Mathematical modelling can help keep the stuff that comes out of your taps clean and fresh

In July, my wife Avril and I celebrated our 40th wedding anniversary in Barbados. We joked with the hotel waiter that we only came for the tap water, which is amazingly good. We found

out why when we visited Harrison’s cave. Barbados is mostly fossilised coral, which acts like a giant filter for rainwater. So the tap water is very clean, with a tangy mineral taste.

Several years ago we went to Slovenia, and were invited to join a group of Chinese karstologists visiting the spectacular caves there. Karst is rugged limestone, all jagged edges and collapsed holes. What’s all this geology got to do with maths? Well, I was idly reading a mathematics research journal and came across an article about karst.

Great stuff for mathematicians and geologists, to be sure, but why should anybody else care about karst?

The answer is: groundwater. Much of the water we drink, and the water that industries use, comes from groundwater.

Because we rely heavily on groundwater, contamination is a serious problem. Industrial waste, excess fertiliser running off fields, landfill sites for everyday rubbish, and dozens of other sources can cause undesirable chemicals to get into our groundwater. To some extent, karst aquifers can clean themselves, given time, but it’s not clear whether they can cope with the level of contamination that is common today. So scientists need to understand how water flows through the porous karst geology.

Traditionally, they use mathematical models of fluid flow through a porous substance. The usual models assume that the rock is equally porous everywhere, because until recently no one knew how to include more realistic effects, such as cracks in the rock, surface sinkholes, and springs. The sums were simply too difficult, even using powerful computers. But those cracks are more important than the porous rock when we want to know how contaminants move from place to place.

That’s where all the stuff about Beavers-Joseph interfaces comes in. It’s how the modellers deal with holes and cracks in porous rock. After many years of effort, the mathematicians who work in this area have discovered a good way to set up realistic models in a computer, and calculate how effective the rock is at filtering out chemical nasties and keeping itself clean.

The Economist

Write an essay to support the following statement: “Mathematics makes the world go round”.

 

UNIT TEN

Scan the article to state the reasons for a wider use of renewable sources of energy.

Read the article again and complete it with a sentence A-E. There is one sentence you don’t need.

A. In order to exploit renewable sources of energy it is often necessary to make a considerable capital investment.

B. Geothermal energy is also becoming more and more widely used in some arrears.

C. This airborne water ultimately falls as rain, creating rivers which may be dammed to produce hydroelectric power.

D. This estimate, however, does not allow for economic and environmental constraints and is therefore somewhat misleading.

E. Indeed, it is the perceived notion of sustainability that is driving governments around the world to introduce legislation promoting the use of renewable energy.

Renewable Energy

Climate change, coupled with concerns about high oil and energy prices, is driving a global trend towards the increased use of renewable energy. Unlike fossil fuels which are rapidly being depleted, renewable energy sources such as sunlight and wind are naturally replenished and therefore sustainable. (1)_____________

Most sources of renewable energy originate either directly or indirectly from the sun. For example, both wind and wave power derive their energy indirectly from the sun. When solar radiation is absorbed by the Earth it is dissipated around the globe in the form of winds and ocean currents. The wind interacts with the oceans and transfers mechanical energy to water thus creating waves. In addition, solar energy promotes evaporation of water from the oceans. (2)_________________

Furthermore, solar energy drives the photosynthesis necessary for the plants that are used to create biofuels. Currently, only about 18% of the world’s energy demand is supplied from renewable energy sources. However, there is great potential to increase this contribution. Indeed, it has been estimated that the technical potential of renewable energy is more than 18 times that of current global primary energy demand. (3)_________________________ Owing to constraints, such as economic

competitiveness, the potential that is likely to be realized in practice will be only a fraction of this value.

(4)_________________This is particularly the case with large infrastructure projects such as hydroelectric or tidal barrage schemes. To be economically viable, such projects must absorb large capital costs and still be able to compete on price with traditional sources of energy – something which in most cases it is difficult to do.

Peggy Daniels Becker, Alternative Energy