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) 712718.
 M. Spivack, Derivations
and nest algebras on Banach space, Israel J. Math. 50
(1985) 193200.
 M. Spivack, Derivations
on commutative operator algebras, Bull. Australian Math.
Soc. 32 (1985) 415418.
 M. Spivack, Contractive
projections on Banach space, Bull. Australian Math. Soc.
34 (1986) 271274.

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 halfspace, Geophys. J. Roy. Astr. Soc. 57 (1979)
463477.
 M. Spivack, Finite difference scheme for fluids with simple
boundaries, City University Physics Dept. Research Report
1978.
 M. Spivack, Two new algorithms for the pipebreak 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)
615634.
 M. Spivack & P.E. Barbone, Disorder
and localization in ribbed structures with fluid loading
Proc. R. Soc. Lond. A 444 (1994) 7389.
 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 07507356).
 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
fluidloaded 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) 509528.
 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) 17411755.
 M. Spivack & B. J. Uscinski, Splitstep
solution for wave propagation in random media, J. Comp.
Applied Math. 27 (1989) 349361.
 M. Spivack, Accuracy
of the moments from simulation of wave propagation in random
media, J. Opt. Soc. Am. A 7 (1990) 790793.
 D. Reeve, S. Leonard, & M. Spivack,
Solution of the fourth
moment equation for a point source, J. Modern
Optics 37 (1990) 965975.
 M. Spivack, Operator
splitting for the random wave moment equations,
Applied Math. Lett. 3 (1990) 8791.
 D.E. Reeve & M. Spivack,
Numerical solution of the second
moment equation for waves in an inhomogeneous waveguide,
J. Mod. Opt. 39 (1992) 13431352.
 BJ Uscinski & M Spivack, High
intensity ribbons in multiply scattering media,
Waves in Random and Complex Media 15 (2005)
339352.

Rough Surface Scattering and Waveguides
 M. Spivack, Numerical
approach to rough surface scattering for the parabolic
equation, J. Acoust. Soc. Am. 87 (1990) 19992004.
 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) 23612366.

 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) 249254.
 M. Spivack, Coherent
field and specular reflection at grazing incidence on rough
surface J. Acoust. Soc. Am. 95 (1994)
694700.
 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, 285290.
 M. Spivack & J.D. Sheard, Wave scattering in an irregular
layer adjoining a fluid halfspace, Proceedings of 2nd European
Conference on Underwater Acoustics Denmark 1994, 213218.
 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)
745753.
 J.D. Sheard & M. Spivack,Wave
scattering in rough elastic layer adjoining a fluid halfspace,
J. Acoust. Soc. Am. 97 (1995) 7283.
 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 twodimensional waveguide, J.
Acoust. Soc. Am. 101 (1997) 12501255.
 M. Spivack, A. Keen, J. Ogilvy & C. Sillence, Validation
of leftright method for scattering by a rough surface, J
Modern Optics 48 (2001) 10211033.
 Y. Hatziioannou & M. Spivack, Electromagnetic
scattering by refractive index variations over a rough conducting
surface, J Modern Optics 48 (2001) 11511160.
 M. Spivack, Scattering by a finite rough plate, Aerotecnica,
Missili e Spazio 79, N34 (2000).
 M. Spivack, J. Ogilvy & C. Sillence, Electromagnetic
propagation in a curved 2dimensional waveguide, Waves in
Random Media 12 (2002) 4762.
 M Spivack, J Ogilvy, & C Sillence, Electromagnetic
scattering by large complex scatterers in 3D, IEE Proc
Science, Measurement & Tech 151 (2004) 464466.
 M Spivack, J Ogilvy, & C Sillence, Leftright
splitting for electromagnetic scattering in 3D, IEE Proc
Computational Electromagnetics 2004 (CEM04), StratforduponAvon.
 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 twoway parabolic integral equation,
Progress in Electromagnetics Research M 56 (2017) 8190.
 M Spivack & O Rath Spivack,
Statistical moments for rough surface scatter from twoway parabolic
integral equation at low grazing angles,
J. Modern Optics 64 (2017) 17681776.
 O Rath Spivack & M Spivack,
Efficient boundary integral
solution for acoustic wave scattering by irregular surfaces,
Engineering Analysis with Boundary Elements
83 (2017) 275280.

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) 32953302.
 M. Spivack, Solution
of the inverse scattering problem for grazing incidence on a rough
surface J. Opt. Soc. Am. A 9 (1992)
13521355.
 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) 3743.
 Y. Chen & M. Spivack
Rough surface reconstruction at grazing angles
by the iterated marching method,
J. Opt. Soc. Am. A, 35 (2018) 504513.
 Y. Chen, O Rath Spivack & M. Spivack
Recovery of rough surface in ducting medium from grazing angle
scattered wave
J. Applied Physics (2018) to appear.

Inverse Problems: Coastal Morphology
 D.E. Reeve & M. Spivack, Determination
of a source term in the linear diffusion equation
Inverse Problems 10 (1994) 13351344.
 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) 585596.
 M. Spivack & D.E. Reeve, Source
reconstruction in a coastal evolution equation J. Comp.
Phys. 161 (2000) 169181.
 D E Reeve & M Spivack, Evolution
of shoreline position moments, Coastal Engineering 51
(2004) 661673.
 D E Reeve & M Spivack, Prediction
of longterm coastal evolution using moment equations,
Proceedings, Coastal Dynamics 2001, Lund, Sweden, 723732,
2001.
 D E Reeve & M Spivack, Source
reconstruction for a coastal evolution equation, Proceedings
of the MEDCOAST99EMECS 99 Joint Conference: Landocean
Interactions  Managing coastal ecosystems, 913 November 1999,
Antalya, Turkey, MEDCOAST, (Ed. E. Ozhan), p17011710, 1999.
 D E Reeve & M Spivack, Stochastic
prediction of longterm coastal evolution, Coastal
Engineering V: Computer Modelling of Seas and Coastal Regions,
Rhodes, 5563, 2001.
 M Spivack & D E Reeve, A
stochastic model for shoreline evolution, Proceedings 28th
ICCE, July 2002, Cardiff, (Ed. J. McKee Smith), World Scientific,
p34333437

H Karunarathna, D E Reeve & M Spivack,
Longterm morphodynamic evolution of estuaries: an inverse problem,
Estuarine, Coastal and Shelf Science 77 (2008) 385395.

H Karunarathna, D E Reeve & M Spivack,
Beach profile evolution as an inverse problem,
Continental Shelf Research 29 (2009) 22342239.

H Karunarathna, J M HorrilloCaraballo, M Spivack & D E Reeve,
Analysis of key parameters in a diffusion type beach profile evolution
model
Continental Shelf Research 31 (2011) 98107.

D E Reeve, A PedrozoAcuna & M Spivack,
Beach memory and ensemble prediction of shoreline evolution near a groyne
Coastal Engineering 86 (2014) 7787.

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, ClosetoGrazing 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 3Dimensional
Geometries, British Aerospace project, (Sept 1997).
 M. Spivack, Electromagnetic Propagation in a 2Dimensional
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 3Dimensional 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).
File translated from T_{E}X
by T_{T}H, version 3.33. On 17 Dec 2004,
15:13.