Chris Budd
Professor C J Budd
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: mascjb@bath.ac.uk
Postal Address:
- Mathematical Sciences
- University of Bath
- Bath
- BA2 7AY
- United Kingdom
Here is my Curriculum Vitae
IMA Vice-President
I am the Vice-President for the Institute for Mathematics and its Applications (IMA)
responsible for Communications and Outreach and also for the 50th Birthday celebrations in 2014
More details of
my activites in maths education and public engagement are given below
CliMathNet
I am co-director of the recently established EPSRC/LWEC CliMathNet network , which has as its aim to bring together
mathematicians, climate scientists and policy makers interested in the science and the impact of climate
change.
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 mesh numerical methods for solving
partial differential equations, with particular application to meteorological problems. My research interests are as follows:
- Adaptive mesh methods, with applications in meteorology and climate
- Data assimilation methods, with applications in meteorology and climate
- Nonlinear elliptic and parabolic partial differential equations, especially problems with singularities.
- Non-smooth dynamical systems
- Complex systems
- Scale invariant adaptive mesh methods
- Optimal transport methods
- Numerical weather prediction
- Structural optimisation
- Power electronics
- Fourth order partial differential equations arising in geology,
structures and in nonlinear optics.
- Industrial problems, especially linked with mechanical and electrical
engineering
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 passionate 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.
If you want to have a look at Bath Taps in action here is a video .
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.
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 or have served 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.
Until recently I was the Education Secretary of the
London Mathematical Society .
Some details of the work of the LMS Education Committee (which I
chaired) are given in the following
LMS Newsletter article
I was one of the authors of the 2011 Vorderman Report on the current state
and future of Maths Education in the UK
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:
Communicating Mathematics
In 2001 I was awarded a National Teaching Fellowship
NTFS
and have used this to create a degree credit programme
on Communicating Maths .
Maths Communicators
is a description of the course and this is a National Coordinating Centre in Public
Engagement
Case Study . Do have a look
and email me if you would like to take this course yourself.
If you are interested in running such a course, then here is a
Guide to Good Practice
on how to do it
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
book on
Piecewise-smooth Dynamical Systems: Theory
and Applications, joint with Mario di Bernardo, Alan Champneys
and Piotr Kowalczyk published by Springer.
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 data assimilation, meteorology, geometric integration and mesh generation
Data Assimilation in Meteorology
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 Centre for Nonlinear Mechanics and the Bath Institute for Complex Systems, BICS:
I am director of the interdisciplinary Bath Centre For Nonlinear Mechanics
which encourages interdisciplinary research through the modelling and application of nonlinear systems.
From 2004-2010 I was director of the Bath Institute for Complex System BICS ,an interdisciplinary institute
exploring the many aspects of complex systems and their applications.
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.
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 Makes Waves A talk on waves presented at the British Science Festival.
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 Facebook
Confessions of an industrial mathematician ..
how to use maths from industry in the classroom (talk for teachers presented at BCME
(April 2010))
Climate Change: Does it all add up? (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 popular book called `50 Visions of Mathematics' will be published by OUP in 2014
Bath Taps Into Science:
Is an annual science road show, 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 for more details
Bath Taps
Into Science Festival
If you want to have a look at Bath Taps in action here is a video .
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
Opening ,
Response ,
Final
Three articles for the Economist debate on the importance of science and maths to the economy, C. Budd, (2012)
Maths makes waves
C. Budd, (2013)
How to add up quickly
C. Budd, (2013)
Eat, drink and be merry, making sure it's safe
C. Budd, (2010)
Eat, drink and be merry, helping it all go down well
C. Budd, (2010)
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)
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.
Academic Publications:
Here are some recent academic publications, preprints and notes
Fast three dimensional r-adaptive mesh redistribution
P.A. Browne, C.J.Budd, C. Piccolo and M.J.P. Cullen, (2013)
The effect of numerical model error on data assimilation
S.E. Jenkins, C.J.Budd, M.A. Freitag, N.D. Smith (2013)
Monge-Ampere based moving mesh methods for numerical weather prediction,
with applications to the Eady Problem
C.J.Budd, M.J.P. Cullen, and E.J. Walsh (2012)
The origin of power-law emergent scaling in large binary networks
D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith (2012)
Multi-layered folding with voids
T.J. Dodwell, M.A. Peletier, C.J. Budd and G.W. Hunt (2012)
Self-similar voiding solutions of a single-layered model of folding rocks
T.J. Dodwell, M.A. Peletier, C.J. Budd and G.W. Hunt (2011)
Resolution of sharp fronts in the presence of model error in
variational data assimilation
M.A. Freitag, N.K. Nichols and C.J. Budd (2011)
A fast method for solving binary programming problems using
first order derivatives, with specific application to topology
optimization with buckling constraints
P. A. Browne, Prof. C. Budd, Prof. N. I. M. Gould,
Dr H. A. Kim and Dr J. A. Scott (2011)
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.
- I'm playing all the right notes, but not necessarily in the right order.
- Call that a band, I've seen better bands on a cigar.
- "Captain, for me to save our lives I have to perform actions
which violate several known laws of physics and require me to develop
a completely new theoretical understanding of five-dimensional
hyperspace, all in under 5 seconds", " Do it Spock!"
- If you think that you know all the answers, then you are not
asking the right questions
- Money cannot buy you happiness. But it can buy you marshmallows.
- He digs deepest who deepest digs.
- All known mathematics has already been discovered by an obscure Russian working in the late 1940's
- If all else fails, hug your teddy.
[University of Bath]
[Dept. of Mathematics]