Hard at work

I had a relaxing day planned. I was to talk to (and play Scattergories with) Patrick on Skype in the morning, before Palm Sunday Mass, lunch with some fellow Australians, an afternoon at the Gondoliers set build (sometimes hard physical work, but most of the time involving no brain power), then probably an early night.

I turned on my computer to talk to Patrick and discovered an email from my supervisor, to the effect:

"I'm going to a conference on Tuesday and would like to talk about [an idea I - I mean Smatthey - had one morning and talked about to the group the next day]. Can you make some slides and graphs for me, and talk to me about them at 12:15 tomorrow, please."

Note that I'm using authorial quotation marks here. This isn't a direct quote, simply the words I would put in his mouth were I writing a factual but dramatic (ie. with actors, not documentary) movie of my life, or something like that (also, it would be a phone message, because emails of more than about four words don't work so well in movies...).

Anyway, back to the point (just didn't want to be misrepresenting him!). The tenor of my day immediately changed. Actually, I still did most of the specific things I had planned: it was just the set build that missed out. After beating Patrick at Scattergories (perhaps I should change the post title to 'Patrick Avenell: moderately talented Scattergories player'?) and having breakfast, I went into the office (it was just about time for Mass, so I only deposited my belongings at that time). I actually only spent around eight hours there, but those hours were 11-1 and 3-9, making this the day I've worked at the office latest since I've been here (I've been at the office later, but only because I was on campus doing fun things until late and needed to return to collect my belongings).

Writing about my idea wasn't difficult: I've spent quite a bit of my time trying to solve relatively complicated equations, but this idea was one I had to avoid doing so. The idea is that, as a battery is discharged, particles of the active material (the stuff that stores the lithium that moves around in the battery in order to make current flow) have to accept the lithium flowing into them. The more lithium a particle has in in, the less it wants to accept more. Smaller particles fill up faster, so if you have a range of particle sizes, it's very difficult to know the potential of the battery at a particular time, (the potential is basically how much the particles want to accept lithium). I realised a much simpler problem is to forget about the complicated dependence of potential, and just think of the particles as either being full or not full, so there is no difference between almost empty and almost full. This makes the equations so much easier that it's essentially not even solving equations. When looking at my work again, I realised there was a further good idea that I had (thinking about the rate the particles fill up by imagining them unfolded into cylinders, then you can imagine them filling like rain gauges of different sizes but the same shape, all sitting in the same rain). Looking at it in this way, it's easy to see how potential will vary just by drawing one graph and comparing its value and its integral (the area underneath it).

It didn't take all that long to make the slides with the explanation and equations: the hard part was the graphs. The problem is that the approach is very general, so I have to decide what is the appropriate thing to graph. I spent a long time trying to use my approach to explain the voltage fall-off in a particular experimental paper my supervisor suggested. It works to some extent, but to make it fit well enough to be worth doing, I'd really be cheating (because my approach is so general, it's bound to fit if I let it). After much thought, I eventually decided that I'd just make up some representative size distributions, and show what the potential would look like for each of them.

If there's interest, I'm happy to put the slides up once I complete them.