John Billingham

Contact

• workRoom B47 Mathematical Sciences Building
  University Park
  Nottingham
  NG7 2RD
  UK
• work0115 9513846
• fax0115 9513837
• john.billingham@nottingham.ac.uk
• http://www.maths.nott.ac.uk/personal/pmzjb1/

Selected Publications

• BILLINGHAM, JOHN, 2020. Slow travelling wave solutions of the nonlocal Fisher-KPP equation NONLINEARITY. 33(5), 2106-2142
• BILLINGHAM, JOHN, 2019. A dam break driven by a moving source: a simple model for a powder snow avalanche JOURNAL OF FLUID MECHANICS. 870, 353-388
• AXINTE, DRAGOS and BILLINGHAM, JOHN, 2019. Time-dependent manufacturing processes lead to a new class of inverse problems PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. 116(12), 5341-5343
• J.T. BRADSHAW and J. BILLINGHAM, 2018. Thick drops climbing uphill on an oscillating substrate Journal of Fluid Mechanics. 840, 131-153

• View all publications

• BILLINGHAM, JOHN, 2020. Slow travelling wave solutions of the nonlocal Fisher-KPP equation NONLINEARITY. 33(5), 2106-2142
• BILLINGHAM, JOHN, 2019. A dam break driven by a moving source: a simple model for a powder snow avalanche JOURNAL OF FLUID MECHANICS. 870, 353-388
• AXINTE, DRAGOS and BILLINGHAM, JOHN, 2019. Time-dependent manufacturing processes lead to a new class of inverse problems PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. 116(12), 5341-5343
• SHANG, ZHENDONG, LIAO, ZHIRONG, SARASUA, JON ANDER, BILLINGHAM, JOHN and AXINTE, DRAGOS, 2019. On modelling of laser assisted machining: Forward and inverse problems for heat placement control INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE. 138, 36-50
• GIDDINGS, JOSEF ADAM and BILLINGHAM, JOHN, 2019. The effect of inclination on the development of slugging in channel flow IMA JOURNAL OF APPLIED MATHEMATICS. 84(2), 366-384
• CHA, D., AXINTE, D. and BILLINGHAM, J., 2019. Geometrical modelling of pulsed laser ablation of high performance metallic alloys INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE. 141, 78-88
• J.T. BRADSHAW and J. BILLINGHAM, 2018. Thick drops climbing uphill on an oscillating substrate Journal of Fluid Mechanics. 840, 131-153
• CADOT, G. B. J., THOMAS, K., BEST, J. P., TAYLOR, A. A., MICHLER, J., AXINTE, D. A. and BILLINGHAM, J., 2018. Investigation of the microstructure change due to phase transition in nanosecond pulsed laser processing of diamond CARBON. 127, 349-365
• M.T. GALLAGHER, D.J. NEEDHAM and J. BILLINGHAM, 2018. The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow Journal of Fluid Mechanics.
• M.T. GALLAGHER, D.J. NEEDHAM and J. BILLINGHAM, 2018. The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 2. Well-posedness and stability of the principal flow Journal of Fluid Mechanics.
• CADOT, G.B.J., BILLINGHAM, J. and AXINTE, D.A., 2017. A study of surface swelling caused by graphitisation during pulsed laser ablation of carbon allotrope with high content of sp3 bounds Journal of Phsyics D. (In Press.)
• A. BILBAO-GUILLERNA, D.A. AXINTE, J. BILLINGHAM and G.B.J. CADOT, 2017. Waterjet and Laser Etching: The Nonlinear Inverse Problem Royal Society Open Science. 4, 161031
• J. BILLINGHAM, D.J. NEEDHAM, R.J. MUNRO and E. KORSUKOVA, 2017. The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface Journal of Fluid Mechanics. 836,
• A. BILBAO-GUILLERNA, R.T. EACHAMBADI, G.B.J. CADOT, D.A. AXINTE, J. BILLINGHAM, F. STUMPF, S. BEUER and M. ROMMEL, 2017. Novel approach based on continuous trench modelling to predict focused ion beam prepared freeform surfaces Journal of Materials Processing Technology.
• DRAGOS AXINTE, JOHN BILLINGHAM and BILBAO GUILLERNA, 2017. New models for energy beam machining enable accurate generation of free forms SCIENCE ADVANCES. 3(9), 1 to 7
• O. BAIN, J. BILLINGHAM, P. HOUSTON and I. LOWNDES, 2016. Flows of Granular Material in Two-Dimensional Channels Journal of Engineering Mathematics. 98(1), 49-70
• J.S. IM and J. BILLINGHAM, 2016. A spectral boundary integral method for inviscid water waves in a finite domain International Journal for Numerical Methods in Fluids.
• BRADSHAW, J. and BILLINGHAM, J., 2016. Thin three-dimensional droplets on an oscillating substrate with contact angle hysteresis PHYSICAL REVIEW E. 93(1),
• TORRUBIA, P. LOZANO, BILLINGHAM, J. and AXINTE, D. A., 2016. Stochastic simplified modelling of abrasive waterjet footprints PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 472(2186), 50836-50836
• G.B.J. CADOT, D.A.AXINTE and J.BILLINGHAM, 2016. Continuous trench, pulsed laser ablation for micro-machining applications International Journal of Machine Tools and Manufacture. 107, 8-20
• A. BILBAO GUILLERNA, D.A. AXINTE and J. BILLINGHAM, 2015. The linear inverse problem in energy beam processing with an application to abrasive waterjet machining International Journal of Machine Tools and Manufacture. 99, 34-42
• TORRUBIA, P. LOZANO, AXINTE, D. A. and BILLINGHAM, J., 2015. Stochastic modelling of abrasive waterjet footprints using finite element analysis INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE. 95, 39-51
• XU, FENG, BILLINGHAM, JOHN and JENSEN, OLIVER E., 2014. Resonance-driven oscillations in a flexible-channel flow with fixed upstream flux and a long downstream rigid segment JOURNAL OF FLUID MECHANICS. 746, 368-404
• MIRON C., BILLINGHAM J., AXINTE D. and KONG M.C., 2013. Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: Part II — overlapped single and multiple straight paths International Journal of Machine Tools and Manufacture. 68, 30-39
• THOMPSON, ALICE B. and BILLINGHAM, JOHN, 2013. Inviscid coalescence in the presence of a surrounding fluid IMA JOURNAL OF APPLIED MATHEMATICS. 77(5), 678-696
• RASHEED, S. and BILLINGHAM, J., 2013. A reaction diffusion model for inter-species competition and intra-species cooperation Mathematical Modelling of Natural Phenomena. 8, 156-183
• XU, FENG, BILLINGHAM, JOHN and JENSEN, OLIVER E., 2013. Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux JOURNAL OF FLUID MECHANICS. 723, 706-733
• KONG, M.C., ANWAR, S., BILLINGHAM, J. and AXINTE, D.A., 2012. Mathematical modelling of abrasive waterjet footprints for arbitrarily moving jets: part I—single straight paths International Journal of Machine Tools and Manufacture. 53(1), 58-68
• BENILOV, E.S. and BILLINGHAM, J., 2011. Drops climbing uphill on an oscillating substrate Journal of Fluid Mechanics. 674, 93-119
• THOMPSON, A.B., BILLINGHAM, J. and TEW, R.H., 2010. Surface-tension-driven flow in a half-plane IMA Journal of Applied Mathematics. 75(6), 857-880
• STEWART, P.S., WATERS, S.L., BILLINGHAM, J. and JENSEN, O.E., 2010. Spatially localised growth within global instabilities of flexible channel flows. In: SCHLATTER, PHILIPP and HENNINGSON, DAN S., eds., Seventh IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Seventh IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009 XXIV. Springer. (In Press.)
• AXINTE, D. A., SRINIVASU, D. S., BILLINGHAM, J. and COOPER, M., 2010. Geometrical modelling of abrasive waterjet footprints: A study for 90^o jet impact angle ANNALS- CIRP. VOL 59(NUMBER 1), 341-346
• STEWART, P.S., WATERS, S.L., BILLINGHAM, J. and JENSEN, O.E., 2010. IUTAM BOOKSERIES. VOL 18, 397-402
• WOOLLARD, H.F., BILLINGHAM, J., JENSEN, O.E. and LIAN, G., 2009. A multi-scale model for solute transport in a wavy- walled channel Journal of Engineering Mathematics. 64, 25-48
• NEEDHAM, D.J. and BILLINGHAM, J., 2009. A note on the unsteady motion under gravity of a corner point on a free surface: a generalization of Stokes' theory Proceedings of The Royal Society A: Mathematical, Physical & Engineering Sciences. 465(2101), 165-173
• CLARKE, R.J and JENSEN, O.E. & BILLINGHAM, J., 2008. Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 78, 056310
• BILLINGHAM, J., 2008. Gravity-driven thin-film flow using a new contact line model IMA JOURNAL OF APPLIED MATHEMATICS. 73(1), 4-36
• NEEDHAM, D.J., BILLINGHAM, J., KING, A.C. and SCHULKES, R.M.S.M., 2008. The development of slugging in two-layer hydraulic flows IMA Journal of Applied Mathematics. 73, 274-322
• SHARPE, G.J., FALLE, S.A.E.G. and BILLINGHAM, J., 2008. Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube IMA Journal of Applied Mathematics. 73, 107-122
• NEEDHAM, D.J., CHAMBERLAIN, P.G. and BILLINGHAM, J., 2008. The initial development of a jet caused by fluid, body and free-surface interaction. Part 3. An inclined accelerating plate Quarterly Journal of Mechanics and Applied Mathematics. 61(4), 581-614
• TILLEY, B.S., BILLINGHAM, J. and HENDRIKS, F., 2008. On the stability of sheared menisci in Hele-Shaw cells Mathematics-In-Industry Case Studies Journal. 1, 9-23
• NEEDHAM, D. J., BILLINGHAM, J. and KING, A. C., 2007. The initial development of a jet caused by fluid, body and free-surface interaction. Part 2. An impulsively moved plate JOURNAL OF FLUID MECHANICS. VOL 578, 67-84
• CLARKE, R J, JENSEN, O E, BILLINGHAM, J, PEARSON, A P and WILLIAMS, P M, 2006. Stochastic elastohydrodynamics of a microcantilever oscillating near a wall. Physical Review Letters. 96(5), 050801
• CLARKE, R. J., JENSEN, O. E., BILLINGHAM, J. and WILLIAMS, P. M., 2006. Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. VOL 462(NUMB 2067), 913-934
• BILLINGHAM, J., 2006. Surface tension-driven flow in a slender wedge SIAM Journal on Applied Mathematics. 66(6), 1949-1977
• BILLINGHAM, J., 2006. On a model for the motion of a contact line on a smooth solid surface European Journal of Applied Mathematics. VOL 17(PART 3), 347-382
• ADAMSON, F., BILLINGHAM, J., KING, A.C. and KENDALL, K., 2006. An asymptotic theory for the propagation of a surface-catalysed flame in a tube Journal of Fluid Mechanics. VOL 546, 363-393
• BILLINGHAM, J., 2005. The initial surface tension-driven flow of a wedge of viscous fluid SIAM Journal on Applied Mathematics. VOL 66(NUMB 2), 510-532
• BILLINGHAM, J. and KING, A.C., 2005. Surface-tension-driven flow outside a slender wedge with an application to the inviscid coalescence of drops Journal of Fluid Mechanics. VOL 533, 193-222
• BILLINGHAM, J., FRANCIS, D.T.I., KING, A.C. and HARRISSON, A.M., 2005. A multiphase model for the early stages of the hydration of retarded oilwell cement Journal of Engineering Mathematics. VOL 53(NUMBER 2), 99-112
• HENDRIKS, F., TILLEY, B. S., BILLINGHAM, J., DELLAR, P. J. and HINCH, R., 2005. Dynamics of the Oil-Air Interface in Hard Disk Drive Bearings IEEE Transactions on Magnetics. VOL 41(NUMB 10), 2884-2886
• BILLINGHAM, J., 2004. Dynamics of a strongly nonlocal reaction-diffusion population model Nonlinearity. VOL 17(PART 1), 313-346
• SCHLEY, D., BILLINGHAM, J. and MARCHBANKS, R. J., 2004. A model of in-vivo hydrocephalus shunt dynamics for blockage and performance diagnostics Mathematical Medicine and Biology. VOL 21(NUMBER 4), 347-368
• BAILEY, P. B., BILLINGHAM, J., COOPER, R. J., EVERITT, W. N., KING, A. C., KONG, Q., WU, H. and ZETTL, A., 2003. On some eigenvalue problems in fuel-cell dynamics Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. VOL 459(JAN), 241-262
• KING,A.C., BILLINGHAM,J. and OTTO,S.R., 2003. Differential equations: linear, nonlinear, ordinary, partial Cambridge University Press; Cambridge, UK.
• SALHAN, A., BILLINGHAM, J. and KING, A. C., 2003. The effect of a retarder on the early stages of the hydration of tricalcium silicate Journal of Engineering Mathematics. VOL 45(NUMBER 3/4), 367-377
• BILLINGHAM, J., 2002. Nonlinear sloshing in zero gravity Journal of Fluid Mechanics. VOL 464, 365-392
• BILLINGHAM, J. and MERCER, G. N., 2001. The effect of heat loss on the propagation of strongly exothermic combustion waves Combustion Theory and Modelling. VOL 5(PART 3), 319-342
• PREECE, S. J., BILLINGHAM, J. and KING, A. C., 2001. On the initial stages of cement hydration Journal of Engineering Mathematics. VOL 40(PART 1), 43-58
• KING, A. C., BILLINGHAM, J. and COOPER, R. J., 2001. Performance modelling of solid oxide fuel cells Combustion Theory and Modelling. VOL 5(PART 4), 639-668
• PREECE, S. J., BILLINGHAM, J. and KING, A. C., 2001. The evolution of travelling waves from chemical-clock reactions Journal of Engineering Mathematics. VOL 39(PART 1/4), 367-385
• COOPER, R. J., BILLINGHAM, J. and KING, A. C., 2000. Flow and reaction in solid oxide fuel cells Journal of Fluid Mechanics. VOL 411, 233-262
• BILLINGHAM, J., KING, A. C., COPCUTT, R. C. and KENDALL, K., 2000. Analysis of a Model for a Loaded, Planar, Solid Oxide Fuel Cell SIAM Journal on Applied Mathematics. VOL 60(PART 2), 574-601
• BILLINGHAM, J., 2000. Steady-state solutions for strongly exothermic ignition in symmetric geometries IMA Journal of Applied Mathematics. VOL 65(PART 3), 283-314
• BILLINGHAM, J., 2000. On modelling the formation of micelles in the presence of a slow influx of monomer Quarterly Journal of Mechanics and Applied Mathematics. VOL 53(PART 2), 285-298
• BILLINGHAM, J., 2000. Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms Dynamics and Stability of Systems. VOL 15(PART 1), 23-34
• BILLINGHAM,J. and KING,A.C., 2000. Wave Motion Cambridge : Cambridge University Press.
• GALLAGHER, M.T., NEEDHAM, D.J. and BILLINGHAM, J., The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow Journal of Fluid Mechanics. (In Press.)
• GALLAGHER, M.T., NEEDHAM, D.J. and BILLINGHAM, J., The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 2. Well-posedness and stability of the principal flow Journal of Fluid Mechanics. (In Press.)