References

Operator Algebras

M. Spivack, Derivations on von Neumann Algebras, M.Sc dissertation, University of Manchester 1980.
M. Spivack, Derivations on Operator Algebras, Ph.D thesis, University of Manchester 1982.
M. Spivack, Certain properties of derivations on operator algebras, Proc. Amer. Math. Soc. 99 (1987) 712-718.
M. Spivack, Derivations and nest algebras on Banach space, Israel J. Math. 50 (1985) 193-200.
M. Spivack, Derivations on commutative operator algebras, Bull. Australian Math. Soc. 32 (1985) 415-418.
M. Spivack, Contractive projections on Banach space, Bull. Australian Math. Soc. 34 (1986) 271-274.

Elastic Waves, Simple Boundaries

A. Ilan, L. Bond & M. Spivack, Interaction of a compressional impulse with a slot normal to the surface of an elastic half-space, Geophys. J. Roy. Astr. Soc. 57 (1979) 463-477.
M. Spivack, Finite difference scheme for fluids with simple boundaries, City University Physics Dept. Research Report 1978.
M. Spivack, Two new algorithms for the pipe-break problem, Reading University Numerical Analysis Report, 1984.

Ribbed Membranes with Fluid Loading: Periodic & Disordered

M. Spivack, Wave propagation in finite periodically ribbed structures with fluid loading,   Proc. Roy. Soc. Lond. A 435 (1991) 615-634.
M. Spivack & P.E. Barbone, Disorder and localization in ribbed structures with fluid loading   Proc. R. Soc. Lond. A 444 (1994) 73-89.
M. Spivack, Wave scattering in ribbed membranes and irregular layers, Proceedings of P.I.C.S., Laboratoire de Mécanique et d'Acoustique, Marseille 1994 (ISSN 0750-7356).
M. Spivack & P.E. Barbone, Order and disorder in ribbed membranes with fluid loading J. Acoust. Soc. Am. 95 Pt 2 (127th Meeting of the ASA) (1994) 2847.
P.D. Cook & M. Spivack, Wave propagation along a ribbed fluid-loaded membrane, J. Acoust. Soc. Am. 100 4 (1996) 2723.

Random Media and Moment Equations

B. J. Uscinski, C. Macaskill & M. Spivack, Path integrals for wave intensity fluctuations in random media,   J. Sound and Vib. 106 (1986) 509-528.
M. Spivack, Numerical simulation of wave propagation in random media,   Proceedings AGARD Conference on Electromagnetic Wave Propagation, Rome 1987.
M. Spivack & B. J. Uscinski, Numerical solution of the fourth moment equation for very large values of gamma,   J. Modern Optics 35 (1988) 1741-1755.
M. Spivack & B. J. Uscinski, Split-step solution for wave propagation in random media, J. Comp. Applied Math. 27 (1989) 349-361.
M. Spivack, Accuracy of the moments from simulation of wave propagation in random media,   J. Opt. Soc. Am. A 7 (1990) 790-793.
D. Reeve, S. Leonard, & M. Spivack, Solution of the fourth moment equation for a point source,   J. Modern Optics 37 (1990) 965-975.
M. Spivack, Operator splitting for the random wave moment equations,   Applied Math. Lett. 3 (1990) 87-91.
D.E. Reeve & M. Spivack, Numerical solution of the second moment equation for waves in an inhomogeneous waveguide,   J. Mod. Opt. 39 (1992) 1343-1352.
BJ Uscinski & M Spivack, High intensity ribbons in multiply scattering media,   Waves in Random and Complex Media 15 (2005) 339-352.

Rough Surface Scattering and Waveguides

M. Spivack, Numerical approach to rough surface scattering for the parabolic equation, J. Acoust. Soc. Am. 87 (1990) 1999-2004.
M. Spivack & B.J. Uscinski, Scattering from a rough surface in a medium with a linear profile   Proceedings Conference on Atmospheric, Volume & Surface Scattering Florence, 1991.
M. Spivack, Moments of wave scattering by a rough surface,   J. Acoust. Soc. Am. 88 (1990) 2361-2366.
M. Spivack & B.J. Uscinski, Numerical solution of scattering from a hard surface in a medium with a linear profile,   J. Acoust. Soc. Am. 93 (1993) 249-254.
M. Spivack, Coherent field and specular reflection at grazing incidence on rough surface   J. Acoust. Soc. Am. 95 (1994) 694-700.
M. Spivack, Moments and angular distribution for wave scattering at low grazing angles from a rough surface Proceedings of 2nd European Conference on Underwater Acoustics Denmark 1994, 285-290.
M. Spivack & J.D. Sheard, Wave scattering in an irregular layer adjoining a fluid half-space, Proceedings of 2nd European Conference on Underwater Acoustics Denmark 1994, 213-218.
M. Spivack, Forward and inverse scattering from rough surfaces at low grazing incidence J. Acoust. Soc. Am. 95 Pt 2 (127th Meeting of the ASA) (1994) 3019.
M. Spivack, Moments and angular spectrum for rough surface scattering at grazing incidence   J. Acoust. Soc. Am. 97 (1995) 745-753.
J.D. Sheard & M. Spivack,Wave scattering in rough elastic layer adjoining a fluid half-space, J. Acoust. Soc. Am. 97 (1995) 72-83.
M. Spivack, Integral equation methods for wave propagation over rough surfaces, (1996) IEE Colloquium on Modelling Techniques for Electromagnetic and Acoustic Wave Propagation (London, March 1996).
P.E. Barbone & M. Spivack, Low grazing angle scattering from a rough ocean floor J. Acoust. Soc. Am. 99 (1996) 2475.
M. Spivack, Sound propagation in an irregular two-dimensional waveguide, J. Acoust. Soc. Am. 101 (1997) 1250-1255.
M. Spivack, A. Keen, J. Ogilvy & C. Sillence, Validation of left-right method for scattering by a rough surface, J Modern Optics 48 (2001) 1021-1033.
Y. Hatziioannou & M. Spivack, Electromagnetic scattering by refractive index variations over a rough conducting surface, J Modern Optics 48 (2001) 1151-1160.
M. Spivack, Scattering by a finite rough plate, Aerotecnica, Missili e Spazio 79, N3-4 (2000).
M. Spivack, J. Ogilvy & C. Sillence, Electromagnetic propagation in a curved 2-dimensional waveguide, Waves in Random Media 12 (2002) 47-62.
M Spivack, J Ogilvy, & C Sillence, Electromagnetic scattering by large complex scatterers in 3D, IEE Proc Science, Measurement & Tech 151 (2004) 464-466.
M Spivack, J Ogilvy, & C Sillence, Left-right splitting for electromagnetic scattering in 3D, IEE Proc Computational Electromagnetics 2004 (CEM04), Stratford-upon-Avon.
M Spivack, `Electromagnetic signature analysis in defence applications', SPIE - Proceedings Great Lakes Photonics Symposium, June 2004.
M Spivack & O Rath Spivack, Sound propagation over arbitrary surfaces with varying impedance, International Congress on Sound and Vibration (ICSV13) July 2006, Vienna.
O Rath Spivack & M Spivack, Fast boundary integral solution for acoustic scattering by large objects, International Congress on Sound and Vibration (ICSV13) July 2006, Vienna.
O Rath Spivack & M Spivack, Efficient boundary integral solution for acoustic wave scattering by irregular surfaces, arXiv:1407.5560, 2014.
M Spivack & O Rath Spivack, Rough surface backscatter and statistics via extended parabolic integral equation , arXiv:1408.1879, 2014.
M Spivack & O Rath Spivack, Rough surface scattering via two-way parabolic integral equation, Progress in Electromagnetics Research M 56 (2017) 81-90.
M Spivack & O Rath Spivack, Statistical moments for rough surface scatter from two-way parabolic integral equation at low grazing angles, J. Modern Optics 64 (2017) 1768-1776.
O Rath Spivack & M Spivack, Efficient boundary integral solution for acoustic wave scattering by irregular surfaces, Engineering Analysis with Boundary Elements 83 (2017) 275-280.

Inverse Problems: Rough Surfaces and Inhomogeneous Media

M. Spivack, Direct solution of the inverse problem for rough surface scattering at grazing incidence,   J. Phys. A: Math. & Gen. 25 (1992) 3295-3302.
M. Spivack, Solution of the inverse scattering problem for grazing incidence on a rough surface   J. Opt. Soc. Am. A 9 (1992) 1352-1355.
M. Spivack, Direct solution of the inverse scattering problem for a rough surface   Proceedings of IUTAM Symposium on Inverse Problems Tokyo 1992 (Springer).
M. Spivack & D. Waymont, Rough surface scattering and the inverse problem at low grazing angles, Proc. IOA Conf. on Underwater Acoustic Scattering, IOA London (1994) 37-43.
Y. Chen & M. Spivack Rough surface reconstruction by the iterated parabolic equation (submitted to Progress in Electromagnetics Research), 2017.

Inverse Problems: Coastal Morphology

D.E. Reeve & M. Spivack, Determination of a source term in the linear diffusion equation   Inverse Problems 10 (1994) 1335-1344.
D.E. Reeve & M. Spivack, Inverse methods in a coastal morphology Proc ICCE Sydney (2000).
M. Spivack & D.E. Reeve, Recovery of variable coefficient in a coastal evolution equation, J. Comp. Phys. 151 (1999) 585-596.
M. Spivack & D.E. Reeve, Source reconstruction in a coastal evolution equation J. Comp. Phys. 161 (2000) 169-181.
D E Reeve & M Spivack, Evolution of shoreline position moments, Coastal Engineering 51 (2004) 661-673.
D E Reeve & M Spivack, Prediction of long-term coastal evolution using moment equations, Proceedings, Coastal Dynamics 2001, Lund, Sweden, 723-732, 2001.
D E Reeve & M Spivack, Source reconstruction for a coastal evolution equation, Proceedings of the MEDCOAST99-EMECS 99 Joint Conference: Land-ocean Interactions - Managing coastal ecosystems, 9-13 November 1999, Antalya, Turkey, MEDCOAST, (Ed. E. Ozhan), p1701-1710, 1999.
D E Reeve & M Spivack, Stochastic prediction of long-term coastal evolution, Coastal Engineering V: Computer Modelling of Seas and Coastal Regions, Rhodes, 55-63, 2001.
M Spivack & D E Reeve, A stochastic model for shoreline evolution, Proceedings 28th ICCE, July 2002, Cardiff, (Ed. J. McKee Smith), World Scientific, p3433-3437
H Karunarathna, D E Reeve & M Spivack, Long-term morphodynamic evolution of estuaries: an inverse problem, Estuarine, Coastal and Shelf Science 77 (2008) 385-395.
H Karunarathna, D E Reeve & M Spivack, Beach profile evolution as an inverse problem, Continental Shelf Research 29 (2009) 2234-2239.
H Karunarathna, J M Horrillo-Caraballo, M Spivack & D E Reeve, Analysis of key parameters in a diffusion type beach profile evolution model Continental Shelf Research 31 (2011) 98-107.
D E Reeve, A Pedrozo-Acuna & M Spivack, Beach memory and ensemble prediction of shoreline evolution near a groyne Coastal Engineering 86 (2014) 77-87.

Visualisation, eScience and Grid

M Spivack, A Usher, X Yang, & M Hayes, Visualisation and grid applications of electromagetic scattering from aircraft, Proceedings AHM03, Nottingham, ISBN.
X Yang, M Hayes, A Usher & M Spivack, Developing web services in a computational grid environment, (2004) Proceedings IEEE Int'l Conference on Services Computing, Shanghai 2004.

Selected Reports

M. Spivack, Close-to-Grazing Radar Backscatter from Statistically Rough Surfaces, Technical report, British Aerospace project (89 pp, August 1995).
M. Spivack, Ultrasonic Modelling of Edges of Rough Cracks, Technical report and literature survey, Nuclear Electric project (25 pp, 1996)
M. Spivack, Statistical Energy Analysis - Technical Report, British Aerospace project (16 pp, September 1996).
M. Spivack, Ultrasonic Modelling of Edges of Rough Cracks, Interim Report, Nuclear Electric project (22pp December 1996).
M. Spivack, Radar Backscatter from Irregular Surfaces, Final report on British Aerospace project, (28pp January 1997).
M. Spivack, Scattering of Scalar Waves in 3-Dimensional Geometries, British Aerospace project, (Sept 1997).
M. Spivack, Electromagnetic Propagation in a 2-Dimensional Sinusoidal Waveguide, Report on British Aerospace project, (40pp Dec 1997).
M. Spivack, Ducting Effects in Coastal Radar, Gassiot Report, (27pp Nov 1997).
M. Spivack, Stochastic Electromagnetics, Report for British Aerospace, (July 1998).
M. Spivack, Radar Propagation in 3-Dimensional Curved Waveguides, Report on British Aerospace project, (Dec 1999).
J.A. Ogilvy & M. Spivack Validation of University of Cambridge intergral equation method for 3 dimensional ducts, British Aerospace Sowerby Research Centre report JS14234 (46pp, May 1999).
M. Spivack, Mathematical and Numerical Modelling of Radar Absorbent Materials, Report on BAE Systems project, (Dec 2002).
M. Spivack & P.E. Barbone, Energy transmission through a rough interface for wave incidence at the critical angle (1998) (NATO report CRG 950042).
M. Spivack & B. Pruin, Phase retrieval from intensity measurements on two planes, (1998) (DAMTP research report).

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