Waterbed Equation

(Beware: nerdy naughtiness alert!)

Bill Press was a general relativity grad student a few years ahead of me in the Caltech physics department. He went on to become a Harvard professor, a senior Los Alamos scientist, a member of the National Academy of Sciences, a JASON, and the recipient of countless honors. (He was also a friendly and enthusiastic user of my primitive free-text information retrieval software; cf. IndexerBrowserFlashback.) Among the many technical papers that Bill published was his "Mathematical Theory of the Waterbed" in the October 1978 American Journal of Physics.

Independently, a few years later in the early 1980s I was meditating on the shape of fluid-filled membranes and derived some of the equations for simple two-dimensional models assuming that the tension in the surface, proportional to its curvature, is the only force that counteracts the pressure in the liquid, which grows linearly with depth. Then I found Bill's work on the more complex (but less æesthetic) configuration of a water bed. Great and, in my case, not-so-great minds, eh?


By varying parameters, as shown in the diagrams, a line with curvature proportional to Z-coordinate assumes <<blushes>> rather interesting configurations.

Challenge: extend the two-dimensional model to 3-D, and/or add the time dimension to show dynamic bouncy behavior!

(cf. NeedForSpeed (2002-08-10), AwesomeProwess (2003-07-17), BrainyJogbra (2004-05-07), ...) - ^z - 2014-04-20