One of my favourite movable feasts of the year took place yesterday, the Postgraduate Research Day.
We partially fulfil our training obligations to our research students, and also celebrate all the great things they are doing. The third-year students give 15-minute talks, while the second-years have a poster competition. I always learn a few things from the talks and the posters, and yesterday was no exception.
Two of my students gave talks, while one presented a poster. They all did well; in fact, Adam Bohn won the poster competition – congratulations Adam! I won’t speak about their work here, which I should be expected to know; more interesting were topics further from my comfort zone.
One of the talks was about chaotic diffusion in a very simple dynamical system. The system is a tweak of the map x → 2x (mod 1), with a parameter h: essentially, there is a window of length h through which the particle can escape from the interval, and enter an identical system on the next interval up or down. The rate of diffusion turns out to be an everywhere continuous, nowhere differentiable, function of h, first considered by Takagi a century ago. It has a fractal structure, with local maxima and minima crowding in on one another.
Another nice talk by an astronomy student calculated how fast the wind blows on Jupiter. He had used data from the Galileo probe which entered the atmosphere of Jupiter in the 1990s. The equation he had to solve contained a lot of unknowns: some were given by the data, some by simple geometry, some by more advanced physics, and one by a photograph of “gravity waves”, the kind of atmospheric waves which on earth occur downwind of a mountain, from which the wavelength could be measured.
From one of the posters I learned what the Pareto distribution is (a kind of “power-law variant” of the exponential distribution); from another, that the mechanism of inflation after the Big Bang is unknown, and some models predict that it will continue indefinitely (an uncomfortable prospect, under which I would presumably not have been standing there reading the poster).
In the past I used to run the poster competition, named after Ann Cook (whom I have mentioned on this blog); I devised the scoring rules which are still used. But the posters have improved out of sight since then. Not only are they glossy and illustrated, but the amount of thought which has gone into the presentation and layout is quite extraordinary.
The posters were in our new foyer, not officially open yet. The outside is tiled rather nicely with Penrose tiles; but, the day after the hoarding came down, a traffic accident resulted in a number of the tiles being destroyed. Not a good omen! But this was the first use of the space for departmental purposes, and it worked well. (However, this morning they were drilling again; work is not finished yet.)