Papers by P. A. Martin in Refereed Journals

  1. On the null-field equations for the exterior problems of acoustics. Quart. J. Mech. Appl. Math. 33 (1980) 385-396.
  2. Diffraction of elastic waves by a penny-shaped crack. Proc. Roy. Soc. A 378 (1981) 263-285.
  3. On the null-field equations for water-wave radiation problems. J. Fluid Mech. 113 (1981) 315-332.
  4. The discontinuity in the elastostatic displacement vector across a penny-shaped crack under arbitrary loads. J. Elasticity 12 (1982) 201-218.
  5. Acoustic scattering and radiation problems, and the null-field method. Wave Motion 4 (1982) 391-408.
  6. The scattering of regular surface waves by a fixed, half-immersed, circular cylinder. (With A.G. Dixon). Appl. Ocean Res. 5 (1983) 13-23.
  7. Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results. (With G.R. Wickham). Proc. Roy. Soc. A 390 (1983) 91-129.
  8. On the null-field equations for water-wave scattering problems. IMA J. Appl. Math. 33 (1984) 55-69.
  9. Integral-equation methods for multiple-scattering problems I. Acoustics. Quart. J. Mech. Appl. Math. 38 (1985) 105-118.
  10. Integral-equation methods for multiple-scattering problems II. Water waves. Quart. J. Mech. Appl. Math. 38 (1985) 119-133.
  11. On the T-matrix for water-wave scattering problems. Wave Motion 7 (1985) 177-193.
  12. Inverse scattering for geophysical problems. III. On the velocity-inversion problems of acoustics. (With A.G. Ramm). Proc. Roy. Soc. A 399 (1985) 153-166.
  13. Orthogonal polynomial solutions for pressurised elliptical cracks. Quart. J. Mech. Appl. Math. 39 (1986) 269-287.
  14. Orthogonal polynomial solutions for elliptical cracks under shear loadings. Quart. J. Mech. Appl. Math. 39 (1986) 519-534.
  15. On single integral equations for the transmission problem of acoustics. (With R.E. Kleinman). SIAM J. Appl. Math. 48 (1988) 307-325.
  16. Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions. (With R.A. Dalrymple). J. Fluid Mech. 188 (1988) 465-490.
  17. On boundary integral equations for crack problems. (With F.J. Rizzo). Proc. Roy. Soc. A 421 (1989) 341-355.
  18. On hypersingular boundary integral equations for certain problems in mechanics. (With F.J. Rizzo and I.R. Gonsalves). Mechanics Res. Comm. 16 (1989) 65-71.
  19. On the scattering of elastic waves by an elastic inclusion in two dimensions. Quart. J. Mech. Appl. Math. 43 (1990) 275-291.
  20. Wave diffraction through offshore breakwaters. (With R.A. Dalrymple). J. Waterway, Port, Coastal, and Ocean Eng. 116 (1990) 727-741.
  21. Identification of irregular frequencies in simple direct integral-equation methods for scattering by homogeneous inclusions. Wave Motion 13 (1991) 185-192.
  22. Reflection and transmission from porous structures under oblique wave attack. (With R.A. Dalrymple and M.A. Losada). J. Fluid Mech. 224 (1991) 625-644.
  23. End-point behaviour of solutions to hypersingular integral equations. Proc. Roy. Soc. A 432 (1991) 301-320.
  24. Exact solution of a simple hypersingular integral equation. J. Integral Equations & Applications 4 (1992) 197-204. Addendum: 5 (1993) 297.
  25. Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis. J. Engineering Maths. 26 (1992) 267-280.
  26. Perfect boundary conditions for parabolic water-wave models. (With R.A. Dalrymple). Proc. Roy. Soc. A 437 (1992) 41-54.
  27. Tip behaviour for cracks in bonded inhomogeneous materials. J. Engineering Maths. 26 (1992) 467-480.
  28. Scattering of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). Appl. Ocean Res. 14 (1992) 313-321.
  29. Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers. J. Nondestructive Evaluation 11 (1992) 167-174.
  30. A normal crack in an elastic half-space with a stress-free surface. (With L. Paivarinta and S. Rempel). Math. Methods in the Appl. Sciences 16 (1993) 563-579.
  31. Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle. (With P. Ola). Proc. Roy. Soc. Edinb. 123A (1993) 185-208.
  32. Karp's theorem in elastodynamic inverse scattering. (With G. Dassios). Inverse Problems 9 (1993) 97-111.
  33. On amphidromic points. (With R.A. Dalrymple). Proc. Roy. Soc. A 444 (1994) 91-104.
  34. On the propagation of water waves along a porous-walled channel. (With R.A. Dalrymple). Proc. Roy. Soc. A 444 (1994) 411-428.
  35. Scattering of water waves by submerged curved plates and by surface-piercing flat plates. (With N.F. Parsons). Appl. Ocean Res. 16 (1994) 129-139.
  36. Spectral methods for forward-propagating water waves in conformally-mapped channels. (With J.T. Kirby and R.A. Dalrymple). Appl. Ocean Res. 16 (1994) 249-266.
  37. Fluid-solid interaction: acoustic scattering by a smooth elastic body. (With C.J. Luke). SIAM J. Appl. Math. 55 (1995) 904-922.
  38. Trapping of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). J. Fluid Mech. 284 (1995) 359-375.
  39. Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves. IMA J. Appl. Math. 54 (1995) 139-157.
  40. Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions. (With J.C. Chao, Y.J. Liu, F.J. Rizzo and L. Udpa). IEEE Trans. on Antennas and Propagation AP-43 (1995) 1416-1422.
  41. Partitioning, boundary integral equations, and exact Green's functions. (With F.J. Rizzo). Int. J. for Numerical Methods in Engng. 38 (1995) 3483-3495.
  42. Mapping flat cracks onto penny-shaped cracks: shear loadings. J. Mech. and Phys. of Solids 43 (1995) 275-294.
  43. Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks. Quart. Appl. Math. 54 (1996) 663-675.
  44. Hypersingular integrals: how smooth must the density be? (With F.J. Rizzo). Int. J. for Numerical Methods in Engng. 39 (1996) 687-704.
  45. Water waves incident on an infinitely long rectangular inlet. (With R.A. Dalrymple). Applied Ocean Res. 18 (1996) 1-11.
  46. A general formulation for light scattering by dielectric bodies near a perfectly conducting surface. (With J.C. Chao, F.J. Rizzo, I. El-Shafiey, Y.J. Liu and L. Udpa). J. Optical Soc. Amer. A 13 (1996) 338-344.
  47. On angular-spectrum representations for scattering by infinite rough surfaces. (With J.A. DeSanto). Wave Motion 24 (1996) 421-433. Corrigendum 32 (2000) 385-386.
  48. On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface. (With J.A. DeSanto). J. Acoustical Soc. Amer. 102 (1997) 67-77.
  49. Radiation of water waves by a heaving submerged horizontal disc. (With L. Farina). J. Fluid Mech. 337 (1997) 365-379.
  50. Smoothness-relaxation strategies for singular and hypersingular integral equations. (With F.J. Rizzo and T.A. Cruse). Int. J. for Numerical Methods in Engng. 42 (1998) 885-906.
  51. On the derivation of boundary integral equations for scattering by an infinite two-dimensional rough surface. (With J.A. DeSanto). J. Math. Phys. 39 (1998) 894-912.
  52. Scattering of water waves by a submerged disc using a hypersingular integral equation. (With L. Farina). Applied Ocean Res. 20 (1998) 121-134. Erratum: 21 (1999) 157-158.
  53. Some efficient boundary integral strategies for time-harmonic wave problems in an elastic halfspace. (With L. Pan and F. Rizzo). Computer Methods in Appl. Mech. and Engng. 164 (1998) 207-221.
  54. On potential flow past wrinkled discs. Proc. Roy. Soc. A 454 (1998) 2209-2221.
  55. On the added mass of rippled discs. J. Engineering Maths. 33 (1998) 421-435.
  56. Multiple scattering and the Rehr-Albers-Fritzsche formula for the propagator matrix. J. Phys. A: Math. and Gen. 31 (1998) 8923-8932.
  57. Reduction of free-edge stress intensities in anisotropic bimaterials. (With J.R. Berger and J.P. Lien). Int. J. Fracture 91 (1998) 165-177.
  58. Electromagnetic scattering by a homogeneous chiral obstacle: boundary integral equations and low-chirality approximations. (With C. Athanasiadis and I.G. Stratis). SIAM J. Appl. Math. 59 (1999) 1745-1762.
  59. Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far-field operator. (With C. Athanasiadis and I.G. Stratis). Math. Methods in the Appl. Sciences 22 (1999) 1175-1188.
  60. Inverting the Sachs-Wolfe formula: an inverse problem in early-Universe cosmology. (With A. Berera). Inverse Problems 15 (1999) 1393-1404.
  61. Waves in rectangular inlet with reflecting or absorbing walls. (With R.A. Dalrymple and L. Li). J. Waterway, Port, Coastal, and Ocean Eng. 126 (2000) 288-296.
  62. Time-harmonic torsional waves in a composite cylinder with an imperfect interface. (With J.R. Berger and S.J. McCaffery). J. Acoust. Soc. Amer. 107 (2000) 1161-1167.
  63. Perturbed cracks in two dimensions: an integral-equation approach. Int. J. Fracture 104 (2000) 317-327.
  64. On spherical-wave scattering by a spherical scatterer and related near-field inverse problems. (With C. Athanasiadis and I.G. Stratis). IMA J. Appl. Math. 66 (2001) 539-549.
  65. G. R. Wickham: an appreciation. (With I.D. Abrahams and A.N. Norris). Wave Motion 33 (2001) 1-6.
  66. The spherical-cap crack revisited. Int. J. Solids & Struct. 38 (2001) 4759-4776.
  67. On wrinkled penny-shaped cracks. J. Mech. & Phys. of Solids 49 (2001) 1481-1495.
  68. Waves in wood: free vibrations of a wooden pole. (With J.R. Berger). J. Mech. & Phys. of Solids 49 (2001) 1155-1178.
  69. On the diffraction of Poincare waves. Math. Methods in the Appl. Sciences 24 (2001) 913-925.
  70. On functionally graded balls and cones. J. Engineering Maths. 42 (2002) 133-142.
  71. A boundary element regularization method for the boundary determination in potential corrosion damage. (With D. Lesnic and J.R. Berger). Inverse Problems in Engineering 10 (2002) 163-182.
  72. Acoustic scattering by inhomogeneous spheres. J. Acoust. Soc. Amer. 111 (2002) 2013-2018.
  73. On Green's function for a three-dimensional exponentially graded elastic solid. (With J.D. Richardson, L.J. Gray and J.R. Berger). Proc. Roy. Soc. A 458 (2002) 1931-1947.
  74. The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics. (With M. Destrade and T.C.T. Ting). J. Mech. & Phys. of Solids 50 (2002) 1453-1468.
  75. Multiple scattering and modified Green's functions. J. Math. Anal. Applics. 275 (2002) 642-656.
  76. On mechanical waves along aluminum conductor steel reinforced (ACSR) power lines. (With J.R. Berger). J. Appl. Mech. 69 (2002) 740-748.
  77. Scattering relations for point sources: acoustic and electromagnetic waves. (With C. Athanasiadis, A. Spyropoulos and I.G. Stratis). J. Math. Phys. 43 (2002) 5683-5697.
  78. The added mass of potential flow past rigid plates. (With N.M.A. Nik Long). International Mathematical Journal 3 (2003) 785--794.
  79. On the scattering of point-generated electromagnetic waves by a perfectly conducting sphere, and related near-field inverse problems. (With C. Athanasiadis and I.G. Stratis). Z. angewandte Mathematik und Mechanik (ZAMM) 83 (2003) 129-136.
  80. The method of fundamental solutions for scattering and radiation problems. (With G. Fairweather and A. Karageorghis). Engineering Analysis with Boundary Elements 27 (2003) 759--769.
  81. On connections between boundary integral equations and T-matrix methods. Engineering Analysis with Boundary Elements 27 (2003) 771-777.
  82. Waves in wood: axisymmetric guided waves along boreholes. (With J.R. Berger). Chinese Journal of Mechanics, Series A 19 (2003) 105-111.
  83. On Green's function for a bimaterial elastic half-plane. Int. J. Solids & Struct. 40 (2003) 2101-2119.
  84. Acoustic scattering by inhomogeneous obstacles. SIAM J. Appl. Math. 64 (2003) 297-308.
  85. Semi-infinite arrays of isotropic point scatterers: a unified approach. (With C.M. Linton). SIAM J. Appl. Math. 64 (2004) 1035-1056.
  86. On Webster's horn equation and some generalizations. J. Acoust. Soc. Amer. 116 (2004) 1381-1388.
  87. Waves in wood: axisymmetric waves in slender solids of revolution. Wave Motion 40 (2004) 387-398.
  88. Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber. (With C.M. Linton). J. Acoust. Soc. Amer. 117 (2005) 3413-3423.
  89. Acoustic waves in slender axisymmetric tubes. J. Sound & Vibration 286 (2005) 55-68.
  90. On flexural waves in cylindrically anisotropic rods. Int. J. Solids & Struct. 42 (2005) 2161-2179.
  91. Fundamental solutions for steady-state heat transfer in an exponentially graded anisotropic material. (With J.R. Berger, V. Mantic and L.J. Gray). J. Appl. Math. Phys. (ZAMP) 56 (2005) 293-303.
  92. Exact solution of some integral equations over a circular disc. J. Integral Equations & Applications 18 (2006) 39-58.
  93. Multiple scattering by multiple spheres: a new proof of the Lloyd-Berry formula. (With C.M. Linton). SIAM J. Appl. Math. 66 (2006) 1649-1668.
  94. Discrete scattering theory: Green's function for a square lattice. Wave Motion 43 (2006) 619-629.
  95. Perturbed cracks in two dimensions: a reprise. Int. J. Fracture 140 (2006) 299-303.
  96. Stress intensity factor computation using the method of fundamental solutions: mixed-mode problems. (With J.R. Berger and A. Karageorghis). Int. J. for Numerical Methods in Engng. 69 (2007) 469-483.
  97. On the T-matrix for scattering by small obstacles. J. Computational & Appl. Math. 204 (2007) 219-230.
  98. Analysis of moire data for near-interface cracks. (With K. Rozenburg, J.R. Berger and I. Reimanis). Int. J. Fracture 143 (2007) 207-217.
  99. Calculating the near field of a line of sources using Mellin transforms. ANZIAM Journal 49 (2007) 99-109.
  100. On functions defined by sums of products of Bessel functions. J. Phys. A: Math & Theor. 41 (2008) 015207 (8 pages).
  101. Multiple scattering by random configurations of circular cylinders: weak scattering without closure assumptions. (With A. Maurel). Wave Motion 45 (2008) 865-880.
  102. Thermal grooving by surface diffusion: Mullins revisited and extended to multiple grooves. Quart. Appl. Math., to appear.

Last modified: 3rd September 2008

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