetic and geophysical wave propagation and scattering, and recently to mathematical finance. Abrahams is enthusiastic about public engagement activities within the applied mathematics community (mainly through IMA and University activities) and gives occasional talks to non-specialists.

Recent Major Conference Organisation

Workshop on Mathematical Aspects of Diffraction by Wedges, Cones and other Canonical Geometries (University of Manchester, 28th June-2nd July 1999). EPSRC funded workshop, co-chaired with Jane B. Lawrie (Brunel University).
42nd British Applied Mathematics Colloquium (UMIST, 25th-28th April 2000). Member of Organising Committee.
IUTAM Symposium 2000/10 on Diffraction and Scattering in Fluid Mechanics and Elasticity(University of Manchester, 16th July-20th July 2000). Chair of international meeting co-organised with Keele University.
5th and 6th Euromech Fluid Mechanics Conferences (Toulouse, 25th-29th August 2003 and Stockholm, 26th-30th June 2006). Member of Organising Committee.
47th British Applied Mathematics Colloquium (University of Liverpool, 4th-7th April 2005). Member of Organising Committee.
Graham Wilks Retirement Meeting (University of Keele, 1st July 2004). Joint chair with Andrew J. Willmott (Proudman Oceanographic Laboratory).
IMA 40th Anniversary Meeting (University of Manchester, 2nd September 2004). Chair.
53rd European Study Group with Industry (University of Manchester, 21st-24th March 2005). Joint chair with David S. Broomhead.
Mathmondes 2 (University of Manchester, June 2006). A two-day Anglo-French workshop jointly chaired with William J. Parnell.
Joint chair with Michael J. Lowe (Imperial College London) of UK section of French Groupe de Recherche (GDR) on Etude de la propagation ultrasonore en milieux non homogenes en vue du controle non destructif (2005--2010). Its function is to organise workshops and large symposia between mathematicians, engineers and industrialists (including bioscientists) in the area of ultrasonic waves in non-destructive evaluation of materials.
50th British Applied Mathematics Colloquium (University of Manchester, March 31st-3rd April 2008). Chair.
7th Euromech Fluid Mechanics Conference (University of Manchester, 14th-18th September 2008). Member of Organising Committee.

Research Publications since 1995

Articles published in 1995:

Abrahams ID, Lawrie JB, On the factorization of a class of Wiener-Hopf kernels, IMA Journal of Applied Mathematics 55, 35-47.
Abrahams ID, Chaotic scattering of sound waves by buckled elastic plates, in Nonlinear Waves in Solids, IUTAM Symposium,eds. J. Wegner and F. Norwood. ASME Book No. AMR137, 41-46.
Abrahams ID, Lawrie JB, Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle I, Proceedings of the Royal Society of London, Series A 451(1943), 657-683.
Zhang B, Abrahams ID, The radiation of sound from a ring-forced cylindrical elastic shell. I: Wiener-Hopf analysis, Proceedings of the Royal Society of London, Series A 450(1938), 89-108.

Articles published in 1996:

Heckl MA, Abrahams ID, Active control of friction-driven oscillations, Journal of Sound and Vibration 193(1), 417-426. (pdf file)
Lawrie JB, Abrahams ID, Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle II, Proceedings of the Royal Society of London, Series A 452(1950), 1649-1677.
Abrahams ID, Radiation and scattering of waves on an elastic half-space; a noncommutative matrix Wiener-Hopf problem, Journal of the Mechanics and Physics of Solids 44(12), 2125-2154. (pdf file)
Abrahams ID, On explicit approximate non-commutative factorization of matrix Wiener-Hopf kernels, Pitman Research Notes in Mathematics, eds. H. Serbest and S. Cloude 361, 41-55.

Articles published in 1997:

Abrahams ID, On the solution of Wiener-Hopf problems involving noncommutative matrix kernel decompositions, SIAM Journal of Applied Mathematics 57(2), 541-567. (pdf file)
Lawrie JB, Abrahams ID, Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle I, IMA Journal of Applied Mathematics 59(1), pp1-23.
{McMillan A, A non-linear friction model for self-excited vibrations, Journal of Sound and Vibration 205(3), 323-335. (pdf file)}

Articles published in 1998:

Abrahams ID, On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type, Proceedings of the Royal Society of London, Series A 454(1974), 1719-1743. (pdf file)
Lawrie JB, Abrahams ID, Applications of a general orthogonality relation to acoustic scattering in ducts with high order boundary conditions, Proceedings of Day on Diffraction 98, St Petersburg, 6-19.

Articles published in 1999:

Abrahams ID, Sound radiation from a line forced perforated elastic sandwich panel, Journal of the Acoustical Society of America 105(6), 3009-3020. (pdf file)
Lawrie JB, Abrahams ID, An orthogonality condition 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. (pdf file)

Articles published in 2000:

Norris AN, Krylov VV, Abrahams ID, 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. (pdf file)
Heckl MA, Abrahams ID, Curve squeal of train wheels: mathematical model for its generation, Journal of Sound and Vibration 229(3), 669-693. (pdf file)
Abrahams ID, Norris AN, On the existence of flexural edge waves on submerged elastic plates, Proceedings of the Royal Society of London, Series A 456(1999), 1559-1582. (pdf file)
Abrahams, ID, The application of Pade approximants to Wiener-Hopf factorization, IMA Journal of Applied Mathematics 65, 257-281. (pdf file)

Articles published in 2001:

Abrahams ID, Wickham GR, On transient oscillations of plates in moving fluids, Wave Motion 33(1), 7-24. (pdf file)
Owen, G, Abrahams, ID, Radiation from a transducer into an elastic half-space, in Mechanical and Electromagnetic Waves in Structured Media, IUTAM Symposium, eds. R.C. McPhedran, A.B. Movchan and L.C. Botten, Kluwer Publishing, 73-88.

Articles published in 2002:

Abrahams ID, Davis AMJ, Matrix Wiener-Hopf approximation for a partially clamped plate, in Diffraction and Scattering in Fluid Mechanics and Elasticity, IUTAM Symposium, eds. I.D. Abrahams, P.A. Martin and M.J. Simon, Kluwer Publishing, 303-312.
Thompson I, Abrahams ID, Norris AN, On the existence of flexural edge waves on thin orthotropic plates, Journal of the Acoustical Society of America 112(5), 1756-1765. (pdf file)
Lawrie JB, Abrahams ID, Scattering of fluid-structural waves in a three dimensional duct, in Diffraction and Scattering in Fluid Mechanics and Elasticity, IUTAM Symposium, eds. I.D. Abrahams, P.A. Martin and M.J. Simon, Kluwer Publishing, 279-288.
Owen GW, Abrahams ID, Willmott AJ, Hughes CW, On the scattering of baroclinic Rossby waves by a ridge in a continuously stratified ocean, Journal of Fluid Mechanics 465,131-155. (pdf file)
Abrahams ID, On the application of the Wiener-Hopf technique to problems in dynamic elasticity, Wave Motion 36(4), 311-333. (pdf file)
Abrahams ID, Owen GW, Willmott AJ, The scattering of Rossby waves by ocean ridges, in Diffraction and Scattering in Fluid Mechanics and Elasticity, IUTAM Symposium, eds. I.D. Abrahams, P.A. Martin and M.J. Simon, Kluwer Publishing, 3-12.

Articles published in 2005:

Owen GW, Willmott AJ, Abrahams ID, Mansley H, The scattering of rossby waves from finite abrupt topography, Geophysical and Astrophysical Fluid Dynamics 99(3), 219-239. (pdf file)
Thompson I, Abrahams, ID, Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I - formal solution, Proceedings of the Royal Society of London, Series A 461(2063), 3413-3436. (pdf file)

Articles published in 2006:

Fusai G, Abrahams ID, Sgarra C, An exact analytical solution for discrete barrier options, Finance and Stochastics 10(1), 1-26. (pdf file)
Parnell WJ, Abrahams ID, Dynamic homogenization in periodic fibre reinforced media; quasi-static limit for SH waves, Wave Motion 43(6), 474-498. (pdf file)
Perrey-Debain E, Abrahams ID, A band factorization technique for transition matrix element asymptotics, Computer Physics Communications 175(5), 315-322. (pdf file)
Owen G, Abrahams ID, Elastic wave radiation from a high frequency finite-length transducer, Journal of Sound and Vibration, 298(1-2), 108-131. (pdf file)
Owen GW, Willmott AJ, Abrahams ID, Scattering of barotropic Rossby waves by the Antarctic circumpolar current, Journal of Geophysical Research Oceans 111(C12), Article No. C12024 (14 pages). (pdf file)

Articles published in 2007:

Veitch BH, Abrahams ID, On the commutative factorization of n by n matrix Wiener-Hopf kernels with distinct eigenvalues, Proceedings of the Royal Society of London, Series A 463(2078), 613-639. (pdf file)
Erbas B, Abrahams ID, Scattering of sound waves by an infinite grating composed of rigid plates, Wave Motion 44(4), 282-303. (pdf file)
Thompson I, Abrahams ID, Diffraction of flexural waves by cracks in orthotropic thin elastic plates. II - far field analysis, Proceedings of the Royal Society of London, Series A 463(2082), 1615-1638. (pdf file)
Parnell WJ and Abrahams ID, Multiple Scattering in Periodic and Random Media: An Overview, in Proceedings of 4th Conference of le Groupement de Recherche GDR 2501: 'Etude de la propagation ultrasonore en milieux non homogenes en vue du controle non destructif', eds. M. Deschamps and A. Leger, 8 pages.
Norris AN, Abrahams ID, A multiple-scales approach to crack-front waves, Journal of Engineering Mathematics 59, 399-417. (pdf file)
Green R, Abrahams ID, Pricing financial claims contingent upon an underlying asset monitored at discrete times, Journal of Engineering Mathematics 59, 373-384. (pdf file)
Harter R, Abrahams ID, Simon MJ, The effect of surface tension on trapped modes in water-wave problems, Proceedings of the Royal Society of London, Series A 463(2088), 3131-3149. (pdf file)
Lawrie JB, Abrahams ID, A brief historical perspective of the Wiener-Hopf technique, Journal of Engineering Mathematics 59, 351-358. (pdf file)
Perrey-Debain E, Abrahams ID, A diffusion analysis approach to TE mode propagation in randomly perturbed optical waveguides, SIAM Journal of Applied Mathematics 68(2), 523-543. (pdf file)

Articles published to-date in 2008:

Perrey-Debain E, Abrahams ID, Love JD, A continuous model for mode mixing in graded-index multimode fibres with random imperfections, Proceedings of the Royal Society of London, Series A 464(2092), 987-1007. (pdf file)
Parnell WJ, Abrahams ID, A new integral equation approach to elastodynamic homogenization, Proceedings of the Royal Society of London, Series A, 464(2094), 1461-1482. (pdf file)
Abrahams ID, Davis AMJ, Llewellyn Smith SG, Asymmetric channel divider in Stokes flow, SIAM Journal of Applied Mathematics 68(5), 1439-1463. (pdf file)

Articles in press:

Parnell WJ, Abrahams ID, Homogenization for wave propagation in periodic fibre-reinforced media with complex microstructure. I - Theory, Journal of the Mechanics and Physics of Solids, approximately 27 pages.
Abrahams ID, Davis AMJ, Llewellyn Smith SG, Matrix Wiener-Hopf approximation for a partially clamped plate, Quarterly Journal of Mechanics and Applied Mathematics, approximately 24 pages.

Articles submitted:

Green R, Fusai G, Abrahams ID, The Wiener-Hopf technique and discretely monitored path independent option pricing, submitted to Mathematical Finance, approximately 26 pages.
Parnell WJ, Abrahams ID, The effective elastic properties of a composite half-space, submitted to Quarterly Journal of Mechanics and Applied Mathematics, approximately 26 pages.
Abrahams ID, Kriegsmann GA, Electromagnetic wave propagation in periodic porous structures, submitted to the European Journal of Applied Mathematics, approximately 15 pages.
Harter R, Simon MJ, Abrahams ID, The effect of surface tension on localized free surface oscillations about surface-piercing bodies, submitted to Proceedings of the Royal Society of London, Series A, approximately 16 pages.

Other Recent Publications

Report on the EPSRC Theme Day in Modelling and Simulation in Engineering, Materials and Mathematics, 1998 EPSRC Publication.
EPSRC Mathematics Programme Evaluation Report, 1998 EPSRC Publication.
EPSRC Mathematics Programme Evaluation Report, 1999 EPSRC Publication.
EPSRC Mathematics Programme Evaluation Report, 2000 EPSRC Publication.
Abrahams ID, Martin PA, Norris AN, G. R. Wickham: an appreciation, Wave Motion 33(1), 1-6 (2001). (pdf file)
Abrahams ID, Martin PA, Simon MJ, Proceedings of the IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity, Kluwer Publishing, 2002.

Major External Activities

I have served on the Mathematics College of the Engineering and Physical Sciences Research Council (EPSRC), 1995-2005, and regularly sit on, or chair, various panels for the Mathematical Sciences and other Programmes.
I was recently external examiner for the undergraduate programmes at University College Cork and University of East Anglia. Prior to this I have been UG external examiner at Cambridge University, Bristol University and University College London.
I was a Vice-President (2002-2004) and recent member of Council of the Instutute of Mathematics and Its Applications. I chaired the IMA's Journals Board of Management (1998-2007) which is the steering body for the portfolio of six journals currently published by the Institute, and serve on its Research Committee. I am currently IMA President (2008-2009).
I was member of Council of the London Mathematical Society (2002-2006), sat on its Research Meetings Committee (1999-2007) and Publications Committee (2006-2007), and Chaired the Personnel and Office Management Committee (2004-2006).
I am a member of the Society for Industrial and Applied Mathematics.
I was member of Council of the European Mechanics Society (EUROMECH) (2000-2006).
I serve on UK Panel of the International Union of Theoretical and Applied Mechanics (IUTAM) (1997-).
I have been Treasurer of the North British Differential Equations Seminar Series (NBDES) since 1994.
I am a Member of the Committee of the Conference of Professors of Applied Mathematics (CPAM) (2002-).
I am one of two UK Delegates to the Board of the International Council for Industrial and Applied Mathematics (ICIAM) (2003-).
Member of RAE 2008 Sub-panel UoA21 Applied Mathematics.

Academic Links

Other Interests

Due to force of circumstance I have, in the past, had to enjoy home restoration including woodworking, plumbing and rewiring. For example, I have designed and built several central heating systems over the years. Also, when time allowed, I enjoyed designing and constructing hi-fi and other electronic equipment.

Unfortunately, my current positions allow me very little time for such creative outlets, but I love watching all sports and especially athletics. I have managed to maintain a limited participation in sport; namely through five-a-side football and distance road running.

Italian & British Motorcycles

I have always loved motorcycles, their design and maintenance. I have ridden the same rusty old monster since 1978, an Italian Moto Guzzi 850 T3 (born on the edge of beautiful Lake Como at Mandello del Lario) and it has now reached its 31st birthday. It has a V-twin engine, bored out to 1000cc and weighs a very hefty 550lb. Anyone interested in Moto Guzzis should check out the websites of Moto Guzzi Club GB or the US Moto Guzzi Club for pictures and parts etc.

I have also recently bought a Trumph Bonneville T140V, born in 1977 at the Meriden factory in Coventry. I have always loved British bikes but have unfortunately never owned one before - thanks to the lure of ebay that is now resolved! The 'bonnie' is perhaps the best known and most loved British bike ever made, and my new purchase is an absolute dream to ride (not as fast as the Guzzi but so much more nippy up until around 50mph). The Triumph Owners Motorcycle Club is one of the oldest and biggest motorcycle clubs in the world.

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Last Modified: 2nd May 2008

School of Mathematics

University of Manchester

I. David Abrahams

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