Icicles

My wife discovered this unusual lineup of icicles hanging off the back of our house:Unusual, in that they form a peak [*] suggesting a Gaussian distribution.

Icicle formation is actually a non-trivial subject. An article available from the Physics Arxiv shows new research from earlier this year on the subject, not just a theoretical model, but also their efforts to create an icicle growing apparatus under controlled (and adjustable conditions). The challenge in the modelling is that the boundary of the icicle is not defined in advance, but is actually the output of the exercise. Combine that with the nonlinearities of flow, heat transfer, external air currents,... and uniquely for icicles, water purity and you have quite a set of equations to work on simultaneously.

This is quite similar to the problems in modeling polymerization fronts - cases where polymerization in a pool of monomers starts on one side and advances through the liquid, also a nasty little problem to solve despite its simplicity to describe and understand.

[*] Let's just pretend that we are all electrical engineers for a moment, shall we, since they are the ones that always have "peaks" upside down from the rest of the world.