confessions of an industrial mathematican chris budd
TRANSCRIPT
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Confessions of an industrial mathematican
Chris Budd
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What can industry learn from maths?
What can maths learn from industry?
Why does this matter, and is it worth the effort?
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Two perspectives on applied maths
Some ‘commonly held views’
• Maths is useless and is best kept that way
• Applied maths is bad maths
• Industrial maths is even worse than applied maths and is only done for the money!
• All mathematicians are mad
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My own view:
• Almost all maths can be applied almost everywhere almost surely
… And this simple fact is truly amazing!!!!
• We can learn lots of new maths from almost all applications
Calculus, Fourier analysis, Nonlinear Dynamics
• Applied maths is a two way process of learning new ideas and transferring them from one application to another .. And this is hard!!
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Maths appears in rocks
Swallow tail catastrophe
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Is maths also present in human behaviour?
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Good applications of maths can change the world
Vectors, Maxwell, Radio, FFT, digital revolution, computers
Google Matrices, eigenvalues
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How does industry fit into all of this?
Can maths be of any possible use in industry?
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Traditional industrial users of maths are
Telecommunications, aerospace, power generation, iron and steel, mining, oil, weather forecasting, security, finance
But they equally well be …
Retail, food, zoos, sport, entertainment, media, forensic service, hospitals, air-sea-rescue, education, transport, risk, health, biomedical, environmental agencies
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All have problems which can potentially be formulated, and solved using mathematics
Maths connects with all areas and knows no bounds!
Too few people recognize that the high technology so celebrated today is essentially a mathematical technology
Edward David, ex-president of Exxon R&D
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Success story for CJB:Non-smooth dynamics
But we can also learn new maths from industry!
How do things rattle, bounce and slide?
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For example: Aircraft undercarriage
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Impact oscillators: the simplest non-smooth system
.,
,),cos(
xxrx
xtxxx
obstacle
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Novel bifurcations as parameters vary.
Period doubling
Grazing
Theory
Experiment
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01.0
2
x
Period-adding route to chaos
Transition to a periodic orbit
Non-impacting
orbit
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Impacts and complexity in human behaviour
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Scramble crossing
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Escape from a lecture theatre!
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Sona African sand patterns
Used to tell stories
(3,4) (2,4)
Another example:
Some early maths from the entertainment industry
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(4,8)
Almost identical to Celtic Knot designs
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(2,2) 2
(3,2) 1
(5,3) 1
(4,4) 4
How many paths are needed?
HCF … proved by a geometrical version of Euclids Algorithm
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Chased Chicken Design
What patterns can we see here?
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But what are the problems of working with industry?
What industry wants
What do universities want
• Short term solutions
• Confidentiality
• Money
• Long term and deep research
• Open publication
• Training of young people
Seem irreconcilable .. But there is a middle way!
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Study groups: a tale of zoos and fish
Study Group Model (in use all over the world)
• Bring academics and industrialists together
• Pose industrial problems on the first day
• Work on the problems for a week in teams
• Present a paper at the end
• Follow up with longer term projects
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A wonderful way to
• Make new contacts
• Find really good research problems
• Train students and staff
• Get great examples for undergraduate teaching
• Make a fool of yourself in public!
ESGI, ECMI, MITACS, PIMS, Australia …
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t
2
2
x=
Example: Artis Zoo Amsterdam
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So why bother?
The challenges of industry make us think ‘out of the box’ and address new challenges
Maths knows no bounds ..
And …
The maths needed to solve and drive industrial problems is boundless
Pointless to differentiate between pure and applied maths!
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We live in interesting times with the way that we apply mathematics in a process of great transition!
20th century .. Great drivers of applied maths are physics, engineering and more recently biology
Expertise in ….
• Fluids
• Solids
• Reaction-diffusion problems
• Dynamical systems
• Signal processing
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Usually deterministic Continuum problems, modelled by Differential Equations
Solutions methods
• Simple analytical methods eg. Separation of variables
• Approximate/asymptotic approaches
• Phase plane analysis
• Numerical methods eg. finite element methods
• PDE techniques eg. Calculus of variations
• Transforms: Fourier, Laplace, Radon
Still pose MAJOR challenges eg. Exponential asymptotics
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What are the drivers of the 21st century applications?
• Information/Bio-informatics/Genetics?
• Commerce/retail sector?
• Complexity?
What new techniques do we need to consider?
• Discrete maths
• Data and data assimilation
• Stochastic methods
• Very large scale computations
• Complex systems and networks
• Optimisation (discrete and continuous)
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We cannot afford to differentiate between pure and applied maths either in research or in teaching if we are to meet these challenges in the future!
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Example: From Farm to Fork and Beyond
Maths and the food industry
We use maths to help grow, store, freeze, defrost, transport, cook, eat and digest food
Maths can do lots of what if? experiments in complete safety
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Example : Finding land mines
Land mines are hidden in foliage and triggered by trip wires
Land mines are well hidden .. we can use maths to find them
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Find the trip wires in this picture
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Digital picture of foliage is taken by camera on a long pole
••
•
•
Radon transform
x
y
f(x,y)
R(ρ,θ)
Points of high intensity in R correspond to trip wires
θ
ρ
Isolate points and transform back to find the wires
Radon Transform
xx
x
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Mathematics finds the land mines!
Who says that maths isn’t relevant to real life?!?