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University of Nottingham
Research
Interdisciplinary research
Modelling
Our People
Research
Our People
Professor
John
Billingham
Professor of Theoretical Mechanics,
Faculty of Science
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Personal Details
Publications
Contact
work
Room B47 Mathematical Sciences Building
University Park
Nottingham
NG7 2RD
UK
work
0115 9513846
fax
0115 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.)
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Nottingham
NG7 2RD
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research@nottingham.ac.uk
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