## School of Mathematics## University of Manchester## I. David AbrahamsBeyer Professor of Applied Mathematics |

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: 12345 |
## IndexResearch ActivityConferences Publications Other Publications External Activity Academic Links Other Interests Motorcycles |
My 1977 Triumph Bonneville T140 V |

(for anyone with plenty of time on his/her hands, here is an interview I gave in IMA's Mathematics Today in December 2007)

**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.

- 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.

- 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.

- 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)}

- 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.

- 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)

- 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)

- 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.

- 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.

- 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)

- 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)

- 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)

- 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)

- 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.

- 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.

- 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.

- 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.

- Department of Mathematics and Statistics, Brunel University
- Department of Mechanical and Aerospace Engineering, Rutgers University NJ, USA
- Department of Mathematics, New Jersey Institute of Technology, Newark NJ, USA
- Department of Mathematics, University of Alabama, Tuscaloosa AL, USA
- Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston IL, USA
- Institute of Mathematics and Its Applications
- London Mathematical Society
- Society for Industrial and Applied Mathematics, USA
- Acoustical Society of America, USA
- European Mechanics Society
- International Union of theoretical and Applied Mechanics

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.

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; Cursory update: 19th Jan 2011.