Former Waves and Field Research Group, LSBU

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 have also designed and developed a Cognitive Tutor, electronic Personal Algebra and Calculus Tutorial to involve students in a Socratic dialogue based on Eulearian sequencing.

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

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

Dr D. Gridin, Dr I. Kamotski, Dr V. Kamotski,Dr V. Kubzin, Ms E. Krylova, Dr A. Nikonov, Dr R. Stacey, Dr D. Zakharov. Dr V. Zalipaev, Dr V. Zernov

• “Asymptotic Description of the Intermediate Field of a Circular   Ultrasonic Transducer”, SBU   Research Scholarship , £25, 000, 1994  (3 months)
•  “Asymptotic Description of the Intermediate Filed of a Circular   Ultrasonic Transducer: Feasibility Study”,   Royal Society Ex-Quota Fellowship for Professor Kiselev, Institute of   Mechanical Engineering, St. Petersburg, £3, 000, 1994 (3 months)
• “Power Laws & Generalised Dimensional Analysis in NDT”, Royal Society Kapitza Fellowship for   Professor Botvina, Institute of Metallurgy, Moscow. Co-investigator:   Professor B. Bridge, £3, 0000, 1995  (3 months)
•  “Dependence of Ultrasonic Attenuation on Inspection Frequency &   Parameters Describing Microstructure   of an Inspected Solid”, Royal Society   Ex-Quota Fellowship for Professor Botvina, Institute of Metallurgy,   Moscow, Co-investigator: Professor B. Bridge, £3, 000 1996  (3 months)
• “Asymptotic Descriptions of Acoustic Fields Scattered by Rough   Cracks: Feasibility Study”, Royal   Society Ex-Quota Fellowship for Professor Borovikov, Institute for   Problems in Mechanics, Moscow, £3, 000, 1998 (3 months) 
• “Mathematical Modelling of Ultrasonic NDT in the Intermediate   Frequency Range'', EPSRC.   Co-investigator: Dr J.Weight, City University, Industrial collaborators: TWI,   AEA Technology, Mitsui Babcock Energy Ltd. , £114,000,  1997-2000 (36 months), IGR – tending to outstanding,
• “Boundary element methods for modelling of scatter of ultrasonic   waves from rectangular cracks situated in the near field of a circular   transducer: Analytical considerations”,   Royal Society Ex-Quota Fellowship for Dr. N. Glushkova, Kuban State   University, Krasnodar, £3, 000, 1998 (1 month)
• “Boundary element methods for modelling of scatter of ultrasonic   waves from rectangular cracks situated in the near field of a circular   transducer: Numerical experiments'',   The London Mathematical Society Grant for Professor E. Glushkov, Kuban State University. , £1, 000, 1998 (1 month)
• “Application of High-Frequency Diffraction Theory to Modelling   Scatter of Elastic Waves from a Cylindrical Side-Drilled Hole: Feasibility   Study'', London Mathematical Society   Grant for Professor V.S. Buldyrev, St. Petersburg University , £1, 000, 1998 (1 months)
•  “Mathematical modelling of ultrasonic wave propagation in a   transversely isotropic elastic half-space'', EPSRC. Industrial collaborator: Mitsui Babcock Energy Ltd. , £173, 000, 1999-2002 (36 months) IGR – tending to outstanding,
• “Diffraction Coefficients for Tilted Surface-Breaking:   Feasibility Study”, British Energy   Generation Ltd. (on behalf of IMC)., £31, 000, 2000 (1 month)
• “Wave Propagation in Viscoelastic Media: Feasibility Study”, LMS Fellowship for Professor Buldyrev, St. Petersburg., £1, 000, 2000  (1 month)

• “Mathematical Modelling of Surface-Breaking Cracks”, EPSRC Visiting Fellowships for   Professor V.M. Babich & Dr B.A. Samokish, St. Petersburg.  £4,000, 2001-2002 (12 months) IGR –  tending to outstanding
• “Ultrasonic Modelling of Cracks with Rough Edges”, EPSRC Visiting Fellowship for Professor   Borovikov. Academic collaborators: Dr J.A. Hudson & Dr M. Spivack,   DAMTP, University of Cambridge. Industrial Collaborator: British Energy   Generation Ltd. , £70, 157,  2001-2004,  IGR – to outstanding
• “Mathematical Modelling of   Angled-Beam Ultrasonic Transducers”, EPSRC. Co-investigator: Prof Grattan,   City University, Industrial collaborators: TWI, Serco, British Energy Generation Ltd. , £184,776, 2002-2003, IGR –  tending to outstanding
• “Interaction of Elastic & Thermo-Elastic Fields with Dynamic   cracks”, EPSRC, £40,582, 2001-2002 (6 months) IGR - tending to outstanding
• “Diffraction Coefficients for Tilted Surface-Breaking Cracks”, British Energy Generation Ltd. (on behalf  of IMC)., £27, 000, 2003  (3 months) 
• “Diffraction Coefficients for a Semi-Infinite Planar Crack   Situated between Two Transversely-Isotropic Half-Spaces”, EPSRC Visiting   Fellowships for Professors Borovikov & Gautesen, £47, 000, 2004 (3 months) 
• “Caustic regions in the field scattered by an embedded elliptic   crack”, British Energy Generation Ltd, £15, 000, 2004  (10 months) 
• “The Theoretical Aspects of Crack Propagation in PMMA”, Leverhume Trust Fellowship for Dr G. Mishuris, £22, 000, 2004 - 2007
•  “An Agent based software   system for 3D Ultrasonic inspection with quantifed capability” , EPSRC   (via the UK Research Centre for NDE Academic collaborators: Professor A. McNabb, Strathclyde Universit, IIndustrial Collaborators: BNFL, Rolls-Royce,  £400, 000, 2005 - 2006
• “Diffraction Coefficients for Plane Cracks in   Transversely-Isotropic Media”, CEA (the   French Atomic Energy Authority), £12, 000, 2005 – 2006
• “Nano-imaging & mechanical testing of soft materials – Basic Technology Proof of Concept”, EPSRC. Academic collaborators: Professor Alford, LSBU (moving to   Imperial); Professor Terentjev, University of Cambridge,  £100, 000, 2005-2006.
• “Development of Ultrasonic Guided Wave Inspection Technology For   the Condition Monitoring of Offshore Structures”,  £70, 000, 2006 - 2009, Co-I on STREP EU project. (total value of project – 1.5 M Euro.)

• L. R. Botvina. L. Ju. Fradkin &   B. Bridge, Power Laws & Generalised Dimensional Analysis in the Ultrasonic NDE. Non-Destructive Testing & Evaluation, 12, 103-118, 1995.
• L. Ju. Fradkin & A. P. Kiselev The two-component representation of time-harmonic elastic body waves. J. Acoust. Soc. Am., 101(1), 52-65, 1997. 
• L. Ju. Fradkin, A. P. Kiselev & E. Krylova The Radiating Near Field Asymptotics of a Time-Harmonic Circular Ultrasonic Transducer. J. Acoust. Soc. Am., 104(3), 1178-1187, 1998.
• D. Gridin & L. Ju. 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, 1998.
•  L. R .Botvina, L. Ju. Fradkin & B. Bridge A new method for assessing mean grain size in polycrystalline materials using ultrasonic NDE. J. Mater. Sci. , 35(18), 4673-4683, 2000.
• D. Gridin  & 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, 2001
•  L.J. Fradkin, V. Zalipaev & D. Gridin  Mathematical Modelling of NDT, J. Appl. Math. & Decision Sci, 5(3), 165 -180, 2001
•  E. Terentjev,  I. Kamotski, D. Zakharov & L. Fradkin,  Propagation of acoustic waves in nematic elastomers, Physice Lett E., 66, 052701(R), 2002
• L. Ju.  Fradkin, I. Kamotski E. Terentjev & D. Zakharov Low frequency acoustic waves in nematic elastomers, Low frequency acoustic waves in nematic elastomers, Proc. Roy. Soc. A , 459, 2627-2642, 2003. 
• V. M. Babich, V. A. Borovikov, L. Ju. Fradkin, V.Kamotski & B.A. Samokish Ultrasonic modelling of tilted surface-breaking cracks, J. NDT & E Int, 37(2), 105-110, 2004
• L. Fradkin, V. Mishakin & N. Alford  Redirection of slow cracks in PMMA, Philosophical Magazine, 85(21), 2345-2362, 2005
• V. Kamotski, L. Fradkin, B.A. Samokish,  V.A. Borovikov & V.M. Babich  On Budaev & Bogy’s approach to diffraction by a 2D traction-free elastic wedge, SIAM J Appl. Maths., 67(1), 235-259, 2006 .
• R. Chapman,   J. Pearce, S. Burch, L. Fradkin & M. Toft, Recent in-house developments in theoretical modelling of ultrasonic inspection, Insight, 93-97, 2006
• A. Dobroskok, L. Fradkin, A. Linkov, G. Mishuris  Crack redirection with thermal secondary loading, Engineering Fracture Mechanics, 74, 1917-1926, 2007.
• A. Gautesen, V. Zernov and L. Fradkin, Diffraction coefficients of a semi-infinite planar crack embedded in a transversely isotropic space, Wave Motion, 46(10), 29 - 46, 2009.
• V. Kubzina, A. Gautesen and L. Fradkin, Diffraction by a semiinfinite interfacial crack sandwiched between two isotropic half planes, SIAM J Appl. Maths, 69 (5), 1309-1333, 2009.
• V A Borovikov & L Ju Fradkin Mathematical modeling of scatter of elastic waves by a crack with rough edge, Russian J Math Phys, 16(2), 139 – 145, 2009.
• L. Fradkin & R Stacey Scatter of a compressional wave by an elliptic crack in the high-frequency approximation, Ultrasonics,50 (4-5), 5029 – 38, 2010.
• V. Zernov, L. Fradkin and P. Mudge, Guided waves in overlapping grouted plates immersed in water, Ultrasonics, 5(1), 57-64, 2011.
  20.     A. Gautesen and L. Fradkin, Diffraction by a two-dimensional traction free wedge, SIAM J. Appl. Math, 70 (8) pp. 3065-3085, 2011.