I spent all day Sunday deriving in Singapore.

No, not driving. There’s no way I would drive here. It’s not that they drive on the wrong side of the road – I’ve done that before. Uncomfortable but manageable. And it’s not that the country is full of crazy, aggressive drivers like China or Taiwan – in fact just the opposite. They are too obedient here, and there are too many rules to obey. Unlike the US, where you basically do whatever you want unless there is a sign telling you that you can’t (no left turn, no parking, no U-turn), in Singapore you can’t do anything unless there is a sign telling you that you can. If I drove here I would stick out like the truculent American that I am – I don’t need the demerit points.

No, I was deriving. It rained all day on Sunday so I stayed in my hotel room and worked on equations. Am I weird? I had a blast! I’m looking for analytical solutions to the Euler-Lagrange equation of photoresist development – a particular nettlesome equation that prefers numerical solutions. Certainly the most common lithographic cases all must be solved with the aid of a computer, and those computer solutions are convenient and useful. But there is just something special about an analytical solution. An exact result in the form of a simple equation. Some results have elegance and, I have to say, true beauty. And it was beauty I was after.

I found two special cases that have analytical solutions. Hopeful these case will prove useful for some problem or another, but if not I’ll still enjoy their beauty and the pleasure that their derivation brought me.