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Industrial Mathematics Initiatives: An (inter)national need?

Graeme Wake Centre for Mathematics in Industry

Massey University Auckland, New Zealand

http://www.mathsinindustry.co.nz g.c.wake@massey.ac.nz

ANZMC 2008

Key Reference: Organisation for Economic Co-operation and Development : Global

Science Forum

Report on Mathematics in Industry July 2008

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Views of MathematicsMathematics is the “software” of science, yet has a life of

its own.

The connections however sustain it.

Features of Mathematics are: Longevity - it lasts forever Open ended-ness Developed by abstraction Universality

However…

“We shall need a new breed of mathematical professionals able to mediate between mathematics and applied science. The cross-fertilization of ideas is crucial for the health of the science and mathematics.” – Michael Gromov, France: AMS Notices 1998.:

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OECD Report: The challenge

• 3.2 The Academic Environment • “The academic discipline of mathematics has

undergone intense intellectual growth, but its applications to industrial problems have not undergone a similar expansion. “

• “The degree of penetration of mathematics in industry is in general unbalanced, with a disproportionate participation from large corporations and relatively little impact in small- and medium-sized enterprises. “

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Across the world there are a wide range of activities in existence which are designed to spread the problem-solving power of mathematics to industry and society-at-large, in order to enhance the knowledge and technical base of organisations.

There are a range of models practised, and there are a few notable examples where a high level of activity has been obtained. This paper traverses the options, and looks at what is achievable in a given instance, such as in South Korea and the nearby countries.

As Director of the Australian and New Zealand Mathematics-in-Industry Study Group 2004-6, I have been privileged to help develop this in our region. Also I have assisted with similar developments in other neighbouring countries around the Pacific, notably in Brunei, Thailand and South Korea.

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Industrial Mathematics is a distinctive activity:

starts from a client’s problems, which, although not described by mathematics, are possibly solvable using quantitative techniques of analysis and/or computation.

Illustrative case-study examples will be described where spectacular results have been obtained in medical and engineering applications.

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This activity has positive spins-off for it serves to* establish better links between industry and

academic mathematics.* enhance the image of mathematics in the

community.* provide improved university education of

mathematicians through - expanded employment prospects for mathematics graduates;       - fresh research problems for mathematicians; - innovative material for teaching courses.

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The lot of an Applied Mathematician

Applied Mathematics seems to be about finding answers to problems. These are not written down in some great book

and in reality the hardest task for an applied mathematician is finding good questions. There seem to

be three types of problems in the real world:o The trivial

o The impossibleo The just solvable

The boundaries between them are very blurred. They vary from person to person, and some of my strongest

memories are of problems that suddenly jump one from category to another, and this is usually with the help of

colleagues!

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Modelling ParadigmsThe 10 commandmentsThe 10 commandments

• Simple models do better!• Think before you compute• A graph is worth 1000 equations• The best computer you’ve got is between your

ears!• Charge a low fee at first, then double it next

time• Being wrong is a step towards getting it right• Build a (hypothetical) model before collecting

data• Do experiments where there is “gross

parametric sensitivity”• Learn the biology etc.• Spend time on “decision support”

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What is Industrial Mathematics?

Means by which industry improves quality of products Starts with a problem posed by industry An equal partner with science and engineering at all stages Must be meaningful to industry and non-mathematical personnel The problem to be solved must be as stated Must include advances in industrial products or processes in addition to containing advances in

the mathematical sciences Will often include new theories, not just algorithms

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What skills are needed to be an Industrial Mathematician?

Covers a vast range of the mathematical sciences:

o Data mining and analysiso Networkso Optimisationo Stochastic processeso Systems models – such as dynamical systemso Discrete and continuous modelso Spatial patternso Conservation principleso Etc

Collaborative team work needing good communication skills

All four stages of the modelling process:o Formulationo Solutiono Interpretationo Underpinning decision support

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What skills are needed for Industrial Mathematics?

Breadth in the mathematical sciences + depth in some area of the mathematical sciences

Breadth in science, technology and commerce Ability to abstract essential mathematical/analytical

characteristics from a situation and formulate them in a fashion meaningful for the context

Computational skills, including numerical methods, data analysis and computational implementation, that lead to accurate solutions

Flexible problem solving skills Communication skills Ability to work in a team with other scientists, engineers,

managers and business people Dedication to see solutions implemented in a way that make a

difference for the enterprise Willingness to follow through to ascertain what real impact the

modelling/analysis has had in the enterprise

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Why aren’t there more mathematical scientists in industry?

Recently the low interest in mathematics was the topic of a report in Britain entitled “Low Interest in Mathematics set to Cripple British Industry”. See “Mathematics Today”, IMA Bulletin, October 2003. The same is true in other countries.

The necessary skills (formulation, modelling, implementation and decision support) are often not part of mathematical sciences training in universities

Collaboration between academics and industrialists requires crossing cultural barriers with high investment costs

Often industry hires well-trained scientists/engineers with strong maths/stats background to take care of mathematical sciences issues. Why?.....

Industrial mathematics is often interdisciplinary and is not appreciated by the mathematical sciences community

We are not producing the right mix of graduates, especially at the postgraduate level

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Recommendations:Departments seeking to create new mathematical

sciences programs should consider including industrial mathematics programs among the many options offered

Departments that wish to set up industrial mathematics programs should start with a program at the master’s level

Staff in a department should start establishing relationships with industry early, preferably with stable local or regional industries, so as to make industrial mathematics programs in the future

Staff and postgraduate students should participate in industrial mathematics workshops held nationally, such as the ANZIAM one.

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The Academic Perspective

Incentives for collaboration with industry– Relevance of expertise to real world applications– Satisfaction arising from knowledge transfer– Source of interesting new problems?– Financial gain?

Disincentives– “Dirty end” of science?– Career structure– Rating = f (research, teaching)

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The Industry Perspective

Is mathematics actually relevant to industry?What benefits can I expect?What are the different mechanisms?How much will it cost?Why can’t I buy it today?Only useful for long-term projects?Will I actually understand the end result?How can I protect our IPR?What’s in it for academics?

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Mathematics in Industry: OpportunitiesOptions (Not mutually exclusive)

• Regular industry days (monthly)• Theme days e.g.. Environmental Modelling, Petroleum,

Biology, Health• Student projects in Industry – Claremont style (funding)• Industrial Mathematics consulting office – on and off

campus• Mathematics in Industry Study Group –

OCIAM/ESGI/ANZIAM style• Dedicated Centre for Mathematics in Industry – e.g. the

Smiths’ Institute, Oxford• International linkages like that of OCCAM http://www.maths.ox.ac.uk/occam A newly-formed Oxford Centre for Collaborative

Applied Mathematics (OCCAM), funded for five years from 1 October 2008 by the Global Research Partnership of the King Abdullah University of Science and Technology (KAUST).

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OCCAM, the Oxford Centre for Collaborative Applied Mathematics. The objectives of OCCAM are to use focused teamwork and

innovative mathematical and computational methods to help understand pressing, unsolved problems. OCCAM's primary focus is within the following four interdisciplinary research areas:

• Methodologies • Resources, Energy and Environment • Biosciences and Bioengineering • Materials Science and Engineering

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Needs

• Commitment and Experience

• New staff member(s)/secondment??

• Industrial linkages and contacts – ex students, friends etc

• Across departments

• Across ANZ – parent body

• Training for staff and graduate students

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Problem Presenters MISG2005• Backyard Technology, Queensland

#5 Problem Sponsor

• Compac Sorting Equipment #6 Problem Sponsor

• Environment Canterbury

#4 Problem Sponsor

• Fisher & Paykel#7 Problem Sponsor

• Lincoln Ventures

#1 Problem Sponsor

• New Zealand Steel#2 Problem Sponsor

• Transpower

#3 Problem Sponsor

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Problem 6: Mark McGuinness, Tim Marchant, Senaratne

Compac Sorting Equipment“Modelling the physics of high speed product-weighing”

MISG 2005

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What we would like

• Mathematical model of the physical process of weighing the fruit

• To be able to use the model to improve the system design by testing different scenarios

• Better signal processing for determining the true weight of the fruit.

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Problem 4: Moderators: Heather North, Rod Weber, Joanne Mann

• Factors Associated With Trends in Bare Ground in the Central South Island High Country

Jeromy CuffEnvironment CanterburyTimaru

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High Country Example 1

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High Country Example 2

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High Country Example 3

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High Country Example 4

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High Country Example 5

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Some South Island Hill and High Country Issues

• Bare ground creates surface erosion risk– Extensive areas of LUC classes VII and VIII

land destocked in the 1960s - 1980s– Objective was to improve ground cover

• Hieracium species have invaded tussock grasslands– Out competes resident vegetation but is not

persistent– Doesn’t provide 100% cover

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MISG 2005 Challenge• Create a mathematical model that identifies and

describes the main effects and interactions of the factors influencing short and long term ground cover trends in the high country.

• Such a model would be invaluable for identifying land management options and could be applied to help ensure soil conservation in the Canterbury high country tussock grassland ecosystems by identifying and quantifying the important factors

• to prevent further deterioration in hign country condition and• improve the condition of presently degraded lands

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Problem 7:Moderators: Clive Marsh, Andy Wilkins, Jane Thredgold

Temperature Control for Wash Water

Steven Mansell Kerry Newnham Josh Cox

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Problem Summary

Need to balance hot and cold intake to get correct wash water temperature

Currently no feedback from bulk water - only from mixing chamber

‘Abnormal’ operating conditions have been identified

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Project Goals

development of a closed loop transfer function

confirmation of correct sensor positiondiscussion of sensitivity issues with regard to

above

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Fisher and Paykel Brainstorming

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Problem 1: Moderators: Sean Oughton, Tony Roberts, Joanne Mann

Modelling the effects of porous barriers on spray drift.

John-Paul Praat

Lincoln Ventures Ltd, Hamilton

Alison Forster and Jerzy. A. Zabkiewicz

Plant Protection ChemistryNZ, Rotorua

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Aim for the week:

Produce a model to predict Produce a model to predict shelter effect on spray driftshelter effect on spray drift

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Produce a model to predict shelter effect on spray drift

Aim for the week:

Variables:Spray characteristics

(eg. droplet size, release height)Environmental factors

(eg. wind velocity, wind direction)Shelter characteristics

(eg. porosity, width, height, length, leaf area index, capture efficiency, shape of the cross-section area)

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Problem 3: Moderators: Kaye Marion, Bill Whiten, Radneesh Suri

Optimising the relationship of electricity spot price to real-time input data

Conrad Edwards,

Transpower Ltd

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Problem summary New Zealand’s electricity market is based on a half-

hourly spot market using ex-post locational marginal prices.

A scheduling, pricing, and dispatch model “SPD” is a linear program used to determine, from bids and offers: dispatch in real-time, and then the corresponding nodal prices, ex-post

“Spring washers” are counter-intuitive but mathematically predictable price patterns where some nodal prices can be >> highest generation offer some nodal prices can be negative

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Challenge for MISG2005

Develop an algorithmic means of identifying occurrences of spring washers where extreme prices are especially sensitive to the constraint specification and other model parameters

Such an algorithm would then trigger a process of checking the constraint and/or input data to determine the actual sensitivity of the nodal price, and if necessary an algorithm for correcting the constraint of parameter causing the sensitivity with better measured values

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Problem 2: Moderators: Tim Marchant, Steve Taylor, Alysha Nickerson

Development of empirical relationships for metallurgical design of hot-rolled steel products.(New Zealand Steel Ltd, Glenbrook)

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Hot Rolled Coil

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MISG 2005 Objectives - Part 1

• Identify processing and product variables which have a significant effect on product mechanical properties

• Develop an empirical model enabling the mechanical properties of hot-rolled coil products to be predicted from the values of the product and process variables

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If time allows:

• Develop a similar model for hot rolled plate products.

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• Outcomes:

- Progress with all problems

- Ongoing collaborative arrangement in most cases

- Industry-specific, in-house, one-off workshops : This should have a national focus.

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Conclusions of the OECD Report

• Conclusions and Recommendations

• “Industry faces problems that extend well beyond the envelope of classical topics in mathematics. Many of these problems have a significant mathematical component, and the intellectual challenges they pose fall in many cases within topical areas of current research in the mathematical sciences. Stronger links between mathematics and industry will be beneficial both to the partners and to national economies. They will inspire new mathematics and enhance the competitive advantage of companies. ….”

Proposal

• The proposed new Masters subject is Industrial Mathematics and Statistics. Core components and applications of Mathematics and Statistics are combined to provide the quantitative methodologies needed by modern technological society. Industry often lacks the in-house expertise that underpins experimental design, data acquisition and analysis. The new MInfSc subject will equip graduates with in-depth understanding and a synergistic set of powerful tools to model industrial systems and optimise decision making.

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Discussion: Comments