Dimensional Analysis, 2013

The course

This course was addressed to teachers of physics. It advanced one answer to the question of how to get the heart of a new subject as quickly as possible. The particular answer involved dimensional arguments as the core technique.

Dimensional analysis was introduced in the first two lectures using some examples. It was shown how dimensional analysis simplifies problems and allows discovery of new phenomena.

In the next two lectures Gauss' approach to measurements and units was introduced, and was applied to developing natural units. Examples of standard physics were analysed using these techniques.

In the final two lectures we discussed asymptotic scaling and the breaking of scaling using the example of Rayleigh-Benard convection and fractals respectively. The notion of breaking of scaling was then applied to critical phenomena.

Reference books and articles

• Scaling by G. I. Barenblatt, Cambridge University Press, 2003.
• How to Solve It by G. Polya and S. Sloan
• Engineering dimensional analysis by A. A. Sonin, here
• On Being the Right Size by J. B. S. Haldane, 1926. Mirrored from a copy of the article. The book in which this is collected is available here.

These books are good sources of problems which illustrate the kinds of methods which we will discuss. Other problems will be constructed from observations and more general reading.