Chris Budd

Professor C J Budd

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Chris and Benji, I am the one with the glasses
Department: Mathematical Sciences
Job Title: Professor of Applied Mathematics at the University of Bath and Professor of Mathematics at the Royal Institution of Great Britain

Telephone: +44 1225 386241
Fax: +44 1225 386492

E-mail Address: cjb@maths.bath.ac.uk

Postal Address:

Here is my Curriculum Vitae

IMA Vice-President

I have recently been elected as the Vice-President for the IMA responsible for Communications and Outreach. More details of my activites in maths education and public engagement are given below

Marie Curie ITN FIRST

Along with Victor Galaktionov and Johannes Zimmer I am a coordinator of the Bath Node of the FIRST (Fronts and Interfaces in Science and Technology) Marie Curie training network. See FIRST Network for more information about the project, workshops and positions.

Research Interests:

I am interested in the theory, application and computation of nonlinear problems (linear problems are for cissies) with special interest in problems which arise in industry. Much of my recent work has been on the development of accurate adaptive methods for solving nonlinear parabolic equations based upon the application of ideas from the theory of Lie groups, which inherit the dynamics and associated conservation laws of the underlying partial differential equations. I also have a very strong interest in interdisciplinary projects closely linked to applications ranging from geology to micro-wave cooking and from digestion to folk dancing.

Education and Public Engagement Interests:

I have a strong interest in promoting mathematics to the general public, especially to young people. I am a member of the CMS Maths Promotion Unit , Professor of Mathematics at the Royal Institution, lecturer for Maths Inspiration , coordinator of the Bath Taps Into Science Festival and of the Wessex Maths Masterclasses.

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In 2010 I was director of the exhibit in the Royal Society Summer Exhibition called Living in a Complex World which gave a hands on experience of the way that maths helps us understand the complexities in the world, from weather forecasting and chaos to energy harvesting and from bouncing balls and sand to flocks and crowds. The website above has lots of resources about complexity. Enjoy! If you are mad enough to want to run such an exhibition your self, then have a look at the user guide A user guide to running a Royal Society Summer Exhibition.


In 2001 I was awarded a National Teaching Fellowship NTFS and have used this to create a degree credit programme on 'Maths Communication'.If you are interested in getting involved in public engagement work and would like to find out more, then have a look at my talk I also have a strong interest in mathematics education and serve on a number of bodies that support mathematical education. These include the MSOR Subject Centre, the MEI Industry Ctee and the More Maths Grads executive committee. I am also the Education Secretary of the London Mathematical Society . Some details of the work of the LMS Education Committee (which I chair) are given in the following LMS Newsletter article

My philosophy for teaching is simple. Be aware of (and enjoy) your audience and be hugely enthusiastic about your subject.

Some of my talks/articles/courses on maths education:

Non-smooth dynamics

What happens to dynamical systems when we remove the constraint of smoothness? Lots of new and exciting dynamics occur!! A review of these is given in my new BOOK on Piecewise-smooth Dynamical Systems: Theory and Applications, joint with Mario di Bernardo, Alan Champneys and Piotr Kowalczyk published by Springer.

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Geometric Integration and Adaptivity:

Geometric integration is a new branch of numerical analysis which aims to reproduce the qualitative features of the solution of the differential equation which is being discretised. An account of this new area is given in the following set of notes (100 sides) which formed the basis of a short course at SCICADE 01
  • Geometric integration and its applications. C.J.Budd and M.D.Piggott (2001)
    • A particular interest of mine is the relationship between geometric integration and adaptive methods for ODEs and (in particular) PDEs.

    Research talks:

    These are some research talks on geometric integration and grid generation
  • Discrete variational derivative methods with applications to PDEs
  • Optimal transport methods for mesh generation with applications to meteorology
  • Introduction to the geometric integration of ODEs
  • Adaptivity, scaling and geometric integration methods for PDEs
  • Some geometric integration methods for PDEs
  • Parabolic Monge-Ampere methods for mesh generation
  • Adaptivity and symmetry for ODEs and PDEs
    • This is a talk on emergent behaviour in large electrical networks, with application to complex dielectric materials
  • Emergent scaling laws in complex dielectric materials
    • These are two talks on maths in the food industry
  • The mathematics of digestion
  • Microwave cooking: theory and experiment
    • These are two talks on non-smooth dynamics
  • Chattering and grazing in impact oscillators
  • Bouncing, sliding and switching: bifurcations in piecewise-smooth systems
    • These are three talks that give a review of piecewise-smooth dynamics and were a mini course delivered at the UK-Japan Winter School in January 2009.
  • Piecewise-smooth dynamics: I. Introduction
  • Piecewise-smooth dynamics: II. Maps
  • Piecewise-smooth dynamics: III. Hybrid systems and the grazing bifurcation.
    • And a talk on folding and geology
  • Level set methods for multilayer geological folding
    • And a talk on GPS, Complexity and the Ionosphere
  • Imaging of complex behaviour in the upper atmosphere

    • Bath Institute for Complex Systems, BICS:

    I am director of the Bath Institute for Complex System BICS which is an interdisciplinary institute exploring the many aspects of complex systems and their applications. It has an active research and workshop programme .. see the web-site.

    MSC in Modern Applications of mathematics:

    I am director of the Bath Msc course in Modern Applications of Mathematics which aims to give a training in modern interdisciplinary applied mathematics to anyone interested in applying mathematics in their career. For further information email or look at the home page for the MSc above.

    Mathematics for the general public:

    I regard it as essential that mathematics is presented in an exciting and stimulating way for a general audience. As part of this I am Chair of Mathematics at the Royal Institution of Great Britain vice-chairman of the Bath/Bristol Royal Institution Masterclasses for 13-14 year olds and served on the EPSRC Public Understanding of Science Committee.

    Public talks, lectures and workshops:

    I love giving talks about maths and its applications and its relevance to our lives to all ages, especially young people. ****DO CONTACT ME**** if you want me to come to give a talk. Here are a collection of some of my talks, which can be given either as stand alone lectures or as part of a workshop with extra activities. I have tried to indicate the age range for the workshops. The workshops have resource materials and worksheets attached. PLEASE DOWNLOAD AND USE them for any reasonable educational purpose.

  • Maths and the making of the modern world A talk about the way that maths has made the modern world possible.
  • Maths, magic and mystery(KS3 workshop) and worksheets. A workshop about mathematical magic together with lots of examples of magic tricks and the maths behind them
  • Inspiring Maths Inspiring maths teaching, a CPD workshop for teachers of secondary school maths.
  • The maths of Google and the IPod (KS3 workshop) and worksheets. A talk about the maths involved in CDs, the IPod and Google, including binary, error correction, data compression and the Page Rank Algorithm.
  • 75 Years of Radar a talk for all ages, originally presented to the British Science Festival to celebrate the 75th anniversary of the invention of Radar(July 2010)
  • Maths in and out of the zoo a talk for all ages, originally presented to the Oxford Alumni showing the may ways that maths can be found in the zoo, and what happens when this exotic animal escapes into the real world (July 2010)
  • The link between Maths, Mazes and Organised Crime (talk presented to the Bath Alumni (May 2010))
  • Confessions of an industrial mathematician .. how to use maths from industry in the classroom (talk for teachers presented at BCME (April 2010))
  • Maths Weather and Climate (Yr 12 Maths Inspiration Presentation)
  • How to amaze your friends (KS3 workshop) and worksheets. A talk about the history, maths and modern uses of mazes.
  • How to lie and get away with it (KS3 workshop) and worksheets. A talk on the mathematics of the information ages, including the maths of the iPod.
  • How maths can help in the fight against crime (KS4 workshop) and worksheets
  • Maths of castles (KS3 workshop) and worksheets
  • Dancing with maths (KS3 workshop) and worksheets
  • 101 Uses of a Quadratic Equation (KS4 workshop) and worksheet 1 , worksheet 2 , Babylonian Numbers
  • Celtic and African Knots (KS3 workshop) and worksheets , grids for the knots . A multicultural talk which shows how the artistic traditions of the Celts and Sub Saharan Africa are linked through mathematics.
  • Why does Rudolph have a shiny nose? A A maths lecture for all ages at Christmas
  • Bath Taps Into Science
  • Eat, drink and be merry with maths (Yr 12 talk)
  • e, i, pi and all that (Yr 12 talk)
  • Making sense of a complex world (KS4 talk)
  • What's the use of chaos (KS4 talk)
  • What have mathematicians done for us? a talk for all ages showing the contribution that mathematicians have made to civilisation.
  • How maths can save your life (KS3 talk)
  • How maths can change your life .. careers which use maths

    • Mathematics Galore:

    My book .Mathematics Galore co-authored with Chris Sangwin, published by OUP is a collection of these classes. See the review in Plus Maths. A new book called `101 uses of a quadratic equation', is underway .. watch this space.

    Bath Taps Into Science:

    Is an annual science road show, funded by EPSRC, which I help to organise at the University of Bath and in Green Park Station in Bath as part of National Science and Engineering Week. The 2002 event won a prize from the Institute of Physics for `outstanding contributions to the public understanding of physics'. The 2009 event won the British Science Association award for the best science festival during National Science and Engineering Week. Click here to see some images of the event and find out more.

    Popular Maths Articles

    I give many public lectures on mathematics and write articles for the Mathematics on-line magasines NRICH and PLUS I was awarded an EPSRC PPU award to produce videos on a series of themes in maths and physics. I am involved with the Motivate programme of video conferencing maths workshops, and can give video talks on Mathematical Magic, Mazes and Navigation, Knots, Quadratic equations etc. if requested. A full listing is given on the Motivate website above.
    In partnership with the LMS I have developed the following set of resources for schools and have also produced the following set of videos and DVDs for a variety of ages Visions of Maths and Science

    Posters and articles:

  • I helped to design Maths Connects poster for the London Underground about mathematical networks

    Here are some of my recent popular articles

  • Confessions of an industrial mathematician
    C. Budd, (2008)
  • Crime fighting maths I
    C. Budd, (2005)
  • 101 Uses of a quadratic equation I
    C. Budd and C. Sangwin, (2004)
  • 101 uses of a quadratic equation II
    C. Budd and C. Sangwin, (2004)
  • Finding order in chaos
    C. Budd, (2003)
  • How Maths Can Make You Rich and Famous I
    C. Budd, (2003)
  • How Maths Can Make You Rich and Famous II
    C. Budd, (2003)
  • Does Nature Really Care About Rational Numbers
    A Friday Evening Discourse at the Royal Institution, C J Budd (2001)
  • Where in the world am I?
    C. Budd (2000)
  • Analemmatic Sundials: How to build one and why they work
    C. Budd and C. Sangwin (2000)
  • Maths aMazes
    C J Budd and C J Sangwin (2000)

    • Visions of Maths and Science:

    This is a series of popular maths and science videos aimed at teachers (and students) from Key stage one through to sixth form. So far these include: Bath Taps Into Science , Mathematical Magic, The Liquid Nitrogen Show, Living in a Complex World, What's the use of chaos and The Maths and Science Christmas Show. To appear shrotly are Bubbles and `All the fun of the fair'. Click here for an order form and more details about the project and click here for some video clips from the NRICH web-site.

    Undergraduate Course Material:

    Worksheets, handouts and general information on courses can be found here
  • MA10208 Methods and Applications a
  • MA10002 Functions, differentiation and analytic geometry
  • Math0014 Numerical analysis
  • Math0060 Nonlinear systems and chaos
  • Math0101 Mathematics for electrical engineers 3
  • XX20164 Mathematical modelling and MATLAB

    • MSc Course Material:

  • MA50174 Advanced Numerical Methods Containing a MATLAB tutorial and a complete set of notes on Advanced Numerical Methods and how to use MATLAB to solve mathematical problems.

    • Appointments and Committees:

    I also have the following appointments and am on the following committees

    Other groups I am Involved With:

    Publications:

    Here are some recent publications, preprints and notes
  • On self-similar blow-up in evolution equations of Monge-Ampere type: a view from reaction-diffusion theory
    C.J.Budd and V.A. Galaktionov, (2010)

  • Breathers in a pinned mechanical lattice
    S.C. Green, C.J.Budd and G.W. Hunt, (2010)
  • Regularization techniques for ill-posed inverse problems in data assimilation
    C.J.Budd, M.A.Freitag and N.K.Nichols, (2010)
  • Emergent behaviour in large electrical networks
    D.P. Almond, C.J.Budd and N.J. McCullen, (2010)
  • The dynamics of a simplified pin-ball machine
    S.R. Pring and C.J.Budd, (2010)
  • How to adaptively resolve evolutionary singularities in differential equations with symmetry
    C.J.Budd and J.F. Williams, (2009)
  • Adaptivity with moving grids
    C.J.Budd, W-Z Huang and R.D. Russell, (2009)
  • Spatial chaos, breathers and phonobreathers in a pinned mechanical lattice
    S. Green, C.J.Budd and G.W. Hunt, (2009)
  • Bifurcations in Nonsmooth Dynamical Systems
    M di Bernardo, C.J.Budd, A. R. Champneys, P. Kowalczyk, A. Nordmark, G. Tost and P. Piiroinen, (2008)
  • The robustness of the emergent scaling property of random RC network models of complex materials
    N.J. McCullen, D.P. Almond, C.J.Budd and G.W. Hunt, (2008)
  • The dynamics of regularised maps with gaps, with applications to impacting and related systems
    S.R. Pring and C.J.Budd, (2008)
  • Moving mesh generation using the Parabolic Monge-Ampere equation
    C.J.Budd and J.F. Williams, (2008)
  • Image-model coupling: a simple information theoretic perspective for image sequences
    N.D. Smith, C.N. Mitchell and C.J.Budd, (2008)
  • Image-model coupling: application to an ionospheric storm
    N.D. Smith, C.N. Mitchell and C.J.Budd, (2008)
  • A comparison of models and methods for the one dimensional microwave heating of foodstuffs
    C.J.Budd and A. Hill, (2007)
  • Experimental and analytic studies of the microwave heating of cuboid moist foodstuffs
    C.J.Budd and A. Hill, (2007)
  • Level set modelling for the parallel folding of layered structures: comparisons with experiment
    J. Boon, C.J.Budd and G.W. Hunt, (2007)
  • Smooth boundary based optimisation using a fixed grid
    C.S. Edwards, H.A. Kim and C. J. Budd (2007)
  • An evaluative study on ESO and SIMP for optimising a cantilever tie-beam
    C. S. Edwards, H. A. Kim and C. J. Budd (2006)
  • Level set methods for the displacement of layered materials
    J.A. Boon, C.J.Budd and G.W. Hunt (2006)
  • A mechanical realisation of a symplectic numerical method with large step size
    S. C. Green, C.J.Budd and G.W. Hunt (2006)
  • Corner bifurcations in non-smoothly forced impact oscillators
    C.J.Budd and P.T. Piiroinen (2006)
  • Bifurcations in Nonsmooth dynamical systems: Review article
    M. di Bernardo, C.J.Budd, A.R. Champneys, P. Kowalczyk, A.B. Nordmark, G. Olivar, P.T. Piiroinen (2005)
  • Parabolic Monge-Ampere methods for blow-up problems in several spatial dimensions.
    C.J.Budd and JF Williams (2005)
  • Localised periodic patterns for the non-symmetric generalized Swift-Hohenberg equation
    C.J.Budd and R.A. Kuske (2005)
  • From nonlinear PDEs to singular ODEs.
    C.J.Budd, O. Koch and E. Weinmuller (2004)
  • Computation of self-similar profiles for the nonlinear Schrodinger equation
    C.J.Budd, O. Koch and E. Weinmuller (2004)
  • Serial parallel folding with friction: a primitive model using cubic B-splines.
    G.W.Hunt, R. Edmunds and C.J.Budd (2004)
  • Multi-bump solutions of the Complex Ginsburg-Landau equation.
    C.J.Budd, V. Rottschaeffer and J. F. Williams (2004)
  • Precise calculations of chemotactic collapse using moving mesh methods.
    C.J.Budd, R. Carretero and R.D.Russell (2003)
  • Generalisations of the Levi-Civita/ Kustaanheimo-Steifel regularisation: scaling invariance.
    S. Blanes and C.J.Budd, (2003)
  • Explicit, adaptive, symplectic (EASY) integrators using scale-invariant regularisations and canonical transformations.
    S. Blanes and C.J.Budd, (2002)
  • Parallel folding of rock layers.
    C.J.Budd, R. Edmunds and G. W. Hunt, Proc. Roy. Soc. (2002)
  • Self-similar blow-up in higher-order semilinear parabolic equations.
    C.J.Budd, J.F. Williams and V.A. Galaktionov (2002)
  • Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in fourth order differential equations.
    R.E.Beardmore, M.A. Peletier, C.J. Budd and M.A. Wadee (2002)
  • Mesh selection for a nearly singular boundary value problem.
    C.J.Budd, H. Huang and R.D.Russell (2001)
  • Symmetry adapted moving mesh schemes for the nonlinear Schrodinger equation.
    C.J. Budd and V. Dorodnitsyn (2001)
  • Unified derivation of normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems
    M. di Bernardo, C.J. Budd and A.R. Champneys (2000)
  • Grazing and Border-Collision in Piecewise-smooth Systems: A Unified Analytical Framework
    M. di Bernardo, C.J. Budd and A.R. Champneys (2000)
  • Cellular buckling of structures close to Maxwell load
    C.J. Budd, R. Kuske and G.W. Hunt (2000)
  • Geometric integration and its applications
    C.J. Budd and M.D. Piggott (2000)
  • Asymptotics of new blow-up self-similar solutions of the nonlinear Schrodinger equation
    C.J. Budd (2000)
  • The geometric integration of scale invariant ordinary and partial differential equations
    C.J. Budd and M.D. Piggott (2000)
  • Bogdanov-Takens bifurcation points and \v{S}il'nikov homoclinicity in a simple power system model of voltage collapse
    C.J. Budd and J.P. Wilson (1999)
  • Numerical and analytical estimates of existence regions for semi-linear elliptic equations with critical Sobolev exponents in cuboid and cylindrical domains
    C.J. Budd and A.R. Humphries (1999)
  • Scaling invariance and adaptivity.
    C.J. Budd, B. Leimkuhler and M. Piggott (1999) Book on Integration on Manifolds ed S. Norsett.
  • Geometric integration: Numerical solution of differential equations on manifolds.
    C.J. Budd and A. Iserles (1998) Introduction to Phil. Trans. Roy. Soc. special edition on Integration on Manifolds.
  • New self-similar solutions of the nonlinear Schrodinger equation and their numerical computation.
    C.J.Budd, S. Chen and R. Russell (1999)
  • Trip wire detection for landmines
    C.J.Budd and J.Stockie (1998) Proceedings of the 1998 PIMS workshop with industry.
  • Self-similar fold evolution under prescribed end-shortening
    C.J. Budd, G.W. Hunt and M.A. Peletier (1998), to appear in J. Mathematical Geology.
  • Efficient implementation of Volterra filters for de-interlacing TV images
    C.J. Budd, J. Gravesen and R.E. Wilson (1998) Submitted to Proc. ESGI98
  • The safety implications of the micro-wave cooking of foodstuffs
    C.J. Budd, (1998) Submitted to TPAC News
  • Proceedings of the 1997 European Study Group with Industry
    C.J. Budd editor, (1998).
  • Grazing, skipping and sliding: analysis of the non-smooth dynamics of the DC/DC buck converter
    Mario di Bernardo, Chris Budd and Alan Champneys (1998).
  • An asymptotic and numerical description of blow-up in quasilinear parabolic equations
    C.J. Budd, G.J. Collins and V.A. Galaktionov, to appear in J. Computational and Applied Mathematics, (1998).
  • Self-similar numerical solutions of the porus medium equation using moving mesh methods
    C.J. Budd, G.J. Collins, W.Z. Huang and R.D. Russell, to appear in Phil. Trans. Roy. Soc. (1998).
  • Symmetry based numerical methods for partial differential equations
    C.J. Budd and G.J. Collins. In Proc. 1997 Dundee Conference in Numerical Analysis, (1997)
  • Analytical and experimental investigation of an impact oscillator
    M. Oestreich, N. Hinrichs, K. Popp and C.J. Budd. In Proc. of DETC'97, ASME Design Engineering Conference, (1997)
  • The finite element approximation of semilinear elliptic PDEs in the cube
    C.J. Budd, A.R. Humphries and A.J. Wathen, (1997)
  • Focusing blow-up for quasilinear parabolic equations
    C.J. Budd, V.A. Galaktionov and J. Chen, (1997), to appear in Proc. Roy. Soc. Edinb.
  • Stability and spectra of blow-up in problems with quasi-linear gradient diffusivity
    Chris Budd and Victor Galaktionov, (1997), to appear in Proc Roy Soc. Lond. A
  • An invariant moving mesh scheme for the nonlinear diffusion equation
    C.J. Budd and G. Collins, (1996), to appear in Applied Numerical Mathematics.

    • Quotes:

    The following summarise my attitude to life, mathematics etc.
    [University of Bath] [Dept. of Mathematics]