Emeritus Professor of Applied Mathematics (Personal Professorship)
Telephone: +44 (0)118 987 1468
email: michael@sewells.org
Main Research Interests
Mechanics of elastic and plastic solids and structures
Mechanics of fluids and continuum mechanics
Meteorology
Variational and extremum principles  duality
Catastrophe and singularity theory  bifurcation theory
Other Interests
Mathematics masterclasses for young people. Local Organiser
of Royal
Institution Masterclasses for
13yearolds in Berkshire (19912000), and for 8 to 10yearolds in
West Berkshire, and in Windsor and Maidenhead (19992011).
Biographies of mathematics teachers (2006/7 below).
Family history (2002/6/7 below).
Appointments
19601962 Assistant Lecturer in Mathematics, University of Nottingham
19621963 Lecturer in Mathematics, University of Nottingham
19631966 Research Associate in Theoretical Mechanics, University of
Bristol
19661977 Reader in Applied Mathematics, University of Reading
19701971 Visiting Professor, Mathematics Research Center, University
of Wisconsin
(also summer 1982, 1983, 1984)
1976 Visiting Professor, Ecole Polytechnique, Paris
(also University of Waterloo, Canada and University of
Mexico)
19771999 Personal Professor of Applied Mathematics, University of
Reading
1999date Emeritus Professor of Applied Mathematics, University of
Reading
2010 Associate Tutor, Faculty of Engineering and Physical
Sciences, University of Surrey
List of Publications
1960
A General Theory of Inelastic Column Failure, Ph.D. Thesis, University of Nottingham.
A General Theory of Inelastic Column Failure, Part I, (with R. Hill), J. Mech. Phys. Solids8, 105  111,
also published in Russian in Mechanika 6, 129  136, 1961.
A General Theory of Inelastic Column Failure, Part II, (with R. Hill), J. Mech. Phys. Solids8, 112 118,
also published in Russian in Mechanika6, 137  144, 1961.
1962
A General Theory of Inelastic Column Failure, Part III, (with R. Hill), J. Mech. Phys. Solids10, 285  300.
1963
On Reciprocal Variational Principles for Perfect Fluids, J. Math. Mech.12, 495  504.
A General Theory of Elastic and Inelastic Plate Failure, Part I, J. Mech. Phys. Solids11, 377  393.
1964
A General Theory of Elastic and Inelastic Plate Failure, Part II, J. Mech. Phys. Solids12, 279  297.
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.
1966
On the Connexion between Stability and the Shape of the Equilibrium Surface, J. Mech. Phys. Solids14, 203  230.
1967
On ConfigurationDependent Loading, Arch. Ratl. Mech. Anal.23, 327  351.
1968
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.
1969
A Method of PostBuckling Analysis, J. Mech. Phys. Solids17, 219  233.
On Dual Approximation Principles and Optimization in Continuum Mechanics, Phil. Trans. Roy. Soc. Lond.A265, 319  351.
1970
On the Branching of Equilibrium Paths, Proc. Roy. Soc. Lond.A315, 499  518.
1972
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.
1973
A Yield Surface Corner Lowers the Buckling Stress of an ElasticPlastic 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.
1974
On Applications of SaddleShaped 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, SpringerVerlag.
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.
1975
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.
1976
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.
1977
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.
1978
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 Nonnegative Unsymmetric Operators, (with I. Herrera), J. Inst. Maths. Applics.21, 95  115.
1980
Complementary Energy and Catastrophes, pp. 163  168 of Variational Methods in the Mechanics of Solids, edited by S. NematNasser, 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.
1983
Mechanical Demonstrations of Buckling and Branching, Bull. Inst. Maths. Applics.19, 61  66.
1985
Properties of a Streamline in Gas Flow, Physics in Technology16, 127  133.
1987
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.
1988
The Parabolic Umbilic and Atmospheric Fronts, (with S. Chynoweth
and D. Porter), Proc. Roy. Soc. Lond.A419, 337  362.
1989
Dual Variables in Semigeostrophic Theory, (with S. Chynoweth), Proc. Roy. Soc. Lond.A424, 155 186.
1990
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.
1991
A Concise Derivation of the SemiGeostrophic Equations, (with S. Chynoweth), Q. Jl. Roy. Met. Soc.117, 1109  1128.
1992
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,
see below.
1993
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. EwingDeremer, Woods Hole Oceanog. Inst. Tech. Rept., WHOI9412.
Mathematics Masterclasses for Young People  Objectives and Scope, Bull. Inst. Maths. Applics.29, 34  41.
1994
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
Press.
1996
Potential Vorticities in Semigeostrophic Theory, (with I. Roulstone), Q. Jl. Roy. Met. Soc.122, 983  992.
1997
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.
2000
Organisation of Mathematics Masterclasses, Mathematics Today36, 173  178.
2001
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.
2002
Some Applications of Transformation Theory in Mechanics, pp. 143

223 (Chapter 5) of LargeScale AtmosphereOcean 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.
2003
Mathematics Masterclasses and their Organization, The Mathematical
Gazette,
87, 267  276.
Mathematics Masterclasses, Speech to the Meteorological Club, 12th
February.
Roots  a Masterclass for 8yearolds.
2005
Generalized SemiGeostrophic Theory on a Sphere, (with M. J. P. Cullen,
R. J. Douglas and I. Roulstone), J. Fluid Mech., 531, 123157.
Vector and Tensor Theorems on Curved Surfaces, Mathematics and
Mechanics of
Solids, 10, 415  426.
A Rugby Riddle, Mathematics Today, 41, 126  128.
The Rugby Riddle Revisited. Letter in Mathematics Today, 41,
196.
A Life at The King's School,
pp. 221230 of Memories of The King's
School Grantham (293 pp.), written and edited by Ruth Crook. The book
is obtainable from The King's School.