Skulls in the Stars

In a previous post, I discussed recent research which demonstrated the creation of an artificial ‘event horizon’ in a fiber optic cable. In that post, I described how a river speeding up as it goes towards a waterfall has an event horizon: waves that are created past the horizon have no possibility of escape. This was illustrated by the figure below:

As you can see, I’ve drawn the wavefronts created by rocks dropped in the water as ellipses, which seems like the obvious solution: waves will be ’stretched out’ along the flow of the river, while they will spread normally perpendicular to the flow. Being a nitpicky sort of guy, though, I wanted to demonstrate that this is the case mathematically, which I do below the fold… (warning: algebra and calculus follow!)

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Over at The Daily Photon, Andrew Dawes has put up a nice post outlining how to use different fonts in LaTeX: including finding a math font that matches the text.

I find this especially helpful because, in writing Powerpoint talks, I often run into a conflict between using TeXPoint for my LaTeX equations and a pretty font for my regular text.  It gets rather annoying having to juggle several fonts in order to make certain that the (inline) equations and variables are comparable to LaTeX’s standard fonts.

There was a nice post on Good Math, Bad Math about Donald Knuth’s classic scientific typesetting software, TeX. In the comments section, a number of people asked about how to learn to use the software. I thought I’d write a little introduction on how to install and use LaTeX, with a nice sample file to play with. Since I often have to do this for my students anyway, it’ll be nice to have it all in one place.
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