Thermal Ellipsoids and Chi-Squared

In solids, atoms vibrate about their equilibrium positions. At higher temperatures atomic motion increases, but not alyways in the way we expect. For instance, the figure below shows iso-probability contours for atoms in the unit cell of a perovskite crystal with chemical formula CsSnBr$_3$ at 300 degrees Kelvin (about 80 degrees Farenheit). The thermal ellipsoids pictured below enclose 95% of the probability density of atomic motion.

In this post we'll explore atomic displacement distributions in the harmonic approximation, and figure out how to calculate the iso-contours of the distribution.

[img: adps]

March Madness Kaggle Competition

This year I participated in Kaggle's March Madness Competition. However, this isn't your typical office pool; instead participants are tasked with assigning every possible match-up in the field of 64 with a probability that a certain team will win.

In this post, I will describe my simple approach to building a machine learning model to predict winning percentages for March Madness games. Then, we'll see how it performed for this years competition!

Here's a sneak peak of my predicted bracket using machine learning... [img: bracket]


Hello! My name is Jonathon Bechtel, and this blog will document my exploration of data science techniques using jupyter notebooks.