At uni on Saturday

Today I went to uni to work.  It's the first time I've needed to go on a weekend since I first became a fulltime research student a little over a year ago.  Admittedly, I did go to uni on the Melbourne Cup public holiday last year, but given that my thesis was due the next day, that was to be expected.

My current main research project involves running simulations of the configuration of a single chain block copolymer in a poor solvent.  Perhaps at a later date I'll explain a little of the statistical physics and mean field theory behind it, but at the moment "simulations" will suffice.  On Tuesday of this week, I had a chat with David (my supervisor) and Min (my officemate) about the program I wrote.  I then began working on improving it so that it can run with finer detail.  Up to this point, I've been using a 21 by 21 by 21 lattice, on which I'm simulating polymer density.  21 may seem like an odd number (well, it is...), but it's because the central point is (0,0,0), and from that I go 10 in each direction.

We decided that it was worth increasing the resolution, to what has ended up as a 51 by 51 by 51 lattice.  Now, this may sound only 2.5 times as big, but in fact it's more than 14 times as big, because it's 2.5 times as big in every direction.  Previously, I had been using one monomer as the unit of my integration, but for a long polymer (eg. 10 000 monomers) I would no longer have enough memory to store all the variables I need.  Thus I decided to decouple the monomer size from the integration step, and I now use 200 integration steps, no matter how long the polymer is.

Unfortunately, that means that my first order expressions for the differential equations I was solving are not sufficient.  I tried a couple of methods, settling on a random sample of surrounding points to find the exponential of the laplacian: basically a Monte Carlo / kernel method.

At this point people who know their applied maths might object that the Monte Carlo method has nothing to do with a kernel.  I'd basically agree, but the kernel is what I'm integrating, and the Monte Carlo method is how I'm integrating, so it makes sense.

Only around 5:45pm yesterday did I settle on this method, and I was to meet my family for dinner not long after 6.  I thus decided that I'd need to go to uni today to set it up.  I have now done so, and it seems to be working very well.  I'll check it once more tomorrow, before leaving it running while I'm away.

I will be away for two and a half weeks, in Sydney and then Mexico.  I'm looking forward to experiencing the International Physics Olympiad as a staff member instead of a student.  I probably won't post while I'm away, but I will keep you updated while I'm away.