My ORCID record is at https://orcid.org/0000-0002-4392-5770.

Refereed Journal Publications

[1] `A note on the properties of a family of travelling wave solutions arising in cubic autocatalysis’, Dynamics and Stability of Systems, 1991, 6, 1, 33-49. (with D.J. Needham). 
[2] `The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves’, Phil. Trans. R. Soc. Lond. A, 1991, 334, 1-24. (with D.J. Needham). 
[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’, Phil. Trans. R. Soc. Lond. A, 1991, 336, 497-539. (with D.J. Needham). 
[4] `The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III. Large time development in quadratic autocatalysis’, Quart. of App. Math., 1992, 50, 347-372. (with D.J. Needham). 
[5] `Mathematical modelling of chemical clock reactions. I. Induction, inhibition and the iodate-arsenous acid reaction’, Phil. Trans. R. Soc. Lond. A, 1992, 340, 569- 591. (with D.J. Needham). 
[6] `Mathematical modelling of chemical clock reactions. II. A class of autocatalytic clock reaction schemes’, J. Eng. Math., 1993, 27, 113-145. (with D.J. Needham). 
[7] `Laminar, unidirectional flow of a thixotropic fluid in a circular pipe’, J. Non-Newt. Fluid Mech., 1993, 47, 21-55. (with J.W.J. Ferguson). 
[8] `Simple chemical clock reactions: Application to cement hydration’, J. Chem. Soc. Farad. Trans., 1993, 89(16), 3021-3028. (with P.V. Coveney). 
[9] `Exploring complexity in some simple nonlinear chemical kinetic schemes’, J. Chem. Phys., 1994, 100(3), 1921-1935. (with A.N. Chaudry and P.V. Coveney). 
[10] `Computer-aided real-time kick analysis and control’, SPE Drilling Engineering, 1994, Sept. 199-205. (with S.I. Jardine and D.B. White). 
[11] `Kinetics of self-replicating micelles’, J. Chem. Soc. Farad. Trans., 1994, 90(13), 1953-1959. (with P.V. Coveney). 
[12] `The interaction of a fluid/fluid interface with a flat plate’, J. Fluid Mech., 1995, 296, 325-351. (with A.C. King). 
[13] `Modelling the response of a vibrating element density meter in a two phase mixture’, J. Fluid Mech., 1997, 340, 343-360. 
[14] `Uniform asymptotic expansions for the Barnes double gamma function’, Proc. Roy. Soc. Lond. A. 1997, 453, 1817-1829 (with A.C. King). 
[15] `The moving contact line between two wedges of fluid on a flat plate’, Quart. J. Mech. Appl. Math. 1999, 53, 453-468 (with A.C. King and D.F. Popple). 
[16] `Surface tension-driven flow in fat fluid wedges and cones’, J. Fluid Mech. 1999, 397, 45-71. 
[17] `Chemical clock reactions: The effect of precursor consumption’, J. Math. Chem. 1999, 26, 47-73 (with S.J. Preece and A.C. King).  
[18] `Analysis of a model for a loaded, planar, solid oxide fuel cell’, SIAM J. Appl. Math. 2000, 60, 574-601 (with A.C. King, R.C. Copcutt and K. Kendall).  
[19] `Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms’, Dynamics and Stability of Systems 2000, 15, 23-33. 
[20] `Flow and reaction in solid oxide fuel cells’, J. Fluid Mech. 2000, 411, 233-262 (with R.J. Cooper and A.C. King).   
[21] `On modelling the formation of micelles in the presence of a slow influx of monomer’, Quart. J. Mech. Appl. Math. 2000, 53, 285-297. 
[22] `Steady state solutions for strongly exothermic thermal ignition in symmetric geometries’, IMA J. of Appl. Math. 2000, 65, 283-313. 
[23] `On the initial stages of cement hydration’, J. Eng. Math. 2001, 40, 43-58 (with S.J. Preece and A.C. King). 
[24] `The evolution of travelling waves from chemical clock reactions’, J. Eng. Math. 2001, 39, 367-385 (with S.J. Preece and A.C. King). 
[25] `The effect of heat loss on the propagation of strongly exothermic combustion waves’, Combustion Theory and Modelling 2001, 5, 319-342 (with G.N. Mercer). 
[26] `Performance modelling of solid oxide fuel cells’, Combustion Theory and Modelling 2001, 5, 639-667 (with R.J. Cooper and A.C. King). 
[27] `Nonlinear sloshing in zero gravity’, J. Fluid Mech. 2002, 464, 365-391 
[28] `Eigenvalue problems in fuel cell dynamics’, Proc. R. Soc. A 2003, 459, 241-262 (with P.B. Bailey, R.J. Cooper, W.N. Everitt, A.C. King, Q. Hong, H. Wu and A. Zettl). 
[29] `The effect of a retarder on the early stages of the hydration of tricalcium silicate’, J. Eng. Math. 2003, 45, 367-377 (with A. Salhan and A.C. King) 
[30] `Dynamics of a strongly nonlocal reaction-diffusion population model’, Nonlinearity 2003, 17, 313-345. 
[31] `A model of in-vivo hydrocephalus shunt dynamics for blockage and performance diagnostics’, Mathematical Medicine and Biology 2004, 21, 347-368. (with D. Schley and R.J. Marchbanks). 
[32] `Surface tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops’, J. Fluid Mech. 2005533, 193-221 (with A.C. King).  
[33] `Dynamics of the oil-air interface in hard disk drive bearings’, IEEE Trans. Mag. 2005, 41, 2884-2886 (with F. Hendriks, B.S. Tilley, P.J. Dellar and R. Hinch).  
[34] `A multiphase model for the early stages of the hydration of retarded oilwell cement’, J. Eng. Math. 2005, 53, 99-112 (with D.T.I. Francis, A.C. King and A.M. Harrisson). 
[35] `The initial surface tension-driven flow of a wedge of viscous fluid’, SIAM J. Appl. Math. 2005, 66510-532 
[36] `An asymptotic theory for the propagation of a surface-catalysed flame in a tube’, J. Fluid Mech. 2006, 546, 363-394 (with F. Adamson, A.C. King and K. Kendall).  
[37] ‘Stochastic elastohydrodynamics of a microcantilever oscillating near a wall’, Phys. Rev. Lett. 2006, 96, 050801 (with R.J. Clarke, O.E. Jensen, A.P. Pearson and P.M. Williams).
[38] `Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender body analysis’, Proc. R. Soc. Lond. 2006, 462,  913-933 (with R.J. Clarke, O.E. Jensen and P.M. Williams).
[39] `On a model for the motion of a contact line on a smooth solid surface’, Euro. Jnl. Appl. Math. 2006, 17, 347-382  
[40] `Surface tension-driven flow in a slender wedge’, SIAM J. Appl. Math. 2006, 66, 1949-1977  
[41] `The initial development of a jet caused by fluid, body and free-surface interaction. Part 2. An impulsively moved plate’, J. Fluid Mech. 2007, 578, 67-84 (with D.J. Needham and A.C. King). 
[42] `Gravity-driven thin film flow using a new contact line model’, IMA J. Appl. Math. 2008, 73, 4-36 
[43] `The development of slugging in two-layer hydraulic flows’, IMA J. Appl. Math. 2008, 73, 274-322 (with D.J.Needham, A.C.King and R.M.S.M.Schulkes) 
[44] `Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube’, IMA J. Appl. Math. 2008, 73, 107-122 (with G.J. Sharpe and S.A.E.G. Falle).
[45] `On the stability of sheared menisci in Hele-Shaw cells’, Mathematics-in-Industry Case Studies Journal 2008, 1, 9-23 (with B.S. Tilley and F. Hendriks).
[46] `The initial development of a jet caused by fluid, body and free-surface interaction. Part 3. An inclined accelerating plate’, QJMAM, 2008, 61, 581-614 (with D.J. Needham and P.G.Chamberlain). 
[47] `A multiscale model for solute transport in a wavy-walled channel’, J. Eng. Maths., 2008, 64, 25-48  (with H.F. Woollard, O.E. Jensen and G. Lian)
[48] `Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall’, Phys. Rev. E, 2008, 78, 056310 (with R. Clarke and O.E. Jensen).
[49] `A note on the unsteady motion under gravity of a corner point on a free surface – a generalization of Stokes’ theory’, Proc. R. Soc. A , 2009, 465, 165-173  (with D.J. Needham).
[50] ‘Surface tension driven flow in a half plane’, IMA J. Appl. Math, 2010, 75, 857-880 (with A.B. Thompson and R.H. Tew).
[51] ‘Geometrical modelling of abrasive waterjet footprints: a study for 90o jet impact angle’ CIRP Annals –  Manufacturing Technology, 2010, 59(1), 341-346 (with D. Axinte, D. Srinivasu and M. Cooper).
[51] ‘Drops climbing uphill on an oscillating substrate’, J. Fluid Mech, 2011, 674, 93-119 (with E.S.Benilov).
[52] ‘Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Part I—single straight paths’, Int. J. Mach. Tools & Manuf, 2012, 53, 58-68 (with M.C. Kong, S. Anwar and  D.A. Axinte).
[53] ‘Inviscid coalescence in the presence of a surrounding fluid’, IMA J. Appl. Math, 2013, 77, 678-696 (with A.B. Thompson).
[54] ‘Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Part II- Overlapped single and multiple straight paths’, Int. J. Mach. Tools & Manuf, 2013, 68, 30-39 (with M.C. Kong, C.B. Miron and  D.A. Axinte).
[55] ‘Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux’, J. Fluid Mech., 2013, 723, 706-733 (with F. Xu and O.E. Jensen).
[56] ‘A reaction diffusion model for inter-species competition and intra-species cooperation’  Math. Mod. Nat. Phenom. 2013, 8,156-183. (with S.Rasheed)
[57] ‘Resonance-driven oscillations in a flexible channel flow with fixed upstream flux and a long downstream rigid segment’, J. Fluid Mech., 2014, 746, 368-404 (with F. Xu and O.E. Jensen).
[58] ‘Stochastic modelling of abrasive waterjet footprints using finite element analysis’, Int. J. Machine Tools and Manu., 2015, 95, 39-51 (with P. Torrubia and D.A.Axinte).
[59] ‘The linear inverse problem in energy beam processing with an application to abrasive waterjet machining’, Int. J. Machine Tools and Manu., 2015, 99, 34-42 (with A. Bilbao Guillerna and D.A.Axinte).
[60] ‘Flows of granular material in two-dimensional channels’, J. Eng. Math, 2016, 98, 49-20 (with O. Bain, P. Houston and I. Lowndes).
[61] ‘Stochastic simplified modelling of abrasive waterjet footprints’, Proc. R. Soc. A, 2016, 472 (with P. Lozano Torrubia and D.A. Axinte).
[62] ‘A spectral boundary integral method for inviscid water waves in a finite domain’, Int. J. Numer. Meth. Fluids, 2016, 82, 437-448 (with J.S. Im).
[63] ‘Continuous trench, pulsed laser ablation for micro-machining applications’, Int. J. Machine Tools and Manu., 2016, 107, 8-20 ( with G.B.J. Cadot and D.A. Axinte).
[64] ‘Thin three-dimensional droplets on an oscillating substrate with contact angle hysteresis’, Phys. Rev. E, 2016, 93, 013123 (with J. Bradshaw).
[65] ‘A study of surface swelling caused by graphitisation during pulsed laser ablation of carbon allotrope with high content of sp3 bounds’, J. Phys. D, 2017, 50, 245301 (with G.B.J Cadot and D.A. Axinte). https://doi.org/10.1088/1361-6463/aa70fe
[66] ‘Waterjet and Laser Etching: The Nonlinear Inverse Problem’, R. Soc. Open Science, 2017,4:161031 (with A. Bilbao Guillerna, D.A. Axinte and G.B.J. Cadot). http://rsos.royalsocietypublishing.org/content/royopensci/4/7/161031.full.pdf
[67] ‘New models for energy beam machining enable accurate generation of free forms’, Science Advances, 2017, 3, e1701202, (with A. Bilbao Guillerna and D.A. Axinte). http://advances.sciencemag.org/content/3/9/e1701201
[68] ‘Novel approach based on continuous trench modelling to predict focused ion beam prepared freeform surfaces’. J. Mat. Proc. Tech., (with A. Bilbao Guillerna, D.A. Axinte, G.B.J. Cadot, M. Rommel, F. Stumpf and S. Beuer). https://doi.org/10.1016/j.jmatprotec.2017.10.024
[69] ‘The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface’, J. Fluid Mech., 2018, 836, 850-872. (with D.J. Needham, R, Munro and E. Korsukova). http://dx.doi.org/10.1017/jfm.2017.843
[70] ‘Thick drops climbing uphill on an oscillating substrate’, J. Fluid Mech., 2018, 840, 131-153 (with J. Bradshaw).
[71] ‘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.’ J. Fluid Mech., 2018, 841, 109-145 (with M.T. Gallagher and D.J.Needham).
[72] ‘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.’ J. Fluid Mech., 841, 146-166 (with M.T. Gallagher and D.J.Needham).
[73] ‘Investigation of the microstructure change due to phase transition in nanosecond pulsed laser processing of diamond’, Carbon, 2018, 127, 349-365 (with G.B.J. Cadot, K. Thomas, J.P. Best, A.A. Taylor, J. Michler and D.A. Axinte)
[74] ‘The effect of inclination on the development of slugging in channel flow’, IMA J. Appl. Math., 2019, 84, 366-384 (with J.A. Giddings).
[75] ‘On modelling of laser assisted machining: Forward and inverse problems for heat placement control’, Int. J. Machine Tools and Manu., 2019, 138, 36-50 ( with Z. Shang, Z. Liao, J.A. Sarasua and D.A. Axinte).
[76] ‘Time-dependent manufacturing processes lead to a new class of inverse problems’, PNAS, 2019, 116, 5341-5343 (with D.A. Axinte).
[77] ‘A dam-break driven by a moving source: a simple model for a powder snow avalanche’, J. Fluid Mech., 2019, 870, 353-388.
[78] ‘Slow travelling wave solutions of the nonlocal Fisher-KPP equation’, Nonlinearity, 2020, 33, 2106.

Books

[1] `Wave Motion’, 2001, Cambridge University Press (with A.C. King).
[2] ‘Differential Equations: Linear, Nonlinear, Ordinary, Partial’, 2003, Cambridge University Press, (with A.C. King and S.R.Otto).

Poker
[1] ‘The Education of a Modern Poker Player’, 2013, D & B Poker Books (with T. Tiroch and E.E. Cinca).
[2] ‘Simplified three player Kuhn poker’, 2017, https://arxiv.org/abs/1704.08124
[3] ‘Full street simplified three player Kuhn poker’, 2017, https://arxiv.org/abs/1707.01392
[4] ‘Equilibrium solutions of three player Kuhn poker with N>3 cards: A new numerical method using regularization and arc-length continuation’, 2018, https://arxiv.org/abs/1802.04670

Study Group Reports

[1] Curvature of the spine: Hydrostatic pressure as an indicator of scoliosis. Proceedings of the Second Mathematics-in Medicine Study Group, Nottingham 2001. (with C. Breward and P. Howell)
[2] In vivo dynamic testing of hydrocephalus shunts. Proceedings of the Third Mathematics-in Medicine Study Group, Nottingham 2002. (with D. Schley)
[3] Free surface cusp formation as a failure mechanism for hard disk drives with fluid dynamic bearings. US Workshop on Mathematical Problems in Industry > 20th MPI [Delaware 21/6/2004 – 25/6/2004] (with lots of other people)
[4] Stability of the Oil-Air Boundary in Fluid Dynamic Bearings of Hard Disk Drives. US Workshop on Mathematical Problems in Industry > 21st MPI [Worcester 13/6/2005 – 17/6/2005] (with lots of other people)
[5] Enhanced Leak Detection. US Workshop on Mathematical Problems in Industry > 21st MPI [Worcester 13/6/2005 – 17/6/2005] (with lots of other people)
[6] Design of microfluidic networks. European Study Group with Industry > 49th ESGI [Oxford 29/3/2004 – 4/4/2004] (with A. Grief, D. Leppinen and N. Ovenden)
[7] Frequency reassignment in cellular phone networks. European Study Group with Industry > 53rd ESGI [Manchester 21/3/2005 – 24/3/2005] (with R. Leese and H. Rajaniemi)
[8] Forecasting triads: the negative feedback problem. European Study Group with Industry > 56th ESGI [Bath 3/4/2006 – 7/4/2006]  (with R.E. Hunt, L.Clarke and J. Byatt-Smith)
[9] Managing product maturity. European Study Group with Industry > 59th ESGI [Nottingham 26/3/2007 – 30/3/2007] (with R. Hadji, D. Hewett, M. Jaroszewski, R. Pachon, D. Szotten and R.E. Wilson)
[10] Emitter-platform association. European Study Group with Industry >  73rd ESGI [Warwick 12/4/2010 – 16/4/2010] (with D.Barton, F. Theil and others)
[11] Optimisation of Car Park DesignsEuropean Study Group with Industry >  91st ESGI [Bristol  15/4/2013 – 19/4/2013] (with  R. Porter, J. Bradshaw and others)

Popular Mathematics

[1] ‘Kissing the Frog: A Mathematician’s Guide to Mating’,  PLUS Magazine.
[2] ‘Bluffing and exploitation: An introduction to poker maths’, PLUS Magazine.