Views of Mathematics

1. 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

2. Views of Mathematics Mathematics 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.:

3. 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. “

4. 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.

5. 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.

6. 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.

7. 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: The trivial The impossible 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!

8. Modelling Paradigms The 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”

9. 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

10. What skills are needed to be an Industrial Mathematician? Covers a vast range of the mathematical sciences: Data mining and analysis Networks Optimisation Stochastic processes Systems models – such as dynamical systems Discrete and continuous models Spatial patterns Conservation principles Etc Collaborative team work needing good communication skills All four stages of the modelling process: Formulation Solution Interpretation Underpinning decision support

11. 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

12. 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

13. 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.

14. 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)‏

15. 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?

16. Mathematics in Industry: Opportunities Options (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).

17. 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

18. 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

19. 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

20. Problem 6: Mark McGuinness, Tim Marchant, SenaratneCompac Sorting Equipment “Modelling the physics of high speed product-weighing” MISG 2005

22. 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.

23. Problem 4: Moderators: Heather North, Rod Weber, Joanne Mann Factors Associated With Trends in Bare Ground in the Central South Island High Country Jeromy Cuff Environment Canterbury Timaru

24. High Country Example 1

25. High Country Example 2

26. High Country Example 3

27. High Country Example 4

28. High Country Example 5

29. 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

30. 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

31. Problem 7:Moderators: Clive Marsh, Andy Wilkins, Jane ThredgoldTemperature Control for Wash Water • Steven Mansell • Kerry Newnham • Josh Cox

32. 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

33. Project Goals • development of a closed loop transfer function • confirmation of correct sensor position • discussion of sensitivity issues with regard to above

34. Fisher and Paykel Brainstorming

35. Problem 1: Moderators: Sean Oughton, Tony Roberts, Joanne MannModelling 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

36. Aim for the week: Produce a model to predict shelter effect on spray drift

37. Aim for the week: Produce a model to predict shelter effect on spray drift • 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)

38. 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

39. 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

40. 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

41. 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)‏

42. Hot Rolled Coil

43. 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

44. If time allows: Develop a similar model for hot rolled plate products.

45. Outcomes: - Progress with all problems - Ongoing collaborative arrangement in most cases - Industry-specific, in-house, one-off workshops : This should have a national focus.

46. 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. ….”

47. 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.

48. Discussion: Comments