Emeritus Professor of Applied Mathematics (Personal Professorship)
Telephone: +44 (0)118 987 1468
Main Research Interests
Mechanics of elastic and plastic solids and structures
Mechanics of fluids and continuum mechanics
Variational and extremum principles - duality
Catastrophe and singularity theory - bifurcation theory
Mathematics masterclasses for young people. Local Organiser
Institution Masterclasses for
13-year-olds in Berkshire (1991-2000), and for 8 to 10-year-olds in
West Berkshire, and in Windsor and Maidenhead (1999-2011).
On the Calculation of Potential Functions defined on Curved Boundaries, Proc. Roy. Soc. Lond.A286, 402 - 411.
The Static Perturbation Technique in Buckling Problems, J. Mech. Phys. Solids13, 247 - 265.
On the Connexion between Stability and the Shape of the Equilibrium Surface, J. Mech. Phys. Solids14, 203 - 230.
On Configuration-Dependent Loading, Arch. Ratl. Mech. Anal.23, 327 - 351.
A General Theory of Equilibrium Paths through Critical Points, Part I, Proc. Roy. Soc. Lond.A306, 201 - 223.
A General Theory of Equilibrium Paths through Critical Points, Part II, Proc. Roy. Soc. Lond.A306, 225 - 238.
A Method of Post-Buckling Analysis, J. Mech. Phys. Solids17, 219 - 233.
On Dual Approximation Principles and Optimization in Continuum Mechanics, Phil. Trans. Roy. Soc. Lond.A265, 319 - 351.
On the Branching of Equilibrium Paths, Proc. Roy. Soc. Lond.A315, 499 - 518.
On Dual Extremum Principles in Applied Mathematics, (with B. Noble), J. Inst. Maths. Applics.9, 123 - 193.
A Survey of Plastic Buckling, pp. 85 - 197 of Stability, edited by H. Leipholz, Waterloo University Press.
A Yield Surface Corner Lowers the Buckling Stress of an Elastic-Plastic Plate under Compression, J. Mech. Phys. Solids21, 19 - 45.
The Governing Equations and Extremum Principles of Elasticity and Plasticity generated from a Single Functional, Part I, J. Struct. Mech.2(1), 1 - 32.
The Governing Equations and Extremum Principles of Elasticity and Plasticity generated from a Single Functional, Part II, J. Struct. Mech.2(2), 135 - 158.
On Applications of Saddle-Shaped and Convex Generating Functionals, pp. 219 - 245 of Physical Structure in Systems Theory, edited by J.J. van Dixhoorn and F.J. Evans, Academic Press.
A Plastic Flow Rule at a Yield Corner, pp. 95 - 97 of Buckling of Structures, edited by B. Budiansky, Springer-Verlag.
The foregoing papers, with the exception of the Ph.D. Thesis, were successfully submitted to The University of Nottingham in 1974 for the award of a D.Sc.
A Plastic Flow Rule at a Yield Vertex, J. Mech. Phys. Solids22, 469 - 490.
Elastic and Plastic Bifurcation Theory, Lectures to the Seminar on the Plasticity Theory and its Application in Techniques, University of Nis, Yugoslavia.
Kitchen Catastrophe, Mathl. Gaz.59, 246 - 249.
Some Mechanical Examples of Catastrophe Theory, Bull. Inst. Maths. Applics.12, 163 - 172,
also published in Polish in Mechanika Teoretyczna i Stosowana 3, 15, 315 - 334.
On Legendre Transformations and Elementary Catastrophes, Math. Proc. Camb. Phil. Soc.82, 147 - 163.
Degenerate Duality, Catastrophes and Saddle Functionals, Lectures to the Summer School on Duality and Complementarity in the Mechanics of Solids, Polish Academy of Sciences, Warsaw, published in Mechanics Today6, 41 - 91, 1981,
and also in Dualnosc w zagadnieniach mechaniki cial odksztalcalnych, Ossolineum, 1979.
Elementary Catastrophe Theory, pp. 391 - 426 of Problem Analysis in Science and Engineering, edited by F.H. Branin, Jr. and K. Huseyin, Academic Press, London.
A Pure Catastrophe Machine, Bull. Inst. Maths. Applics.14, 212 - 214.
On Legendre Transformations and Umbilic Catastrophes, Math. Proc. Camb. Phil. Soc.83, 273 - 288.
Some Global Equilibrium Surfaces, Int. J. Mech. Engng. Educ.6, 163 - 174.
General Estimates for Linear Functionals in Nonlinear Problems, (with B. Noble), Proc Roy. Soc. Lond.A361, 293 - 324.
Dual Extremum Principles for Non-negative Unsymmetric Operators, (with I. Herrera), J. Inst. Maths. Applics.21, 95 - 115.
Complementary Energy and Catastrophes, pp. 163 - 168 of Variational Methods in the Mechanics of Solids, edited by S. Nemat-Nasser, Pergamon Press, Oxford.
Constitutive Surfaces in Fluid Mechanics, (with D. Porter), Math. Proc. Camb. Phil. Soc.88, 517 - 546.
Book: Mechanics of Solids. The Rodney Hill 60th Anniversary Volume, (edited with H.G.Hopkins), xxiv + 693 pp., Pergamon Press, Oxford.
Rodney Hill : Biographical Note, (with Geoffrey Hopkins), pp. ix - xiv of the above book.
Legendre Transformations and Extremum Principles, pp. 563 - 605 of the above book.
Mechanical Demonstrations of Buckling and Branching, Bull. Inst. Maths. Applics.19, 61 - 66.
Properties of a Streamline in Gas Flow, Physics in Technology16, 127 - 133.
Book: Maximum and Minimum Principles. A Unified Approach, with
Applications, xvi + 468 pp., Cambridge University
Press. Reprinted 1990 and 2007.
Mathematical Modelling of the Quench Region in the Continuous Casting of Bimetallic Strip. Preliminary Assessment, (with H.J. Sewell), Math. Engng. Ind.1, 289 - 312.
Temperature distribution in the quench region in continuous casting of bimetallic strip, (with H.J. Sewell), pp. 313 - 314 of Solidification Processing 1987, Proceedings of the Third International Conference, published by Sheffield University and The
Institute of Metals.
The Parabolic Umbilic and Atmospheric Fronts, (with S. Chynoweth
and D. Porter), Proc. Roy. Soc. Lond.A419, 337 - 362.
Dual Variables in Semigeostrophic Theory, (with S. Chynoweth), Proc. Roy. Soc. Lond.A424, 155 -186.
Demonstrations of Buckling by Bifurcation and Snapping, pp. 315 - 345 of Elasticity: Mathematical Methods and Applications. The Ian Sneddon 70th Birthday Volume, edited by G. Eason and R.W. Ogden, Ellis Horwood Ltd.
Mesh Duality and Legendre Duality, (with S. Chynoweth), Proc. Roy. Soc. Lond.A428, 351 - 377.
Branching and Snapping in Mechanics, a Mathematics Masterclass, xiv + 34 pp.
A Concise Derivation of the Semi-Geostrophic Equations, (with S. Chynoweth), Q. Jl. Roy. Met. Soc.117, 1109 - 1128.
A New Approach to Shallow Flow over an Obstacle. I General Theory, (with A.S. Broad and D. Porter), U.K. Meteorological Office Short Range Forecasting Division Scientific Paper No. 11, 54 pp.
A New Approach to Shallow Flow over an Obstacle. II Plane Flow over a Monotonic Mountain, (with A.S. Broad and D. Porter), U.K. Meteorological Office Short Range Forecasting Division Scientific Paper No. 12, 58 pp. Published in revised form in 1997,
Anatomy of the Canonical Transformation, (with I. Roulstone), Phil. Trans. Roy. Soc. Lond.A345, 577 - 598.
Structure of the Canonical Transformation, (with I. Roulstone), pp. 337 - 341 of Geometrical Methods in Fluid Dynamics, edited by R. Salmon and B. Ewing-Deremer, Woods Hole Oceanog. Inst. Tech. Rept., WHOI-94-12.
Mathematics Masterclasses for Young People - Objectives and Scope, Bull. Inst. Maths. Applics.29, 34 - 41.
Families of Lift and Contact Transformations, (with I. Roulstone), Proc. Roy. Soc Lond.A447, 493 - 512.
Shallow Flow over General Topography with Applications to
Monotonic Mountains, (with A.S. Broad and D. Porter), pp. 133 - 138 of
Proceedings of the Fourth IMA Conference on Stably Stratified
Flows, edited by I. Castro and N. Rockliff, Oxford University
Potential Vorticities in Semigeostrophic Theory, (with I. Roulstone), Q. Jl. Roy. Met. Soc.122, 983 - 992.
Book: Mathematics Masterclasses - Stretching the
Imagination, (edited), pp. xiii + 233, Oxford University
Press. Reprinted 2000.
Balloons and Bubbles, pp. 124 - 148 of the above book.
Dynamics of Dinosaurs, pp. 149 - 175 of the above book.
The Mathematical Structure of Theories of Semigeostrophic Type, (with I. Roulstone), Phil. Trans. Roy. Soc. Lond.A355. 2489 - 2517.
New Shallow Flows over an Obstacle, (with A.S. Broad and D. Porter), Q. Jl. Mech. Appl. Math.50, 625 - 653.
Some Applications of Transformation Theory in Mechanics,
U.K. Meteorological Office Forecasting Research Division
Scientific Paper No. 49, 101 pp.
Published in revised form in 2002 - see below.
Organisation of Mathematics Masterclasses, Mathematics Today36, 173 - 178.
Mathematics Masterclasses and their Organisation. Invited lecture to
the annual conference of Heads of Departments of Mathematical Sciences
in universities (HODOMS), University of Birmingham.
Published in The Mathematical Gazette, July 2003 - see below.
A Play on Graphs. Invited contribution to a Summer School for
Gifted and Talented Children, Bisham Primary School, Windsor and
Maidenhead Education Department.
Some Applications of Transformation Theory in Mechanics, pp. 143
223 (Chapter 5) of Large-Scale Atmosphere-Ocean Dynamics, Volume II,
Geometric Methods and Models,
edited by J.Norbury and I.Roulstone, Cambridge University Press.
Review of Elastoplasticity Theory by V.A.Lubarda, CRC Press, 2002,
in SIAM Review 44, No. 4, 741 - 742.
Jacqueline's Gems. 23 pp. Privately printed.
Mathematics Masterclasses and their Organization, The Mathematical
87, 267 - 276.
Mathematics Masterclasses, Speech to the Meteorological Club, 12th
Roots - a Masterclass for 8-year-olds.
Generalized Semi-Geostrophic Theory on a Sphere, (with M. J. P. Cullen,
R. J. Douglas and I. Roulstone), J. Fluid Mech., 531, 123-157.
Vector and Tensor Theorems on Curved Surfaces, Mathematics and
Solids, 10, 415 - 426.
A Rugby Riddle, Mathematics Today, 41, 126 - 128.
The Rugby Riddle Revisited. Letter in Mathematics Today, 41,