## 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. *2005*, ***533***,* 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,* ***66***, *510-532* *

[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 90^{o} 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] ‘Geometrical modelling of pulsed laser ablation of high performance metallic alloys’, *IJMTM*, 2019, **141**, 78-88 (with D. Cha and D.A. Axinte)

[78] ‘A dam-break driven by a moving source: a simple model for a powder snow avalanche’, *J. Fluid Mech., *2019, **870**, 353-388.

[79] ‘Slow travelling wave solutions of the nonlocal Fisher-KPP equation’, *Nonlinearity*, 2020, **33**, 2106.

[80] ‘Slugging in horizontal channel flow’, *IMA Applied Math*., 2022, (with J.A. Giddings and S.M. Cox).

[81] ‘Nonlocal effects on travelling waves arising in a moving boundary reaction-diffusion model’, *J. Phys. A*, 2022, (with N. Fadai).

[82] ‘Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I General theory and the near local limit’. *Nonlinearity*, 2022 (with D.J. Needham).

[83] ‘On modelling coolant penetration into the microchannels at the tool-workpiece interface’, *J. Man. Proc*., 2022 (with D.A. Axinte et al).

[84] ‘The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large-time asymptotics’, *St. App. Math*., 2023 (with D.J. Needham and J.C. Meyer)

[85] ‘A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem’, *Proc. R. Soc A.*, 2023 (with Yang, Y., Axinte, D.A. and Liao, Z.).

[86] The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line, submitted to *EJAM* (with D.J. Needham), https://arxiv.org/abs/2304.10922.

[87] 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), https://arxiv.org/abs/2304.10935.

[88] The nonlocal Lotka – Volterra system with a top hat kernel. Part 1. Dynamics and steady states with small diffusivity, *Proc. R Soc. A., *2023* *(with D.J. Needham).

[89] A shape Newton method for free-boundary problems subject to the Bernoulli boundary condition, (with Y. Fan and K. van der Zee). https://doi.org/10.48550/arXiv.2305.14254.

[90] Efficient and scalable inverse kinematics for continuum robots,* IEEE Robotics and Automation Letters*, 2023 (with S. Wild, D.A. Axinte et al), http://dx.doi.org/10.1109/LRA.2023.3331291.

[91] Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth, *Math. Med. Bio.*, 2023 (with J. Jepson, N. Fadai and R. O’Dea), https://doi.org/10.1093/imammb/dqad008

[92] The inverse heat placement problem in metal additive manufacturing: Why a rational approach is needed for powder bed fusion, *J. Mat. Proc. Tech.*, 2024 (with H. Yeung, D. Axinte and J. Fox), https://www.sciencedirect.com/science/article/pii/S0924013624001651

[93] Lubrication flow in grinding,* J. Eng. Math*, 2024 (with Z. Crowson and P. Houston), https://link.springer.com/article/10.1007/s10665-024-10383-x

## 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 Designs*. *European 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.