(Ultra)Sound Mathematics Ltd.

Research Projects

Former Research Students and Postdocs

Former Academic Visitors and Collaborators

Publications

Research Interests

The group works on interdisciplinary projects on the applied mathematics-statistics-engineering-physics interface. It is led by Professor Larissa Fradkin whose mathematical interests revolve mainly around non-linear mathematics, inverse problems, Hamiltonian systems, Lagrangian description and asymptotic approximation. Statistical aspects of her work have been concentrated on exploratory data analysis based on the system identification methods for the purposes of mathematical modelling large real-world systems. Her engineering projects have been in thermal combustion, energy generation (geothermal, thermonuclear, nuclear), hydrology and structural integrity (NDE), mainly of nuclear plants, but recent projects are also of importance to safety in rail engineering and (potentially) safety of oil pipelines. In physics Larissa has worked on multi-scale description of geothermal reservoirs, characterisation of parameters of immiscible flows, underwater acoustics, turbulence in Tokamak plasmas, particle tracking, chaotic advection and since she moved to LSBU, propagation and scattering of elastic waves.

The main aim of Waves and Fields Research Group is to develop a new generation of fast and accurate semi-analytical codes for modelling ultrasonic inspection. The work culminated in the group solving a long standing problem of diffraction by an elastic wedge – of interest in both applied mathematics and engineering. The codes developed by the group are now being implemented in various commercial packages.

The group initiated exciting experiments on physics of crack propagation and re-direction in PMMA, got involved in studying acoustics of exciting new materials known as nematics elastomers and now secured a prestigious DTI/EPSRC grant under the Basic Technology – Proof of concept call on Nano-imaging and mechanical testing of soft materials.

We are also designing and developing a Cognitive Tutor, electronic Personal Algebra and Calculus Tutorial to involve students in a Socratic dialogue based on Eulearian sequencing.

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Aspects of Ultrasonic Wave Propagation

Funding body: CEA (The French Atomic Commission)

Grant total: € 75,000

End date: 1 October 2009

Development of Ultrasonic Guided Wave Inspection Technology For the Condition Monitoring of Offshore Structures

Funding body: EU

Academic collaborators: Kaunas University, Lithuania

Industrial collaborators: 10 European companies

Grant total: € 1.5 M, with € 70,000 going to LSBU

End date: 28 February 2009

An Agent Based Software System for D Ultrasonic Inspection with Quantified Capability

Funding body: EPSRC

Industrial collaborators: BNFL Magnox Generation; Mitsui-Babcock Ltd; NDT Soft; Rolls-Royce - Naval Marine

Grant total: £ 211,201

End date: 13 June 2007

Nano-imaging and mechanical testing of soft materials

Funding body: EPSRC

Academic collaborators: Neil Alford, London South Bank University

Grant total: £ 100,000

End date: 30 September 2006

Diffraction coefficients for isotropic and transversely isotropic media

Funding body: CEA (The French Atomic Commission)

Grant total: £ 12,000

End date: 31 October 2006

Theoretical Aspects of Crack Propagation in PMMA

Funding body: Leverhume Trust

Visiting Fellow: Professor G. Mishuris

Grant Total: £ 22,000

End Date: 8 January 2005

An intelligent tutorial in engineering maths

Funding body: EPSRC

Research student: Luis Marcelo

End dare: 30 September 2006

Ultrasonic wave propagation, with application to NDE

Funding body: LSBU

Research student: Victoria Kubzin

End date: 31 July 2007

Mathematical Modelling of Angle Beam Ultrasonic Transducers

Funding body: EPSRC

Industrial Collaborators: British Energy Generation Ltd., AEA

Technology Ltd

Co-Investigator: Professor K.T.V. Gratan, City University

Postdoctoral Research Fellows: Dr Anatoly Nikonov and Dr Dmitry Zakharov

Grant total: £ 125,020

End date: 31 March 2004; duration: 36 months

Caustic regions in the field scattered by an embedded elliptic crack

Funding Body:British Energy Generation Ltd

Grant Total: £15,000

End Date: 31 March 2004

Diffraction coefficients of a semi-infinite planar crack situated between two transversely-isotropic half-spaces

Funding body: EPSRC

Visiting Fellows: Professor V A Borovikov and Professor A. Gautesen

Grant total: ? 44,690

End date: 1 December 2003, duration: 3 months

Interaction between the tip of dynamic crack and elastic and thermo-elastic fields

Funding body: EPSRC

Postdoctoral Research Fellow: Vassili Mishakin

The grant total: £43,000

End date: 31 March 2003 Duration: 12 months

Mathematical Modelling of Ultrasonic Inspection of Cracks with Rough Edges

Funding body: EPSRC

Co-Investigators: Dr J A Hudson, Dr M Spivack, Cambridge University;

Visiting Fellow: Professor V A Borovikov

Grant total: £ 36, 939

End date: 1 July 2002, duration: 12 months

Mathematical Modelling of Ultrasonic Wave Propagation in a Transversely

Isotropic Elastic Half-Space

Funding body: EPSRC

Industrial collaborator: Mitsui Babcock Energy Ltd.

Consultant: Prof V A Borovikov

Postdoctoral Research Fellows: Dr Dmitri Gridin, Dr Dmitry Zakharov and Dr Ilia Kamotski

Grant total: £ 176, 276

End date: 31 March 2002, duration: 36 months

Diffraction Coefficients for Tilted Surface-Breaking Cracks

Funding body: IMC

Research Fellows: Professor V.M. Babich, Professor V.A. Borovikov,

Dr V. Kamotski, Dr B.A. Samokish

Duration: 6 months, End date: 31 March 2002

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Dr D. Gridin

Dr I. Kamotski

Dr V. Kubzin

Ms E. Krylova

Dr V. Mishakin

Dr A. Nikonov

Dr R. Stacey

Dr D. Zakharov

Dr V. Zalipaev

Dr V. Zernov

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Professor V.M. Babich, Steklov Mathematical Institute, St. Petersburg, Russia

Professor V.A. Borovikov, Institute for Problems in Mechanics. Moscow, Russia

Professor L.R. Botvina, Institute of Metallurgy, Academy of Sciences, Russia

Professor V.S. Buldyrev, Physics Department, St. Petersburg State University, Russia

Professor Art Gautesen, Mathematics Department, Iowa State University, USA

Professor K.T.V. Grattan, Electrical, Electronic and Information Engnng, Dept., City University

Professor E. Glushkov, Kuban State University, Russia

Dr N. Glushkov, Kuban State University, Russia

Dr J. Hudson, DAMTP, Cambridge University

Dr V. Kamotski, University of Bath, U.K.

Professor A.P. Kiselev, Steklov Mathematical Institute, St. Petersburg, Russia

Professor G. Mishuris, Rzeszow University of Technology, Poland

Dr B.A. Samokish, Department of Mathematics and Mechanics, St. Petersburg, Russia

Dr B.Singh, Department of Mathematics, Government College, Sector 11, Chandigarh, India

Dr M. Spivak, DAMTP, Cambridge University

Professor. E. Terentjev, Cavendish Laboratory, Cambridge University

Dr J. Weight, Electrical, Electronic and Information Engnng, Dept., City University

Ms S. Zehraoui, University of Bordeaux, France

Mr S. Rascle, University of Bordeaux, France

Ms G Pancher, University of Bordeaux, France

Ms A. Coradi, University of Bordeaux, France

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2009

1. V. Kubzin, A. Gautesen and L. Fradkin, Diffraction by interfacial cracks, SIAM J Appl. Math., 69 (5), 1309-1333.

2. A. Gautesen, V. Zernov and L. Fradkin, Diffraction coefficients of a semi-infinite planar crack embedded in a transversely-isotropic medium, by interfacial cracks, Wave Motion, 46(10), 29 - 46.

3. V. Borovikov and L. Fradkin, "Scatter of a plane elastic wave by a rough crack edge" Russian Journal of Mathematical Physics, 16(2), 166-187

4. J. Kaplunov, A. Pichugin and V. Zernov “Extensional edge modes in elastic plates and shells”, Journal of the Acoustical Society of America, 125(2), 621–623.

2007

1. A. Dobroskok, L. Fradkin, A. Linkov and G. Mishuris, Crack redirection with thermal secondary loading, Engineering Fracture Mechanics, 74, 1917-1926.

2. R. Chapman, J. Pearce, S. Burch, L. Fradkin and M.Toft, Recent in-house developments in theoretical modelling of ultrasonic inspection, Insight, 93-97.

3. V. Zernov and J. Kaplunov, Three dimensional edge waves in plates, Proceedings of the Royal Society A., 464, 301--318.

2006

1. A. Gautesen, V. Zernov and L. Fradkin, Diffraction coefficients of a semi-infinite planar crack embedded in a transversely-isotropic medium, by interfacial cracks,. Rev. Prog. QNDE 26A, 595--602.

2. V. Zernov, J. Kaplunov and A. Pichugin, Eigenvalue of a semi-infinite elastic strip, Proceedings of the Royal Society A., 462, 1255--1270.

3. R. Chapman, J. Pearce, S. Burch, L. Fradkin and M.Toft, Recent in-house developments in theoretical modelling of ultrasonic inspection, Insight, 93-97.

4. V. Kamotski, L. Fradkin, V.M. Babich, V.A. Borovikov and B.A.Samokish, The diffraction of a plane wave by a 2D traction free isotropic wedge, Mathematical Modelling of Wave Phenomena, AIP Conference Proceedings, edited by B. Nilsson and L. Fishman, pp. 165--174.

5. V. Kamotski, L. Fradkin, V.M. Babich, V.A. Borovikov and B.A.Samokish, On Budaev and Bogy’s approach to diffraction by 2D traction-free elastic wedge, SIAM J Appl. Math, 67(1), 235-259.

6. D.D. Zakharov, High Order Approximate Dynamic Theory of Elastic Anisotropic Lining and Coating, J. Acoust. Soc. Am., 119(4), 1961--1970.

2005

1. L. Fradkin, V. Mishakin and N. Alford, Redirection of slow cracks in PMMA, Philosophical Magazine, 85 (21), 2345--2362.

2. D.D. Zakharov and A.V. Nikonov, Approximate Description of the Dynamic of Thin Isotropic Elastic Coatings and Interlayers by Using Asymptotics of High Order of Accuracy, Mechanics of Composite Materials, 41(6), 528--534.

3. D.D. Zakharov, Approximate high-order dynamic theory of a fluid layer in between two thick solids, J. Acoust. Soc. Am., 117(2), 518--527.

2004

1. A. Gautesen, V. Kubzin and L. Fradkin 2004 Modelling Scatter from 2D interfacial crack, Rev. Prog. QNDE 24A, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York.

2. D.D. Zakharov, Edge localized bending waves in anisotropic media: energy and dispersion, in: Surface waves in anisotropic laminated bodies and defects detection (Eds. R.V. Goldstein and G.A. Maugin), 173—186, Netherlands: Kluwer publ.

3. D.D. Zakharov, Analysis of the acoustical edge flexural mode in a plate using refined asymptotics, J. Acoust. Soc. Am., 116(2), 872—878.

4. D.D. Zakharov, Approximate high order dynamic theory of a fluid layer in between two thick solids, J. Acoust. Soc. Am., 117(2), 518—527.

2003

1. I. Kamotski, D. Zakharov, E. Terentjev and L. Fradkin, Propagation of acoustic waves in nematic elastomers, Physics Lett E.,66, 052701®.

2. L. Ju. Fradkin, I. Kamotski, E. Terentjev, and D. Zakharov, Low frequency acoustic waves in nematic elastomers, Proc. Roy. Soc. A ., 459, 2627-2642.

3. D. Gridin, The high-frequency description of the qP transducer radiating into the transversely isotropic half-space, J. Acoust. Soc., 114(2), 583-590.

4. V.M. Babich, V.A. Borovikov, L.Ju. Fradkin, D., V. Kamotski and B.A.Samokish, Ultrasonic modelling of tilted surface-breaking cracks, J. NDT & E Int, 37(2),105-110.

5. L. Fradkin, Recent Developments in the High-Frequency Modelling of Ultrasonic Inspection of Industrial Materials. In Recent Research Developments in Acoustics (Transworld Research Network), 205-228.

2002

1. V.M. Babich, V.A. Borovikov, L.Ju. Fradkin, V. Kamotski and B.A.Samokish, Ultrasonic modelling of tilted surface - breaking cracks, Proc. Rail Engineering Conference, London.

2. V.A. Borovikov and L.Ju.Fradkin , Scattering by a rough crack edge, Rev. Prog. QNDE 22, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York.

3. L. Fradkin, V. Kamotski, V.M. Babich, V.A. Borovikov and B.A. Samokish, Diffraction Coefficients for tilted surface- breaking cracks, Proc. NDT Conference, Southport, U.K.

4. Zakharov, D.D. Konenkov’s waves in anisotropic layered plates, Acoust. Physics, 48(2),171—175.

2001

1. L..J. Fradkin, V. Zalipaev and D. Gridin, Mathematical Modelling of NDT, J. Appl. Math. and Decision Sci, 5(3), 165-180.

2. D. Gridin and L.Ju. Fradkin, The complete far-field asymptotic description of a point source acting on a transversely isotropic half-space, Proc. R. Soc. Lond. A, 457, 2675-2698.

3. D. Gridin and L.Ju. Fradkin, Modelling Point-Source and Transducer Wave-Fields in Transversely Isotropic Half-Space, Rev. Prog.QNDE 21B, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York, 2001., 831-838.

4. V.A. Borovikov and D. Gridin, Kiss singularities of Green's functions of non-strictly hyperbolic equations, Proc. R. Soc. Lond. A, 457, 1059-1077.

5. V.A. Borovikov and D. Gridin, Kiss singularities of Green's functions of non-strictly hyperbolic equations, to appear in Diffraction and Scattering in Fluid Mechanics and Elasticity, eds. ID Abrahams, CJ Chapman, PA Martin, MJ Simon, AJ Willmott (Kluwer, New York).

2000

1. L. Botvina, L. Ju. Fradkin, and B. Bridge A new method for assessing mean grain size in polycrystalline materials using ultrasonic NDE. J. Mater. Sci. , 35(18), 4673-4683.

2. L. Ju. Fradkin. and V.A. Borovikov, Scatter of a toroidal wave by a plane. Rev. Prog. QNDE 19, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York, 81-88.

3. V.M. Babich, V.A. Borovikov., L. Ju. Fradkin., D. Gridin, V. Kamotski and V.M. Smyshlyaev, Diffraction coefficients for tilted surface-breaking cracks. IUTAM Symposium on Wave Diffraction and Scattering in Fluid Dynamics and Elasticity, Manchester.

4. D. Gridin,. Far-field asymptotics of the Green's tensor for a transversely isotropic solid, Proceedings of the Royal Society of London A456, 571-591.

5. D Gridin , Far-field of a point source in a transversely isotropic elastic solid, Rev. Prog. QNDE 19, eds. DO Thompson and DE Chimenti (American Institute of Physics, New York), 169-176.

1999

1. L. Ju. Fradkin., L. R. Botvina. and B. Bridge, Ultrasonic interaction of polycrystalline materials. Rev. Prog. QNDE 18, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York.

2. D. Gridin and L. Ju. Fradkin, The radiating near field of an ultrasonic transducer directly coupled to an isotropic solid half-space. Rev. Prog.QNDE 18, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York.

3. L. Ju. Fradkin and V. Zalipaev, Scatter by elastic cracks. Rev. Prog. QNDE 19, edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New-York, 41-48.

4. L. Ju. Fradkin, V. Zalipaev and D. Gridin, New models of propagation and scatter of ultrasound. Proc. Joint National Conference NDT'99 & UK Corrosion '99, Poole, Dorset, U.K.

5. D. Gridin, The radiating near field of a circular normal transducer of arbitrary apodization on an elastic half-space, J. Acoust. Soc. Am. 106(3), 1237-1246.

6. D. Gridin, On the radiation of ultrasound into an isotropic elastic half-space via wave-front expansions of the impulse response, J. Acoust. Soc. Am105(5), 2565-2573.

1998

1. L. Fradkin, A. P. Kiselev and E. Krylova The Radiating Near Field Asymptotics of a Time-Harmonic Circular Ultrasonic Transducer. J. Acoust. Soc. Am., 104(3), 1178-1187.

2. D. Gridin and L. Fradkin High-Frequency Asymptotic Description of Pulses Radiated by a Circular Normal Transducer into an Elastic Half-Space. J. Acoust. Soc. Am., 104(6), 3190-3198.

3. L.Ju. Fradkin, A.P. Kiselev, D. Gridin and E. Krylova, The radiating near field of a compressional circular transducer. Non-Destructive Testing: An Eastern-Western Perspective, edited by B. Bridge, A. Khalid and B. Yochev, British Institute of NDT, Northampton, 129-152.

4. D. Gridin, A fast method for simulating the propagation of pulses radiated by a rectangular normal transducer into anelastic half-space, J. Acoust. Soc. Am. 104(6), 3199-3211.

5. D. Gridin, High-frequency asymptotic description of head waves and boundary layers surrounding the critical rays in an elastic half-space, J. Acoust. Soc. Am. 104(3), 1188-1197.

1997

1. L. Ju. Fradkin and A. R. Osborne, A new model for fluid parcel motions in large and meso-scale flows, in Stochastic Models in Geosystems (Eds. S. A. Molchanov and W.A. Woyczynski), Springer-Verlag), 83-96.

2. L. Ju. Fradkin and A. P. Kiselev, The two-component representation of time-harmonic elastic body waves. J. Acoust. Soc. Am., 101(1), 52-65.

1995

1. L.R. Botvina. L. Fradkin, and B. Bridge, Power Laws and Generalised Dimensional Analysis in the Ultrasonic NDE. Non-Destructive Testing and Evaluation, 12, 103-118.

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