POST #3: Theory Behind the Initial Solution

So far I have discussed most of the practical knowledge that a crystallographer needs, but I have not mentioned much of the theory. Crystallography requires the careful analysis of thousands of reflections by a computer, but at one point, it was all done by hand. The math behind the initial solutions is very tedious, but in short, it relies on Fourier transforms. Fourier transforms are used to break complicated oscillations into only sines and cosines. A Fourier transform lets us look at the repeating patterns of reflections (similar to a harmonic function) and determine what the unit cell looks like, as well as the arrangement of its contents.

[Read more…]

Post 1: Where have I been?

So, I started my research on June 10. This, my first blog post, was written (is being written?) on July 3. That makes it… 23 days since I started. The question now becomes, “Where in the world have you been?”

[Read more…]

The Oberwolfach Problem

My web browsing habits, especially my use of wikipedia, bears a striking similarity to the basic principles of Graph Theory: I begin with at a page—say, a list of mathematical concepts named after places—and eventually “command-click” my way down the blue hyperlink rabbit hole that ultimately and inevitably leads to an obscene number of tabs in my browser and hours of procrastination. Were I to plot a series click on a specific session, I would most likely use a directed graph. Each vertex would be a webpage and edges would point in the direction of which pages linked to which. This is one simple example of the many applications and analytical potential of graph theory.

[Read more…]