1. ### Ultriviolet catastrophe and the beginning of quantum mechanics

We just finished a very long explication of the fundamentals of dimensional analysis and the Buckingham Pi theorem (well, not "just", since it took me significantly longer than I anticipated to finish up this post). That could be the end of this series, but it would be a shame to ...

2. ### Automated dimensional analysis

Last time we showed that the Buckingham Pi theorem follows directly from one of the central results of linear algebra: the rank-nullity theorem.

The normal approach to dimensional analysis involves a certain amount of playing with the parameters, reorganizing them, and looking for their nondimensional combinations. The understanding from a ...

3. ### Linear algebra and the Buckingham Pi theorem

We previously spent two longish posts on motivating, and then semi-quantitatively describing the Buckingham Pi theorem. Here we will try to describe the theorem more precisely and more generally, and the tool we use will be linear algebra. As is always the case with mathematics, a more precise and general ...

4. ### Nondimensional numbers and the Buckingham Pi theorem

In my previous post I tried to establish the context for nondimensional analysis, which allowed us to ask the central questions that the Buckingham Pi theorem will allow us to answer. At the heart of the matter was the relationship between the units of the physical parameters which are important ...

5. ### Introduction to dimensional analysis

This is the beginning of what I intend to be a multi-part series on dimensional analysis. The goal for this post is to set the stage for why dimensional analysis is a powerful tool, and to ask the questions which will lead us to the Buckingham Pi theorem.

The Buckingham ...

6. ### Introduction

Welcome to the inaugural post of this blog, where I plan to write about anything that strikes me as interesting. For the most part these things will be related to geology, geophysics, or scientific computing. At the moment I am titling the site "Blueschisting," with which I am not necessarily ...

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