Papers by P. A. Martin in Refereed Journals


  1. Asymptotic approximations for radial spheroidal wavefunctions with complex size parameter. Studies in Applied Mathematics
  2. On mixed boundary-value problems in a wedge. Quarterly Journal of Mechanics and Applied Mathematics doi
  3. On the far-field computation of acoustic radiation forces. Journal of the Acoustical Society of America 142 (2017) 2094-2100. doi
  4. Bounds on ratios of modified Bessel functions with complex arguments. Journal of Mathematical Analysis and Applications 454 (2017) 429-438. doi
  5. Acoustic scattering by a sphere in the time domain. Wave Motion 67 (2016) 68-80. doi pdf
  6. The pulsating orb: solving the wave equation outside a ball. Proceedings of the Royal Society A 472 (2016) 20160037 (20 pages). doi pdf
  7. One-dimensional reflection by a semi-infinite periodic row of scatterers. (With I.D. Abrahams and W.J. Parnell). Wave Motion 58 (2015) 1-12. doi pdf
  8. On acoustic and electric Faraday cages. Proceedings of the Royal Society A 470 (2014) 20140344 (14 pages). doi pdf
  9. Shear-wave resonances in a fluid-solid-solid layered structure. Wave Motion 51 (2014) 1161-1169. doi pdf
  10. Concentration-dependent chemical expansion in lithium-ion battery cathode particles. (With V. Malavé and J.R. Berger). Journal of Applied Mechanics 81 (2014) 091005 (9 pages). doi pdf
  11. Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method. (With L. Farina and V. Péron). Journal of Computational and Applied Mathematics 269 (2014) 118-131. doi pdf
  12. A scaled mapping parabolic equation for sloping range-dependent environments. (With A.M. Metzler, D. Moran, J.M. Collis and W.L. Siegmann). Journal of the Acoustical Society of America 135 (2014) EL172-EL178. doi pdf
  13. Time-domain BEM for 3-D transient elastodynamic problems with interacting rigid movable disc-shaped inclusions. (With V.V. Mykhas'kiv and O.I. Kalynyak). Computational Mechanics 53 (2014) 1311-1325. doi pdf
  14. On the long-time limit of the Garvin-Alterman-Loewenthal solution for a buried blast load. (With E. Kausel). International Journal of Solids and Structures 51 (2014) 1516-1520. doi pdf
  15. N masses on an infinite string and related one-dimensional scattering problems. Wave Motion 51 (2014) 296-307. doi pdf
  16. Scattering from a large cylinder with an eccentrically embedded core: an orders-of-scattering approximation. (With A.J. Yuffa and J.A. Scales). Journal of Quantitative Spectroscopy and Radiative Transfer 133 (2014) 520-525. doi pdf
  17. Propagation in one-dimensional crystals with positional and compositional disorder. (With A. Maurel). European Physical Journal B 86 (2013) 486 (10 pages). doi pdf
  18. Explicit energy calculation for a charged elliptical plate. Applied Mathematics Letters 26 (2013) 893-898. doi pdf pdf with addendum
  19. Fritz Joseph Ursell. (With I.D. Abrahams). Biographical Memoirs of Fellows of the Royal Society 59 (2013) 407-421. doi pdf bibliography
  20. Peter Waterman and T-matrix methods. (With M.I. Mishchenko). Journal of Quantitative Spectroscopy and Radiative Transfer 123 (2013) 2-7. doi pdf
  21. Singularities in auxetic bimaterials. (With M.M. Adam and J.R. Berger). Mechanics Research Communications 47 (2013) 102-105. doi pdf
  22. Two-dimensional acoustic scattering, conformal mapping, and the Rayleigh hypothesis. Journal of the Acoustical Society of America 132 (2012) 2184-2188. doi pdf
  23. Jet noise: sound generation by disc and cylinder sources. (With M.J. Carley). Proceedings of the Royal Society A 468 (2012) 3947-3964. doi pdf
  24. Maurice Jaswon and boundary element methods. Engineering Analysis with Boundary Elements 36 (2012) 1699-1704. doi pdf
  25. Generation of internal gravity waves by an oscillating horizontal elliptical plate. (With S.G. Llewellyn Smith). SIAM Journal on Applied Mathematics 72 (2012) 725-739. doi pdf
  26. Comment on "Elastic wave propagation in a solid layer with laser-induced point defects" [J. Appl. Phys. 110, 064906 (2011)]. Journal of Applied Physics 112 (2012) 056101 (2 pages). doi pdf
  27. Moshinsky's shutter problem: an initial-value problem for the Klein-Gordon equation. (With F.V. Kowalski). Applicable Analysis 91 (2012) 309-322. doi pdf
  28. Finding a source inside a sphere. (With N.L. Tsitsas). Inverse Problems 28 (2012) 015003 (11 pages) doi pdf
  29. Internal gravity waves, boundary integral equations and radiation conditions. (With S.G. Llewellyn Smith). Wave Motion 49 (2012) 427-444. doi pdf
  30. Generation of internal gravity waves by an oscillating horizontal disc. (With S.G. Llewellyn Smith). Proceedings of the Royal Society A 467 (2011) 3406-3423. doi pdf
  31. Scattering by defects in an exponentially graded layer and misuse of the method of images. International Journal of Solids and Structures 48 (2011) 2164-2166. doi pdf
  32. Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions. Journal of the Acoustical Society of America 129 (2011) 1685-1695. doi pdf
  33. The horn-feed problem: sound waves in a tube joined to a cone, and related problems. Journal of Engineering Mathematics 71 (2011) 291-304. doi pdf
  34. Multiple scattering of flexural waves by random configurations of inclusions in thin plates. (With W.J. Parnell). Wave Motion 48 (2011) 161-175. doi pdf
  35. Estimating the dynamic effective mass density of random composites. (With A. Maurel and W.J. Parnell). Journal of the Acoustical Society of America 128 (2010) 571-577. doi pdf
  36. Waves around almost periodic arrangements of scatterers: Analysis of positional disorder. (With A. Maurel). Mathematical Methods in the Applied Sciences 33 (2010) 2215-2224. doi pdf
  37. Effective propagation in a one-dimensional perturbed periodic structure: comparison of several approaches. (With A. Maurel and V. Pagneux). Waves in Random and Complex Media 20 (2010) 634-655. doi pdf
  38. Harry Bateman: from Manchester to Manuscript Project. Mathematics Today 46 (2010) 82-85. pdf
  39. Scattering by a cavity in an exponentially graded half-space. Journal of Applied Mechanics 76 (2009) 031009 (4 pages). doi pdf
  40. Thermal grooving by surface diffusion: Mullins revisited and extended to multiple grooves. Quarterly of Applied Mathematics 67 (2009) 125-136. doi pdf
  41. On functions defined by sums of products of Bessel functions. Journal of Physics A: Mathematical and Theoretical 41 (2008) 015207 (8 pages). doi pdf
  42. Multiple scattering by random configurations of circular cylinders: weak scattering without closure assumptions. (With A. Maurel). Wave Motion 45 (2008) 865-880. doi pdf
  43. Calculating the near field of a line of sources using Mellin transforms. ANZIAM Journal 49 (2007) 99-109. doi pdf
  44. Analysis of moire data for near-interface cracks. (With K. Rozenburg, J.R. Berger and I. Reimanis). International Journal of Fracture 143 (2007) 207-217. doi pdf
  45. On the T-matrix for scattering by small obstacles. Journal of Computational and Applied Mathematics 204 (2007) 219-230. doi pdf
  46. Stress intensity factor computation using the method of fundamental solutions: mixed-mode problems. (With J.R. Berger and A. Karageorghis). International Journal for Numerical Methods in Engineering 69 (2007) 469-483. doi pdf
  47. Perturbed cracks in two dimensions: a reprise. International Journal of Fracture 140 (2006) 299-303. doi pdf
  48. Discrete scattering theory: Green's function for a square lattice. Wave Motion 43 (2006) 619-629. doi pdf
  49. Multiple scattering by multiple spheres: a new proof of the Lloyd-Berry formula. (With C.M. Linton). SIAM Journal on Applied Mathematics 66 (2006) 1649-1668. doi pdf
  50. Exact solution of some integral equations over a circular disc. Journal of Integral Equations and Applications 18 (2006) 39-58. doi pdf
  51. Fundamental solutions for steady-state heat transfer in an exponentially graded anisotropic material. (With J.R. Berger, V. Mantic and L.J. Gray). Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) 56 (2005) 293-303. doi pdf
  52. On flexural waves in cylindrically anisotropic rods. International Journal of Solids and Structures 42 (2005) 2161-2179. doi pdf
  53. Acoustic waves in slender axisymmetric tubes. Journal of Sound and Vibration 286 (2005) 55-68. doi pdf
  54. Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber. (With C.M. Linton). Journal of the Acoustical Society of America 117 (2005) 3413-3423. doi pdf
  55. Waves in wood: axisymmetric waves in slender solids of revolution. Wave Motion 40 (2004) 387-398. doi pdf
  56. On Webster's horn equation and some generalizations. Journal of the Acoustical Society of America 116 (2004) 1381-1388. doi pdf
  57. Semi-infinite arrays of isotropic point scatterers: a unified approach. (With C.M. Linton). SIAM Journal on Applied Mathematics 64 (2004) 1035-1056. doi pdf
  58. Acoustic scattering by inhomogeneous obstacles. SIAM Journal on Applied Mathematics 64 (2003) 297-308. doi pdf
  59. On Green's function for a bimaterial elastic half-plane. International Journal of Solids and Structures 40 (2003) 2101-2119. doi pdf
  60. Waves in wood: axisymmetric guided waves along boreholes. (With J.R. Berger). Chinese Journal of Mechanics, Series A 19 (2003) 105-111. pdf
  61. On connections between boundary integral equations and T-matrix methods. Engineering Analysis with Boundary Elements 27 (2003) 771-777. doi pdf
  62. 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. doi pdf
  63. 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). Zeitschrift fur angewandte Mathematik und Mechanik (ZAMM) 83 (2003) 129-136. doi pdf
  64. The added mass of potential flow past rigid plates. (With N.M.A. Nik Long). International Mathematical Journal 3 (2003) 785-794.
  65. Scattering relations for point sources: acoustic and electromagnetic waves. (With C. Athanasiadis, A. Spyropoulos and I.G. Stratis). Journal of Mathematical Physics 43 (2002) 5683-5697. doi pdf
  66. On mechanical waves along aluminum conductor steel reinforced (ACSR) power lines. (With J.R. Berger). Journal of Applied Mechanics 69 (2002) 740-748. doi pdf
  67. Multiple scattering and modified Green's functions. Journal of Mathematical Analysis and Applications 275 (2002) 642-656. doi pdf
  68. The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics. (With M. Destrade and T.C.T. Ting). Journal of the Mechanics and Physics of Solids 50 (2002) 1453-1468. doi pdf
  69. On Green's function for a three-dimensional exponentially graded elastic solid. (With J.D. Richardson, L.J. Gray and J.R. Berger). Proceedings of the Royal Society A 458 (2002) 1931-1947. doi pdf
  70. Acoustic scattering by inhomogeneous spheres. Journal of the Acoustical Society of America 111 (2002) 2013-2018. doi pdf
  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. doi pdf
  72. On functionally graded balls and cones. Journal of Engineering Mathematics 42 (2002) 133-142. doi pdf
  73. On spherical-wave scattering by a spherical scatterer and related near-field inverse problems. (With C. Athanasiadis and I.G. Stratis). IMA Journal of Applied Mathematics 66 (2001) 539-549. doi pdf
  74. On the diffraction of Poincaré waves. Mathematical Methods in the Applied Sciences 24 (2001) 913-925. doi pdf
  75. Waves in wood: free vibrations of a wooden pole. (With J.R. Berger). Journal of the Mechanics and Physics of Solids 49 (2001) 1155-1178. doi pdf
  76. On wrinkled penny-shaped cracks. Journal of the Mechanics and Physics of Solids 49 (2001) 1481-1495. doi pdf
  77. The spherical-cap crack revisited. International Journal of Solids and Structures 38 (2001) 4759-4776. doi pdf
  78. G. R. Wickham: an appreciation. (With I.D. Abrahams and A.N. Norris). Wave Motion 33 (2001) 1-6. doi pdf
  79. Perturbed cracks in two dimensions: an integral-equation approach. International Journal of Fracture 104 (2000) 317-327. doi pdf
  80. Time-harmonic torsional waves in a composite cylinder with an imperfect interface. (With J.R. Berger and S.J. McCaffery). Journal of the Acoustical Society of America 107 (2000) 1161-1167. doi pdf
  81. Waves in rectangular inlet with reflecting or absorbing walls. (With R.A. Dalrymple and L. Li). Journal of Waterway, Port, Coastal, and Ocean Engineering 126 (2000) 288-296. doi pdf
  82. Inverting the Sachs-Wolfe formula: an inverse problem in early-Universe cosmology. (With A. Berera). Inverse Problems 15 (1999) 1393-1404. doi pdf
  83. Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far-field operator. (With C. Athanasiadis and I.G. Stratis). Mathematical Methods in the Applied Sciences 22 (1999) 1175-1188. doi pdf
  84. Electromagnetic scattering by a homogeneous chiral obstacle: boundary integral equations and low-chirality approximations. (With C. Athanasiadis and I.G. Stratis). SIAM Journal on Applied Mathematics 59 (1999) 1745-1762. doi pdf
  85. Reduction of free-edge stress intensities in anisotropic bimaterials. (With J.R. Berger and J.P. Lien). International Journal of Fracture 91 (1998) 165-177. doi pdf
  86. Multiple scattering and the Rehr-Albers-Fritzsche formula for the propagator matrix. Journal of Physics A: Mathematical and General 31 (1998) 8923-8932. doi pdf
  87. On the added mass of rippled discs. Journal of Engineering Mathematics 33 (1998) 421-435. doi pdf
  88. On potential flow past wrinkled discs. Proceedings of the Royal Society A 454 (1998) 2209-2221. doi pdf
  89. Some efficient boundary integral strategies for time-harmonic wave problems in an elastic halfspace. (With L. Pan and F. Rizzo). Computer Methods in Applied Mechanics and Engineering 164 (1998) 207-221. doi pdf
  90. Scattering of water waves by a submerged disc using a hypersingular integral equation. (With L. Farina). Applied Ocean Research 20 (1998) 121-134. doi pdf. Erratum: 21 (1999) 157-158. pdf
  91. On the derivation of boundary integral equations for scattering by an infinite two-dimensional rough surface. (With J.A. DeSanto). Journal of Mathematical Physics 39 (1998) 894-912. doi pdf
  92. Smoothness-relaxation strategies for singular and hypersingular integral equations. (With F.J. Rizzo and T.A. Cruse). International Journal for Numerical Methods in Engineering 42 (1998) 885-906. doi pdf
  93. Radiation of water waves by a heaving submerged horizontal disc. (With L. Farina). Journal of Fluid Mechanics 337 (1997) 365-379. doi pdf
  94. On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface. (With J.A. DeSanto). Journal of the Acoustical Society of America 102 (1997) 67-77. doi pdf
  95. On angular-spectrum representations for scattering by infinite rough surfaces. (With J.A. DeSanto). Wave Motion 24 (1996) 421-433. doi pdf. Corrigendum 32 (2000) 385-386. doi pdf
  96. 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). Journal of the Optical Society of America A 13 (1996) 338-344. doi pdf
  97. Water waves incident on an infinitely long rectangular inlet. (With R.A. Dalrymple). Applied Ocean Research 18 (1996) 1-11. doi pdf
  98. Hypersingular integrals: how smooth must the density be? (With F.J. Rizzo). International Journal for Numerical Methods in Engineering 39 (1996) 687-704. doi pdf
  99. Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks. Quarterly of Applied Mathematics 54 (1996) 663-675. pdf
  100. Mapping flat cracks onto penny-shaped cracks: shear loadings. Journal of the Mechanics and Physics of Solids 43 (1995) 275-294. doi pdf
  101. Partitioning, boundary integral equations, and exact Green's functions. (With F.J. Rizzo). International Journal for Numerical Methods in Engineering 38 (1995) 3483-3495. doi pdf
  102. 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 Transactions on Antennas and Propagation AP-43 (1995) 1416-1422. doi pdf
  103. Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves. IMA Journal of Applied Mathematics 54 (1995) 139-157. doi pdf
  104. Trapping of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). Journal of Fluid Mechanics 284 (1995) 359-375. doi pdf
  105. Fluid-solid interaction: acoustic scattering by a smooth elastic body. (With C.J. Luke). SIAM Journal on Applied Mathematics 55 (1995) 904-922. doi pdf
  106. Spectral methods for forward-propagating water waves in conformally-mapped channels. (With J.T. Kirby and R.A. Dalrymple). Applied Ocean Research 16 (1994) 249-266. doi pdf
  107. Scattering of water waves by submerged curved plates and by surface-piercing flat plates. (With N.F. Parsons). Applied Ocean Research 16 (1994) 129-139. doi pdf
  108. On the propagation of water waves along a porous-walled channel. (With R.A. Dalrymple). Proceedings of the Royal Society A 444 (1994) 411-428. doi pdf
  109. On amphidromic points. (With R.A. Dalrymple). Proceedings of the Royal Society A 444 (1994) 91-104. doi pdf
  110. Karp's theorem in elastodynamic inverse scattering. (With G. Dassios). Inverse Problems 9 (1993) 97-111. doi pdf
  111. Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle. (With P. Ola). Proceedings of the Royal Society of Edinburgh 123A (1993) 185-208. doi pdf
  112. A normal crack in an elastic half-space with stress-free surface. (With L. Paivarinta and S. Rempel). Mathematical Methods in the Applied Sciences 16 (1993) 563-579. doi pdf
  113. Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers. Journal of Nondestructive Evaluation 11 (1992) 167-174. doi pdf
  114. Scattering of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). Applied Ocean Research 14 (1992) 313-321. doi pdf
  115. Tip behaviour for cracks in bonded inhomogeneous materials. Journal of Engineering Mathematics 26 (1992) 467-480. doi pdf
  116. Perfect boundary conditions for parabolic water-wave models. (With R.A. Dalrymple). Proceedings of the Royal Society A 437 (1992) 41-54. doi pdf
  117. Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis. Journal of Engineering Mathematics 26 (1992) 267-280. doi pdf
  118. Exact solution of a simple hypersingular integral equation. Journal of Integral Equations and Applications 4 (1992) 197-204. doi pdf. Addendum: 5 (1993) 297.
  119. End-point behaviour of solutions to hypersingular integral equations. Proceedings of the Royal Society A 432 (1991) 301-320. doi pdf
  120. Reflection and transmission from porous structures under oblique wave attack. (With R.A. Dalrymple and M.A. Losada). Journal of Fluid Mechanics 224 (1991) 625-644. doi pdf
  121. Identification of irregular frequencies in simple direct integral-equation methods for scattering by homogeneous inclusions. Wave Motion 13 (1991) 185-192. doi pdf
  122. Wave diffraction through offshore breakwaters. (With R.A. Dalrymple). Journal of Waterway, Port, Coastal, and Ocean Engineering 116 (1990) 727-741. doi pdf
  123. On the scattering of elastic waves by an elastic inclusion in two dimensions. Quarterly Journal of Mechanics and Applied Mathematics 43 (1990) 275-291. doi pdf
  124. On hypersingular boundary integral equations for certain problems in mechanics. (With F.J. Rizzo and I.R. Gonsalves). Mechanics Research Communications 16 (1989) 65-71. doi pdf
  125. On boundary integral equations for crack problems. (With F.J. Rizzo). Proceedings of the Royal Society A 421 (1989) 341-355. doi pdf
  126. Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions. (With R.A. Dalrymple). Journal of Fluid Mechanics 188 (1988) 465-490. doi pdf
  127. On single integral equations for the transmission problem of acoustics. (With R.E. Kleinman). SIAM Journal on Applied Mathematics 48 (1988) 307-325. doi pdf
  128. Orthogonal polynomial solutions for elliptical cracks under shear loadings. Quarterly Journal of Mechanics and Applied Mathematics 39 (1986) 519-534. doi pdf
  129. Orthogonal polynomial solutions for pressurised elliptical cracks. Quarterly Journal of Mechanics and Applied Mathematics 39 (1986) 269-287. doi pdf
  130. Inverse scattering for geophysical problems. III. On the velocity-inversion problems of acoustics. (With A.G. Ramm). Proceedings of the Royal Society A 399 (1985) 153-166. doi pdf
  131. On the T-matrix for water-wave scattering problems. Wave Motion 7 (1985) 177-193. doi pdf
  132. Integral-equation methods for multiple-scattering problems II. Water waves. Quarterly Journal of Mechanics and Applied Mathematics 38 (1985) 119-133. doi pdf
  133. Integral-equation methods for multiple-scattering problems I. Acoustics. Quarterly Journal of Mechanics and Applied Mathematics 38 (1985) 105-118. doi pdf
  134. On the null-field equations for water-wave scattering problems. IMA Journal of Applied Mathematics 33 (1984) 55-69. doi pdf
  135. Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results. (With G.R. Wickham). Proceedings of the Royal Society A 390 (1983) 91-129. doi pdf
  136. The scattering of regular surface waves by a fixed, half-immersed, circular cylinder. (With A.G. Dixon). Applied Ocean Research 5 (1983) 13-23. doi pdf
  137. Acoustic scattering and radiation problems, and the null-field method. Wave Motion 4 (1982) 391-408. doi pdf
  138. The discontinuity in the elastostatic displacement vector across a penny-shaped crack under arbitrary loads. Journal of Elasticity 12 (1982) 201-218. doi pdf
  139. On the null-field equations for water-wave radiation problems. Journal of Fluid Mechanics 113 (1981) 315-332. doi pdf
  140. Diffraction of elastic waves by a penny-shaped crack. Proceedings of the Royal Society A 378 (1981) 263-285. doi pdf
  141. On the null-field equations for the exterior problems of acoustics. Quarterly Journal of Mechanics and Applied Mathematics 33 (1980) 385-396. doi pdf

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