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The talk will take place in RIII seminar room on 28th of September at 19:00.

Notes prepared for this talk are now available (CLICK).

The structure of the talk will be as follows:

  1. Interlude to Dimensional Analysis, Quantities and the Principle of Dimensional Homogeniety
  2. Physical dimensions as a vector space
  3. RayleighBridgmann's method of Dimensional Analysistheorem
  4. Examples, and some interesting applications
  5. Limitations of Rayleigh's
  6. Dimensionless quantities as a group, the Buckingham PI theorem and the principle of dynamical similaritySystems of units and restrictions
  7. Deriving Kepler's third law with Dimensional Analysis

Dimensional analysis is one of the finest tools in the tool-set of a physicist. The idea of dimensional analysis is very simple: In physics, we're not dealing with numbers alone. We're dealing with quantities equipped with a physical dimension. The main way to play physics is as a game of restriction, and dimensional analysis is one of the tools for the job. At its simplest, dimensional analysis tells you that you can't have a physical law that relates a left hand side of position to a right hand side of time; that's the principle of time. In the depths of theoretical physics, it restricts the form of your Lagrangians, objects that determine all, to a very large degree. In fluid mechanics, particularly computational fluid dynamics, it plays a major role in determining analytical laws of very complicated systems. Even when your problem is not physics, sometimes you can manually inject dimensions as sensible to then farther figure out things about the problem with dimensional analysis.