Approximation Theory

I spent three hours of this afternoon in a church hall in Guildford. I haven't found religion - far from it. I was there on purely secular matters, taking an exam for an Open University module on Approximation Theory. A few years ago I decided to start an MSc in Mathematics to learn more about various topics that I've never formally learned before. At the time, I approached my head of department to see if the University would part-fund, and he said no. Why couldn't someone like me with a PhD just pick a book to learn a new topic? A good question, but the answer is that without the rod of the assignment deadlines, I'd never in practice get round to learning the material.

So, today was the culmination of the year of learning all about different ways of approximating functions - polynomial approximations, splines, all that kind of stuff. As ever, I didn't revise perhaps quite as much as I should have (here I am learning about all the things my students understand very well), but it was okay. The exam was fair, especially after I asked the invigilators to turn the speakers off so that I stopped hearing them cut up paper with scissors next to the microphone (I have no idea what they were doing to bide the time). I'll find out the results in December, but I'm happy with how the course went, and there are even a few ways I might bring some of what I've learnt in to my research.

It's a shame the OU are putting up their fees so highly. It's not a good time to be a player in the HE market, but I can't see that their new fee regime will be good for them. Fortunately for me the existing MSc fees will be held for current students.

Bananas!

There's a nice article on the BBC News website talking about the Banana Equivalent Dose as a measure of radiation. It's a kind of nice idea, since it's motivated by the desire to point out that everyday objects are radioactive. Bananas are more radioactive than most things since they are high in potassium, which has a radioactive primordial isotope, Potassium-40 (K-40). K-40 is also responsible for the last item in the table in the BBC article - sleeping with someone is equivalent to half a banana's worth of radiation dose, because your bed partner is partly made of potassium, as are you. Around 5000 radioactive potassium decays occur every second in a typical adult.

Spot the difference

With due deference to Private Eye, and Peter Coles's Astronomy Look-a-likes, I must say that I have been struck (as pointed out by Kate Lancaster), by the similarity between neutron discoverer James Chadwick, and Old Vic artistic Director Kevin Spacey:

Spacey

Chadwick

On the train through K-25

I'm in Oak Ridge, Tennessee. It's an important place in the history of nuclear physics, being built in the second world war for the Manhattan Project. One of the main jobs that Oak Ridge had was to separate the two main isotopes of Uranium that are found in Uranium ore, Uranium-235 and Uranium-238. U-235 is the one that is needed for nuclear reactors and bombs, but makes up a little under 1% of natural Uranium. For fission in either bombs or a reactor, a much higher concentration of U-235 is needed - the Little Boy bomb that was dropped on Hiroshima consisted of two lumps of enriched Uranium, which were pushed together by a chemical explosion in the bomb to create one lump exceeding critical mass. The average enrichment of those lumps of Uranium was around 80% U-235.

Three different enrichment techniques were developed at Oak Ridge: Gaseous diffusion, electromagnetic separation, and liquid diffusion, with gaseous diffusion taking place at the K-25 plant. The Uranium ore, which came from mines in the Belgian Congo, and bought by the US on the open market, was processed into Uranium Hexaflouride, which is is gaseous at about 55°C. The plant works by repeatedly allowing the gas (containing both isotopes of Uranium) to diffuse through a porous membrane, with the lighter U-235 finding it easier to do so, and so being more concentrated after diffusion. To get high concentrations, the process must be repeated many times, and a huge cascade of diffusing membranes was built, making the plant building enormous.

The picture on the right shows the main building. Each arm of the "U" is half a mile long, and it was reportedly the biggest building under a single roof at the time of completion.

The building is now part-way through being demolished, but today I took a train journey through the site, and saw some of what was left. The Secret City Scenic Excursion Train is a volunteer-run railway that does occasional trips over about a 7 mile distance and back, starting from the edge of the old K-25 plant, through the plant, and then on through some East Tennessee countryside, before getting to the junction with a freight line it's not allowed to use. It's been in existence for coming up for 10 years, so just young enough that it wasn't here when I lived in Oak Ridge, and I was glad I found out about it while I'm over visiting. It would be even better to have really got to look inside the K-25 plant while it was still operational. During decommissioning, the plan had been to preserve the top of the U-shaped building, but it turned out to be too corroded and contaminated to make it viable. A shame...