# So what is mathematical modelling?

Prof. Marcus du Sautoy said "Mathematics can often appear arcane, esoteric, unworldly and irrelevant."   In that New Statesman article Prof. du Sautoy then went on to counter that and outline his views on relevance and importance of mathematics.  (Aside - [If you're into mathematics/physics/Hitchhikers Guide to the Galaxy - you may also enjoy Prof. du Sautoy's thoughts on why 42 is in the fact the "Answer to the Ultimate Question of Life, the Universe, and Everything" published here.)

Like Prof. du Sautoy I believe mathematics offers us tremendous insight into the way the world works.  In the work we do in the Department of Engineering Science we describe the process of using mathematics to understand the world as "mathematical modelling".   So what is mathematical modelling? Wikipedia gives a definition of  "A mathematical model is a description of a system using mathematical concepts and language."   While I agree that's a valid definition - if we met at a cocktail party and I told you that was what I do, you may be politely looking for ways to break off the conversation (depending on your level of interest in mathematics).

The word "language" in the Wikipedia definition is however very important to me.  When I was at school I loved learning languages (and still do).  I studied French to 7th form (now called Year 13) and Latin to Year 12.  I frequently comment that for me mathematics is in many ways just another language.   The mathematical modelling process involves a translation of a problem that arises from a community, industry, science, government etc. into a set of mathematical statements that capture the relevant details.

Once translated into mathematical language do I end up with a set of mathematical equations that I can solve by hand (on paper)?  Not usually!  I sometimes say in jest that while I am a reasonable mathematician, I specalise in writing down equations I can't solve.   This means the modelling process typically includes a phase of translating the mathematics involved into a form that can be solved by a computer.  All going to plan the computer-based version of the model then becomes a "crystal ball" where the modeller can ask "what if?" questions to explore uncertainty (e.g. in a traffic flow model what happens if 50% more cars per hour travel on a certain road due to a special event in the area?)  To make meaningful predictions of the future behaviour of a system the model must be validated against previous observations of that system (e.g. if I want to predict future flow rates and temperatures in a geothermal well, my model should ideally be able to retroactively recover previous flow behaviour).

Finally modellers need to be able to address the "Why?" question ... why was the model constructed?  Does it provide a robust answer to that question?  Through the modelling process having an appreciation of the topic being addressed is very helpful.  Within the Engineering Science degree we allow students to build their understanding of various domains where modelling may be applied (from financial markets to environmental engineering) by having the flexibility to include electives from outside the Department throughout the degree.  We hope that makes them better mathematical modellers!

Save

# Driving electric • 2 Comments

Like many New Zealanders I was (till July last year) the owner of an older car (I won't say how old!) that had a lot of kilometres on the clock.  When it came time to change vehicles I decided to "walk the talk" and buy an electric car.  I took the plunge and bought a second hand Nissan Leaf - and it was "love at first drive".  The car is very quiet, accelerates beautifully and is generally fun to drive. There's no petrol engine in the car, and it charges overnight (in about 6 hours) from a household plug (with a higher current "caravan" socket).  So does "driving electric" make sense?  There were about 1,250 electric vehicles registered in NZ when I bought mine - today there are more like 2,250 (see www.driveelectric.org.nz for current stats).  That means more and more NZers think it does make sense.

Nissan Leaf vehicles charging at a Vector charging station in Takanini. Mine was headed on a day trip further south that day.

I was pleased to see research published by EECA in New Zealand that confirmed the environmental benefits of electric cars.  They state:

"Across the lifecycle, pure EVs have around 60% fewer CO2 emissions than petrol vehicles. When we just look at the CO2 emissions from use, New Zealand’s high proportion of renewable electricity generation means EVs have around 80% fewer CO2 emissions when driven in New Zealand.  As the renewable proportion of New Zealand’s electricity continues to grow, the CO2 emissions from an EV will reduce further."

EECA's research also dispels concerns re net environmental impacts associated with lithium production for electric vehicle batteries.

So what's the catch?  The typically advertised range of my model of Nissan Leaf, with its 24 kWh battery capacity, is 125 km on a full charge.  That assumes driving on the flat on smooth roads etc. - so in reality I get less commuting range than that since we live at the top of a long winding hill.  I have a fairly significant commute so I charge the car every night at home.  What happened to my power bill?  I opened the first one with bated breath!  However the car's energy demands are relatively modest - so I traded filling up on a full tank of petrol every week, for an increase of \$20 to \$30 on my monthly power bill (I have a discounted rated for night rate electricity, and also have solar panels on the roof of my home that help charge the car when it's home at the weekends).

Colleagues in the Department are interested in supporting NZ's transition to more electric vehicles.  We've had a student project building web-based mapping tools that assess the viability of the use of an electric vehicle in Auckland for commuting taking into account speed limits and terrain (note that driving downhill regenerates charge in the car battery).  The tool is not quite ready for public use but I looked forward to seeing it deployed.

Companies such as Vector are deploying fast chargers that will charge a car like mine in 20 minutes or so.  Their chargers are currently free for public use, but that will change at some point.  The Government, via EECA are also trying to accelerate the transition to  electric vehicles, via the Low Emission Vehicles Contestable Fund.

So, a longer post than usual, but I have a lot of love for driving electric!

Save

Save

Save

Save

Save

# Why?

Happy New Year!  Are you happy to be back at work, or looking forward to being back in class in 2017?  Do you know why?

In 2016 I served on various panels and committees (on campus and beyond) in which decisions were made that offered people or organisations opportunities and resources, or that looked to make decisions on process/structure in organisations.  I won't elaborate on the details since it many cases they are confidential.  However when I reflect on the most successful interactions they were normally with people who had clearly answered the "why" question for themselves and let that show.

The "why" that gets me out of bed in the morning is the the belief that engineering mathematics is a toolbox that can offer businesses, government and communities insight and novel solutions to the problems they face - in turn creating value for shareholders and society.  As a Department Head I aim to create an environment where students can develop their expertise with those mathematical tools (and create new tools). Anyone shadowing me in my office would see "what" I do in business hours - meetings, financial approvals, paperwork etc.  Connecting what I do to the underlying reason why I do it ensures I stay energised.

One of my colleagues tells me I have a look in my eye that tips them off I am about to ask "Why .... ?"  That person has learned to be prepared for the fact I may ask a series of questions to try to connect what they asking me for/about to a wider context.  That helps make sure everyone is on the same page and that we are taking action that supports a common purpose (or conversely identifies that taking that a certain action doesn't support that purpose and won't be pursued).

If you're a student looking for an opportunity after graduation (employment, or postgraduate study) I'd encourage you to make sure you not only communicate what you can do, but why using those skills in a particular organisation excites you and aligns with what makes you tick.  If you can join those dots I believe there is a better chance that doors will open.

For anyone who wants to think more about their own "why" a one good place to start may be this page from Forbes.  If you can stay connected to why you do what you do then 2017 will be all the more exciting!

Save

Save

Save