{"id":25,"date":"2020-11-10T15:00:37","date_gmt":"2020-11-10T15:00:37","guid":{"rendered":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/?page_id=25"},"modified":"2024-11-29T16:33:35","modified_gmt":"2024-11-29T16:33:35","slug":"my-publications","status":"publish","type":"page","link":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/my-publications\/","title":{"rendered":"My Publications"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">My ORCID record is at&nbsp;<a href=\"https:\/\/orcid.org\/0000-0002-4392-5770\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/orcid.org\/0000-0002-4392-5770.<\/a><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\">Refereed Journal Publications<\/h2>\n\n\n\n<p>[1] `A note on the properties of a family of travelling wave solutions arising in cubic autocatalysis&#8217;,&nbsp;<em>Dynamics and Stability of Systems<\/em>, 1991,&nbsp;<strong>6<\/strong>, 1, 33-49. (with D.J.&nbsp;Needham).&nbsp;<br>[2] `The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves&#8217;,&nbsp;<em>Phil. Trans. R. Soc. Lond. A<\/em>, 1991,&nbsp;<strong>334<\/strong>, 1-24. (with D.J.&nbsp;Needham).&nbsp;<br>[3] `The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II. An initial value problem with an immobilized or nearly immobilized autocatalyst&#8217;,&nbsp;<em>Phil. Trans. R. Soc. Lond. A<\/em>, 1991,&nbsp;<strong>336<\/strong>, 497-539. (with D.J.&nbsp;Needham).&nbsp;<br>[4] `The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III. Large time development in quadratic autocatalysis&#8217;,&nbsp;<em>Quart. of App. Math.<\/em>, 1992,&nbsp;<strong>50<\/strong>, 347-372. (with D.J.&nbsp;Needham).&nbsp;<br>[5] `Mathematical modelling of chemical clock reactions. I. Induction, inhibition and the iodate-arsenous acid reaction&#8217;,&nbsp;<em>Phil. Trans. R. Soc. Lond. A<\/em>, 1992,&nbsp;<strong>340<\/strong>, 569- 591. (with D.J.&nbsp;Needham).&nbsp;<br>[6] `Mathematical modelling of chemical clock reactions. II. A class of autocatalytic clock reaction schemes&#8217;,&nbsp;<em>J. Eng. Math.<\/em>, 1993,&nbsp;<strong>27<\/strong>, 113-145. (with D.J.&nbsp;Needham).&nbsp;<br>[7] `Laminar, unidirectional flow of a thixotropic fluid in a circular pipe&#8217;,&nbsp;<em>J. Non-Newt. Fluid Mech.<\/em>, 1993,&nbsp;<strong>47<\/strong>, 21-55. (with J.W.J. Ferguson).&nbsp;<br>[8] `Simple chemical clock reactions: Application to cement hydration&#8217;,&nbsp;<em>J. Chem. Soc. Farad. Trans.<\/em>, 1993,&nbsp;<strong>89<\/strong>(16), 3021-3028. (with P.V. Coveney).&nbsp;<br>[9] `Exploring complexity in some simple nonlinear chemical kinetic schemes&#8217;,&nbsp;<em>J. Chem. Phys.<\/em>, 1994,&nbsp;<strong>100<\/strong>(3), 1921-1935. (with A.N. Chaudry and P.V. Coveney).&nbsp;<br>[10] `Computer-aided real-time kick analysis and control&#8217;,&nbsp;<em>SPE Drilling Engineering<\/em>, 1994, Sept. 199-205. (with S.I. Jardine and D.B. White).&nbsp;<br>[11] `Kinetics of self-replicating micelles&#8217;,&nbsp;<em>J. Chem. Soc. Farad. Trans.<\/em>, 1994,&nbsp;<strong>90<\/strong>(13), 1953-1959. (with P.V. Coveney).&nbsp;<br>[12] `The interaction of a fluid\/fluid interface with a flat plate&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>, 1995,&nbsp;<strong>296<\/strong>, 325-351. (with A.C. King).&nbsp;<br>[13] `Modelling the response of a vibrating element density meter in a two phase mixture&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>, 1997,&nbsp;<strong>340<\/strong>, 343-360.&nbsp;<br>[14] `Uniform asymptotic expansions for the Barnes double gamma function&#8217;,&nbsp;<em>Proc. Roy. Soc. Lond. A<\/em>. 1997,&nbsp;<strong>453<\/strong>, 1817-1829 (with A.C. King).&nbsp;<br>[15] `The moving contact line between two wedges of fluid on a flat plate&#8217;,&nbsp;<em>Quart. J. Mech. Appl. Math.<\/em>&nbsp;1999,&nbsp;<strong>53<\/strong>, 453-468 (with A.C. King and D.F. Popple).&nbsp;<br>[16] `Surface tension-driven flow in fat fluid wedges and cones&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>&nbsp;1999,&nbsp;<strong>397<\/strong>, 45-71.&nbsp;<br>[17] `Chemical clock reactions: The effect of precursor consumption&#8217;,&nbsp;<em>J. Math. Chem.<\/em>&nbsp;1999,&nbsp;<strong>26<\/strong>, 47-73 (with S.J. Preece and A.C. King).&nbsp;&nbsp;<br>[18] `Analysis of a model for a loaded, planar, solid oxide fuel cell&#8217;,&nbsp;<em>SIAM&nbsp;J. Appl. Math.&nbsp;<\/em>2000,&nbsp;<strong>60<\/strong>, 574-601 (with A.C. King, R.C. Copcutt and K. Kendall).&nbsp;&nbsp;<br>[19] `Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms&#8217;,&nbsp;<em>Dynamics and Stability of Systems<\/em>&nbsp;2000,&nbsp;<strong>15<\/strong>, 23-33.&nbsp;<br>[20] `Flow and reaction in solid oxide fuel cells&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>&nbsp;2000,&nbsp;<strong>411<\/strong>, 233-262 (with R.J. Cooper and A.C. King).&nbsp;&nbsp;&nbsp;<br>[21] `On modelling the formation of micelles in the presence of a slow influx of monomer&#8217;,&nbsp;<em>Quart. J. Mech. Appl. Math.&nbsp;<\/em>2000,&nbsp;<strong>53<\/strong>, 285-297.&nbsp;<br>[22] `Steady state solutions for strongly exothermic thermal ignition in symmetric geometries&#8217;,&nbsp;<em>IMA J. of Appl. Math.&nbsp;<\/em>2000,&nbsp;<strong>65<\/strong>, 283-313.&nbsp;<br>[23] `On the initial stages of cement hydration&#8217;,&nbsp;<em>J. Eng. Math.<\/em>&nbsp;2001,&nbsp;<strong>40<\/strong>, 43-58 (with S.J. Preece and A.C. King).&nbsp;<br>[24] `The evolution of travelling waves from chemical clock reactions&#8217;,&nbsp;<em>J. Eng. Math.<\/em>&nbsp;2001,&nbsp;<strong>39<\/strong>, 367-385 (with S.J. Preece and A.C. King).&nbsp;<br>[25] `The effect of heat loss on the propagation of strongly exothermic combustion waves&#8217;,&nbsp;<em>Combustion Theory and Modelling<\/em>&nbsp;2001,&nbsp;<strong>5<\/strong>, 319-342 (with G.N. Mercer).&nbsp;<br>[26] `Performance modelling of solid oxide fuel cells&#8217;,&nbsp;<em>Combustion Theory and Modelling<\/em>&nbsp;2001,&nbsp;<strong>5<\/strong>, 639-667 (with R.J. Cooper and A.C. King).&nbsp;<br>[27] `Nonlinear sloshing in zero gravity&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>&nbsp;2002,&nbsp;<strong>464<\/strong>, 365-391<strong>&nbsp;<\/strong><br>[28] `Eigenvalue problems in fuel cell dynamics&#8217;,&nbsp;<em>Proc. R. Soc. A&nbsp;<\/em>2003,&nbsp;<strong>459<\/strong>, 241-262 (with P.B. Bailey, R.J. Cooper, W.N. Everitt, A.C. King, Q. Hong, H. Wu and A. Zettl).&nbsp;<br>[29] `The effect of a retarder on the early stages of the hydration of tricalcium silicate&#8217;,&nbsp;<em>J. Eng. Math.&nbsp;<\/em>2003,&nbsp;<strong>45<\/strong>, 367-377 (with A. Salhan and A.C. King)&nbsp;<br>[30] `Dynamics of a strongly nonlocal reaction-diffusion population model&#8217;,&nbsp;<em>Nonlinearity&nbsp;<\/em>2003,&nbsp;<strong>17<\/strong>, 313-345.&nbsp;<br>[31] `A model of in-vivo hydrocephalus shunt dynamics for blockage and performance diagnostics&#8217;,&nbsp;<em>Mathematical Medicine and Biology&nbsp;<\/em>2004,&nbsp;<strong>21<\/strong>, 347-368. (with D. Schley and R.J. Marchbanks).&nbsp;<br>[32] `Surface tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops&#8217;,&nbsp;<em>J. Fluid Mech.&nbsp;<\/em>2005<em>,&nbsp;<\/em><strong>533<\/strong><em>,<\/em>&nbsp;193-221 (with A.C. King).&nbsp;&nbsp;<br>[33] `Dynamics of the oil-air interface in hard disk drive bearings&#8217;,&nbsp;<em>IEEE Trans. Mag.<\/em>&nbsp;2005,&nbsp;<strong>41<\/strong>, 2884-2886 (with F. Hendriks, B.S. Tilley, P.J. Dellar and R. Hinch).&nbsp;&nbsp;<br>[34] `A multiphase model for the early stages of the hydration of retarded oilwell cement&#8217;,&nbsp;<em>J. Eng. Math.&nbsp;<\/em>2005,<strong>&nbsp;53<\/strong>, 99-112 (with D.T.I. Francis, A.C. King and A.M. Harrisson).&nbsp;<br>[35] `The initial surface tension-driven flow of a wedge of viscous fluid&#8217;,&nbsp;<em>SIAM&nbsp;J. Appl. Math.&nbsp;<\/em>2005,<em>&nbsp;<\/em><strong>66<\/strong><em>,&nbsp;<\/em>510-532<em>&nbsp;<\/em><br>[36] `An asymptotic theory for the propagation of a surface-catalysed flame in a tube&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>&nbsp;2006,&nbsp;<strong>546<\/strong>, 363-394 (with F. Adamson, A.C. King and K. Kendall).&nbsp;&nbsp;<br><a href=\"submitted_paper.pdf\"><\/a>[37] &#8216;Stochastic elastohydrodynamics of a microcantilever oscillating near a wall&#8217;,&nbsp;<em>Phys. Rev. Lett.<\/em>&nbsp;2006,&nbsp;<strong>96,<\/strong>&nbsp;050801 (with&nbsp;R.J. Clarke, O.E. Jensen, A.P. Pearson and P.M. Williams).<br>[38] `Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender body analysis&#8217;,&nbsp;<em>Proc. R. Soc. Lond<\/em>. 2006,&nbsp;<strong>462<\/strong>,&nbsp; 913-933 (with R.J. Clarke, O.E. Jensen and P.M. Williams).<br>[39] `On a model for the motion of a contact line on a smooth solid surface&#8217;,&nbsp;<em>Euro. Jnl. Appl. Math<\/em>. 2006,&nbsp;<strong>17<\/strong>, 347-382&nbsp;&nbsp;<br>[40] `Surface tension-driven flow in a slender wedge&#8217;,&nbsp;<em>SIAM&nbsp;J. Appl. Math.&nbsp;<\/em>2006,<strong>&nbsp;66<\/strong>, 1949-1977<em>&nbsp;&nbsp;<\/em><br>[41] `The initial development of a jet caused by fluid, body and free-surface interaction. Part 2. An impulsively moved plate&#8217;,&nbsp;<em>J. Fluid Mech.&nbsp;<\/em>2007,&nbsp;<strong>578<\/strong>, 67-84<em>&nbsp;<\/em>(with D.J. Needham and A.C. King).&nbsp;<br><a href=\"InitialDevelopment3.pdf\"><\/a>[42] `Gravity-driven thin film flow using a new contact line model&#8217;,&nbsp;<em>IMA J. Appl. Math<\/em>. 2008,&nbsp;<strong>73<\/strong>, 4-36&nbsp;<br>[43] `The development of slugging in two-layer hydraulic flows&#8217;,&nbsp;<em>IMA J. Appl. Math.&nbsp;<\/em>2008,&nbsp;<strong>73<\/strong>, 274-322&nbsp;(with D.J.Needham, A.C.King and R.M.S.M.Schulkes)&nbsp;<br>[44] `Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube&#8217;,&nbsp;<em>IMA J. Appl. Math.&nbsp;<\/em>2008,&nbsp;<strong>73<\/strong>, 107-122 (with G.J. Sharpe and S.A.E.G. Falle).<br>[45] `On the stability of sheared menisci in Hele-Shaw cells&#8217;,&nbsp;<em>Mathematics-in-Industry Case Studies Journal&nbsp;<\/em>2008,&nbsp;<strong>1<\/strong>, 9-23<a href=\"MICS_tbh_final.pdf\">&nbsp;<\/a>(with B.S. Tilley and F. Hendriks).<br>[46] `The initial development of a jet caused by fluid, body and free-surface interaction. Part 3. An inclined accelerating plate&#8217;,&nbsp;<em>QJMAM<\/em>, 2008,&nbsp;<strong>61<\/strong>, 581-614&nbsp;(with D.J. Needham and P.G.Chamberlain).&nbsp;<br>[47] `A multiscale model for solute transport in a wavy-walled channel&#8217;,&nbsp;<em>J. Eng. Maths<\/em>., 2008,&nbsp;<strong>64<\/strong>, 25-48<em>&nbsp;<\/em>&nbsp;(with H.F. Woollard, O.E. Jensen and G. Lian)<br>[48] `Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall&#8217;,&nbsp;<em>Phys. Rev. E<\/em>, 2008,&nbsp;<strong>78<\/strong>, 056310 (with R. Clarke and O.E. Jensen).<br>[49] `A note on the unsteady motion under gravity of a corner point on a free surface &#8211; a generalization of Stokes&#8217; theory&#8217;,&nbsp;<em>Proc. R. Soc. A<\/em>&nbsp;, 2009,&nbsp;<strong>465<\/strong>, 165-173&nbsp;&nbsp;(with D.J. Needham).<br>[50] &#8216;Surface tension driven flow in a half plane&#8217;,&nbsp;<em>IMA J. Appl. Math,&nbsp;<\/em>2010,&nbsp;<strong>75<\/strong>, 857-880&nbsp;(with A.B. Thompson and R.H. Tew).<br>[51] &#8216;Geometrical modelling of abrasive waterjet footprints: a study for 90<sup>o<\/sup>&nbsp;jet impact angle&#8217;&nbsp;<em>CIRP Annals &#8211; &nbsp;Manufacturing Technology,&nbsp;<\/em>2010,&nbsp;<strong>59<\/strong>(1), 341-346<em>&nbsp;<\/em>(with D. Axinte, D. Srinivasu and M. Cooper).<br>[51] &#8216;Drops climbing uphill on an oscillating substrate&#8217;,&nbsp;<em>J. Fluid Mech,&nbsp;<\/em>2011,<strong>&nbsp;674<\/strong>, 93-119 (with E.S.Benilov).<br>[52] &#8216;Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Part I\u2014single straight paths&#8217;,<em>&nbsp;Int. J. Mach. Tools &amp; Manuf,<\/em>&nbsp;2012,<strong>&nbsp;53<\/strong>, 58-68 (with M.C. Kong, S. Anwar and&nbsp; D.A. Axinte).<br>[53] &#8216;Inviscid coalescence in the presence of a surrounding fluid&#8217;,<em>&nbsp;IMA J. Appl. Math<\/em>, 2013,&nbsp;<strong>77<\/strong>, 678-696 (with A.B. Thompson).<br>[54] &#8216;Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Part II- Overlapped single and multiple straight paths&#8217;,<em>&nbsp;Int. J. Mach. Tools &amp; Manuf,<\/em>&nbsp;2013,<strong>&nbsp;68<\/strong>, 30-39 (with M.C. Kong, C.B. Miron and&nbsp; D.A. Axinte).<br>[55] &#8216;Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux&#8217;,<em>&nbsp;J. Fluid Mech.<\/em>, 2013<strong>, 723<\/strong>, 706-733 (with F. Xu and O.E. Jensen).<br>[56] &#8216;A reaction diffusion model for inter-species competition and intra-species cooperation&#8217; &nbsp;<em>Math. Mod. Nat. Phenom.<\/em>&nbsp;2013,&nbsp;<strong>8<\/strong>,156-183. (with S.Rasheed)<br>[57] &#8216;Resonance-driven oscillations in a flexible channel flow with fixed upstream flux and a long downstream rigid segment&#8217;,&nbsp;<em>J. Fluid Mech.,&nbsp;<\/em>2014,&nbsp;<strong>746<\/strong>, 368-404 (with F. Xu and O.E. Jensen).<br>[58] &#8216;Stochastic modelling of abrasive waterjet footprints using finite element analysis&#8217;,<em>&nbsp;Int. J. Machine Tools and Manu.<\/em>, 2015,&nbsp;<strong>95<\/strong>, 39-51 (with P. Torrubia and D.A.Axinte).<br>[59] &#8216;The linear inverse problem in energy beam processing with an application to abrasive waterjet machining&#8217;,<em>&nbsp;Int. J. Machine Tools and Manu.<\/em>, 2015,&nbsp;<strong>99<\/strong>, 34-42 (with A. Bilbao Guillerna and D.A.Axinte).<br>[60] &#8216;Flows of granular material in two-dimensional channels&#8217;,&nbsp;<em>J. Eng. Math<\/em>, 2016,&nbsp;<strong>98<\/strong>, 49-20 (with O. Bain, P. Houston and I. Lowndes).<br>[61]&nbsp;&#8216;Stochastic simplified modelling of abrasive waterjet footprints&#8217;,&nbsp;<em>Proc. R. Soc. A<\/em>, 2016,&nbsp;<strong>472<\/strong>&nbsp;(with P. Lozano Torrubia and D.A. Axinte).<br>[62] &#8216;A spectral boundary integral method for inviscid water waves in a finite domain&#8217;,&nbsp;<em>Int. J. Numer. Meth. Fluids<\/em>, 2016,&nbsp;<strong>82<\/strong>, 437-448 (with J.S. Im).<br>[63] &#8216;Continuous trench, pulsed laser ablation for micro-machining applications&#8217;,<em>&nbsp;Int. J. Machine Tools and Manu.,&nbsp;<\/em>2016,&nbsp;<strong>107<\/strong>, 8-20 ( with G.B.J. Cadot and D.A. Axinte).<br>[64] &#8216;Thin three-dimensional droplets on an oscillating substrate with contact angle hysteresis&#8217;,&nbsp;<em>Phys. Rev. E<\/em>, 2016,&nbsp;<strong>93<\/strong>, 013123 (with J. Bradshaw).<br>[65] &#8216;A study of surface swelling caused by graphitisation during pulsed laser ablation of carbon allotrope with high content of sp3 bounds&#8217;,<em>&nbsp;J. Phys. D<\/em>, 2017,&nbsp;<strong>50<\/strong>, 245301 (with G.B.J Cadot and D.A. Axinte).&nbsp;<a href=\"https:\/\/doi.org\/10.1088\/1361-6463\/aa70fe\">https:\/\/doi.org\/10.1088\/1361-6463\/aa70fe<\/a><br>[66] &#8216;Waterjet and Laser Etching: The Nonlinear Inverse Problem&#8217;,&nbsp;<em>R. Soc. Open Science,&nbsp;<\/em>2017<em>,<\/em><strong>4<\/strong>:161031<em>,&nbsp;<\/em>&nbsp;(with A. Bilbao Guillerna, D.A. Axinte and G.B.J. Cadot).&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1707.01392\">http:\/\/rsos.royalsocietypublishing.org\/content\/royopensci\/4\/7\/161031.full.pdf<\/a><br>[67] &#8216;New models for energy beam machining enable accurate generation of free forms&#8217;,&nbsp;<em>Science Advances,<\/em>&nbsp;2017,&nbsp;<strong>3<\/strong>, e1701202,&nbsp;(with A. Bilbao Guillerna and D.A. Axinte).&nbsp;<a href=\"http:\/\/advances.sciencemag.org\/content\/3\/9\/e1701201\">http:\/\/advances.sciencemag.org\/content\/3\/9\/e1701201<\/a><br>[68] &#8216;Novel approach based on continuous trench modelling to predict focused ion beam prepared freeform surfaces&#8217;.&nbsp;<em>J. Mat. Proc. Tech.<\/em>, (with A. Bilbao Guillerna, D.A. Axinte, G.B.J. Cadot, M. Rommel, F. Stumpf and S. Beuer).&nbsp;<a href=\"https:\/\/doi.org\/10.1016\/j.jmatprotec.2017.10.024\">https:\/\/doi.org\/10.1016\/j.jmatprotec.2017.10.024<\/a><br>[69] &#8216;The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface&#8217;,&nbsp;<em>J. Fluid Mech.<\/em>, 2018,&nbsp;<strong>836<\/strong>, 850-872. (with D.J. Needham, R, Munro and E. Korsukova).&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/dx.doi.org\/10.1017\/jfm.2017.843\" target=\"_blank\">http:\/\/dx.doi.org\/10.1017\/jfm.2017.843<\/a><br>[70] &#8216;Thick drops climbing uphill on an oscillating substrate&#8217;,&nbsp;<em>J. Fluid Mech<\/em>., 2018,&nbsp;<strong>840<\/strong>, 131-153 (with J. Bradshaw).<br>[71] &#8216;The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerating or retreating plate. Part 1. The principal flow.&#8217;&nbsp;<em>J. Fluid Mech.,&nbsp;<\/em>2018,&nbsp;<strong>841<\/strong>, 109-145 (with M.T. Gallagher and D.J.Needham).<br>[72] &#8216;The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerating or retreating plate. Part 2. Well-posedness and stability of the principal flow.&#8217;&nbsp;<em>J. Fluid Mech.,&nbsp;<\/em><strong>841<\/strong>, 146-166 (with M.T. Gallagher and D.J.Needham).<br>[73] &#8216;Investigation of the microstructure change due to phase transition in nanosecond pulsed laser processing of diamond&#8217;,&nbsp;<em>Carbon<\/em>, 2018,&nbsp;<strong>127<\/strong>, 349-365 (with G.B.J. Cadot, K. Thomas, J.P. Best, A.A. Taylor, J. Michler and D.A. Axinte)<br>[74] &#8216;The effect of inclination on the development of slugging in channel flow&#8217;,&nbsp;<em>IMA J. Appl. Math.,&nbsp;<\/em>2019,&nbsp;<strong>84<\/strong>, 366-384 (with J.A. Giddings).<br>[75] &#8216;On modelling of laser assisted machining: Forward and inverse problems for heat placement control&#8217;,<em>&nbsp;Int. J. Machine Tools and Manu.,&nbsp;<\/em>2019,&nbsp;<strong>138<\/strong>, 36-50 ( with Z. Shang, Z. Liao, J.A. Sarasua and D.A. Axinte).<br>[76] &#8216;Time-dependent manufacturing processes lead to a new class of inverse problems&#8217;,&nbsp;<em>PNAS<\/em>, 2019,&nbsp;<strong>116<\/strong>, 5341-5343 (with D.A. Axinte).<\/p>\n\n\n\n<p>[77] &#8216;Geometrical modelling of pulsed laser ablation of high performance metallic alloys&#8217;, <em>IJMTM<\/em>, 2019, <strong>141<\/strong>, 78-88 (with D. Cha and D.A. Axinte)<br>[78] &#8216;A dam-break driven by a moving source: a simple model for a powder snow avalanche&#8217;,&nbsp;<em>J. Fluid Mech.,&nbsp;<\/em>2019,&nbsp;<strong>870<\/strong>, 353-388.<br>[79] &#8216;Slow travelling wave solutions of the nonlocal Fisher-KPP equation&#8217;,&nbsp;<em>Nonlinearity<\/em>, 2020,&nbsp;<strong>33<\/strong>, 2106.<\/p>\n\n\n\n<p>[80] &#8216;Slugging in horizontal channel flow&#8217;, <em>IMA Applied Math<\/em>., 2022, (with J.A. Giddings and S.M. Cox).<\/p>\n\n\n\n<p>[81] &#8216;Nonlocal effects on travelling waves arising in a moving boundary reaction-diffusion model&#8217;, <em>J. Phys. A<\/em>, 2022, (with N. Fadai).<\/p>\n\n\n\n<p>[82] &#8216;Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I General theory and the near local limit&#8217;. <em>Nonlinearity<\/em>, 2022 (with D.J. Needham).<\/p>\n\n\n\n<p>[83] &#8216;On modelling coolant penetration into the microchannels at the tool-workpiece interface&#8217;, <em>J. Man. Proc<\/em>., 2022 (with D.A. Axinte et al).<\/p>\n\n\n\n<p>[84] &#8216;The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large-time asymptotics&#8217;, <em>St. App. Math<\/em>., 2023 (with D.J. Needham and J.C. Meyer)<\/p>\n\n\n\n<p>[85] &#8216;A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem&#8217;, <em>Proc. R. Soc A.<\/em>, 2023 (with Yang, Y., Axinte, D.A. and Liao, Z.).<\/p>\n\n\n\n<p>[86] The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 2. The Cauchy problem on a finite interval, (with D.J. Needham), <a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/2304.10935\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2304.10935<\/a>.<\/p>\n\n\n\n<p>[87]  The nonlocal Lotka &#8211; Volterra system with a top hat kernel. Part 1. Dynamics and steady states with small diffusivity, <em>Proc. R Soc. A., <\/em>2023<em> <\/em>(with D.J. Needham).<\/p>\n\n\n\n<p>[88] Efficient and scalable inverse kinematics for continuum robots,<em> IEEE Robotics and Automation Letters<\/em>, 2023 (with S. Wild, D.A. Axinte et al), <a href=\"http:\/\/dx.doi.org\/10.1109\/LRA.2023.3331291\">http:\/\/dx.doi.org\/10.1109\/LRA.2023.3331291<\/a>.<\/p>\n\n\n\n<p>[89] Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth, <em>Math. Med. Bio.<\/em>, 2023 (with J. Jepson, N. Fadai and R. O&#8217;Dea), <a href=\"https:\/\/doi.org\/10.1093\/imammb\/dqad008\">https:\/\/doi.org\/10.1093\/imammb\/dqad008<\/a><\/p>\n\n\n\n<p>[90] The inverse heat placement problem in metal additive manufacturing: Why a rational approach is needed for powder bed fusion, <em>J. Mat. Proc. Tech.<\/em>, 2024 (with H. Yeung, D. Axinte and J. Fox), <a rel=\"noreferrer noopener\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0924013624001651\" target=\"_blank\">https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0924013624001651<\/a><\/p>\n\n\n\n<p>[91] Lubrication flow in grinding,<em> J. Eng. Math<\/em>, 2024 (with Z. Crowson and P. Houston), <a rel=\"noreferrer noopener\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s10665-024-10383-x\" target=\"_blank\">https:\/\/link.springer.com\/article\/10.1007\/s10665-024-10383-x<\/a><\/p>\n\n\n\n<p>[92] The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line, <em>EJAM<\/em>, 2024 (with D.J. Needham) <a href=\"https:\/\/doi.org\/10.1017\/s0956792524000688\">https:\/\/doi.org\/10.1017\/s0956792524000688<\/a><\/p>\n\n\n\n<p>[93] Slow travelling wave solutions of the mixed local-nonlocal Fisher-KPP equation can have multiple sharp wavefronts. <em>Proc. R. Soc. A<\/em>, 2024 (with J. Lee) <a href=\"https:\/\/doi.org\/10.1098\/rspa.2024.0508\">https:\/\/doi.org\/10.1098\/rspa.2024.0508<\/a><\/p>\n\n\n\n<p>[94] A Shape-Newton method for free boundary problems subject to the Bernoulli boundary condition. <em>SIAM J. Sci. Comp.<\/em>, 2024 (with Y. Fan and K. van der Zee) <a href=\"https:\/\/doi.org\/10.1137\/23m1590263\">https:\/\/doi.org\/10.1137\/23m1590263<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Books<\/h2>\n\n\n\n<p>[1]&nbsp;<a href=\"http:\/\/uk.cambridge.org\/catalogue\/catalogue.asp?isbn=0521634504\">`Wave Motion&#8217;<\/a>, 2001,&nbsp;Cambridge&nbsp;University&nbsp;Press (with A.C. King).<br>[2]&nbsp;<a href=\"http:\/\/uk.cambridge.org\/catalogue\/catalogue.asp?isbn=0521016878\">&#8216;Differential Equations: Linear, Nonlinear, Ordinary, Partial&#8217;<\/a>, 2003,&nbsp;Cambridge&nbsp;University&nbsp;Press, (with A.C. King and S.R.Otto).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Poker<\/strong><br>[1]<a href=\"https:\/\/arxiv.org\/abs\/1802.04670\">&nbsp;<\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.amazon.co.uk\/Education-Modern-Poker-Player\/dp\/1909457116\/ref=tmm_pap_swatch_0?_encoding=UTF8&amp;qid=1700565214&amp;sr=8-4\" target=\"_blank\">&#8216;The Education of a Modern Poker Player&#8217;<\/a>,&nbsp;2013, D &amp; B Poker Books (with T. Tiroch and E.E. Cinca).<br>[2] &#8216;Simplified three player Kuhn poker&#8217;, 2017,&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1704.08124\">https:\/\/arxiv.org\/abs\/1704.08124<\/a><br>[3] &#8216;Full street simplified three player Kuhn poker&#8217;, 2017,&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1707.01392\">https:\/\/arxiv.org\/abs\/1707.01392<\/a><br>[4] &#8216;Equilibrium solutions of three player Kuhn poker with N&gt;3 cards: A new numerical method using regularization and arc-length continuation&#8217;, 2018,&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1802.04670\">https:\/\/arxiv.org\/abs\/1802.04670<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Study Group Reports<\/h2>\n\n\n\n<p>[1]&nbsp;<em>Curvature of the spine: Hydrostatic pressure as an indicator of scoliosis.<\/em>&nbsp;Proceedings of the Second Mathematics-in Medicine Study Group, Nottingham 2001. (with C. Breward and P. Howell)<br>[2]&nbsp;<em>In vivo dynamic testing of hydrocephalus shunts.<\/em>&nbsp;Proceedings of the Third Mathematics-in Medicine Study Group, Nottingham 2002. (with D. Schley)<br>[3]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/140\/index.html\"><em>Free surface cusp formation as a failure mechanism for hard disk drives with fluid dynamic bearings.<\/em><\/a>&nbsp;US Workshop on Mathematical Problems in Industry&nbsp;&gt;&nbsp;20th MPI [Delaware&nbsp;21\/6\/2004 &#8211; 25\/6\/2004]&nbsp;(with lots of other people)<br>[4]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/72\/index.html\"><em>Stability of the Oil-Air Boundary in Fluid Dynamic Bearings of Hard Disk Drives.<\/em><\/a>&nbsp;US Workshop on Mathematical Problems in Industry&nbsp;&gt;&nbsp;21st MPI [Worcester&nbsp;13\/6\/2005 &#8211; 17\/6\/2005]&nbsp;(with lots of other people)<br>[5]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/71\/index.html\"><em>Enhanced Leak Detection.<\/em><\/a>&nbsp;US Workshop on Mathematical Problems in Industry&nbsp;&gt;&nbsp;21st MPI [Worcester&nbsp;13\/6\/2005 &#8211; 17\/6\/2005]&nbsp;(with lots of other people)<br>[6]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/34\/index.html\"><em>Design of microfluidic networks.<\/em><\/a>&nbsp;European Study Group with Industry&nbsp;&gt;&nbsp;49th ESGI [Oxford&nbsp;29\/3\/2004 &#8211; 4\/4\/2004]&nbsp;(with&nbsp;A. Grief, D. Leppinen&nbsp;and&nbsp;N.&nbsp;Ovenden)<br>[7]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/69\/index.html\"><em>Frequency reassignment in cellular phone networks.<\/em><\/a>&nbsp;European Study Group with Industry&nbsp;&gt;&nbsp;53rd ESGI [Manchester&nbsp;21\/3\/2005 &#8211; 24\/3\/2005]&nbsp;(with R.&nbsp;Leese&nbsp;and&nbsp;H. Rajaniemi)<br>[8]&nbsp;<em><a href=\"https:\/\/miis.maths.ox.ac.uk\/101\/index.html\">Forecasting triads: the negative feedback problem<\/a>.<\/em>&nbsp;European Study Group with Industry&nbsp;&gt;&nbsp;56th ESGI [Bath 3\/4\/2006 &#8211; 7\/4\/2006]&nbsp; (with R.E.&nbsp;Hunt, L.Clarke&nbsp;and J.&nbsp;Byatt-Smith)<br>[9]&nbsp;<em><a href=\"https:\/\/miis.maths.ox.ac.uk\/138\/index.html\">Managing product maturity<\/a>.<\/em>&nbsp;European Study Group with Industry&nbsp;&gt;&nbsp;59th ESGI [Nottingham&nbsp;26\/3\/2007 &#8211; 30\/3\/2007] (with&nbsp;R. Hadji, D. Hewett, M. Jaroszewski, R. Pachon, D.&nbsp;Szotten&nbsp;and&nbsp;R.E. Wilson)<br>[10]<em>&nbsp;<\/em><a href=\"https:\/\/miis.maths.ox.ac.uk\/716\/index.html\">Emitter-platform association.<\/a><em>&nbsp;<\/em>European Study Group with Industry &gt; &nbsp;73rd ESGI [Warwick 12\/4\/2010 &#8211; 16\/4\/2010] (with D.Barton, F. Theil and others)<br>[11]&nbsp;<a href=\"https:\/\/miis.maths.ox.ac.uk\/726\/index.html\">Optimisation of Car Park Designs<\/a><em>.&nbsp;<\/em>European Study Group with Industry &gt; &nbsp;91st ESGI [Bristol &nbsp;15\/4\/2013 &#8211; 19\/4\/2013] (with &nbsp;R. Porter, J. Bradshaw and others)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Popular Mathematics<\/h2>\n\n\n\n<p>[1] &#8216;Kissing the Frog: A Mathematician&#8217;s Guide to Mating&#8217;,&nbsp;&nbsp;<a href=\"http:\/\/plus.maths.org\/content\/os\/issue48\/features\/billingham\/index\">PLUS Magazine<\/a>.<br>[2] &#8216;Bluffing and exploitation: An introduction to poker maths&#8217;,<a href=\"http:\/\/plus.maths.org\/content\/bluffing-and-exploitation-introduction-poker-maths\">&nbsp;PLUS Magazine<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>My ORCID record is at&nbsp;https:\/\/orcid.org\/0000-0002-4392-5770. Refereed Journal Publications [1] `A note on the properties of a family of travelling wave&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/pages\/25"}],"collection":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/comments?post=25"}],"version-history":[{"count":19,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/pages\/25\/revisions"}],"predecessor-version":[{"id":91,"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/pages\/25\/revisions\/91"}],"wp:attachment":[{"href":"https:\/\/www.maths.nottingham.ac.uk\/personal\/pmzjb1\/wp-json\/wp\/v2\/media?parent=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}