John Billingham's Publications

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. Download PDF preprint
[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). Download PDF preprint
[16] `Surface tension-driven flow in fat fluid wedges and cones', J. Fluid Mech. 1999, 397, 45-71. Download PDF preprint
[17] `Chemical clock reactions: The effect of precursor consumption', J. Math. Chem. 1999, 26, 47-73 (with S.J. Preece and A.C. King). Download PDF preprint
[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).  Download PDF preprint
[19] `Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms', Dynamics and Stability of Systems 2000, 15, 23-33. Download PDF preprint
[20] `Flow and reaction in solid oxide fuel cells', J. Fluid Mech. 2000, 411, 233-262 (with R.J. Cooper and A.C. King).  Download PDF preprint
[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. Download PDF preprint
[22] `Steady state solutions for strongly exothermic thermal ignition in symmetric geometries', IMA J. of Appl. Math. 2000, 65, 283-313. Download PDF preprint
[23] `On the initial stages of cement hydration', J. Eng. Math. 2001, 40, 43-58 (with S.J. Preece and A.C. King). Download PDF preprint
[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). Download PDF preprint
[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). Download PDF preprint
[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 Download PDF preprint
[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) Download PDF preprint
[30] `Dynamics of a strongly nonlocal reaction-diffusion population model', Nonlinearity 2003, 17, 313-345. Download PDF preprint
[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). Download PDF preprint
[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).  Download PDF preprint
[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).  Download PDF preprint
[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). Download PDF preprint

[35] `The initial surface tension-driven flow of a wedge of viscous fluid', SIAM J. Appl. Math. 2005, 66, 510-532 Download PDF preprint

[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).  Download PDF preprint

[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  Download PDF preprint

[40] `Surface tension-driven flow in a slender wedge', SIAM J. Appl. Math. 2006, 66, 1949-1977  Download PDF preprint

[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). Download PDF preprint

[42] `Gravity-driven thin film flow using a new contact line model', IMA J. Appl. Math. 2008, 73, 4-36 Download PDF preprint.

[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)  Download PDF preprint. Movies of simulations can be found here.

[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  Download PDF preprint (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). Download PDF preprint

[47] `A multiscale model for solute transport in a wavy-walled channel', J. Eng. Maths., 2008, 64, 25-48 Download PDF preprint (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 Download PDF preprint (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)

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).
[3] 'The Education of a Modern Poker Player', to appear in 2013, D & B Poker Books (with T. Tiroch and E.E. Cinca).

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)

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.