Vorticity

This post is part of a series on key concepts in atmospheric science and geophysical fluid dynamics. You can find previous posts at the following links: Geostrophic Balance, Thermal Wind Balance. This post will focus on vorticity, a local measure of rotation in flows. Continue reading

Advertisements

November-December Dance Performances

Most of the performances I saw in November and December were at the Joyce, but I also saw some special holiday shows: the Rockettes, Martha Graham’s Appalachian Spring (I have no idea why this was the choice for a holiday show), and two Nutcrackers. Continue reading

ABT Met Season 2018

I saw five ABT performances this past Met season. I continue to prefer the variety of the fall season. All five performances were of story ballets, and only the two performances of Romeo and Juliet weren’t a restaging or reconstruction of a Petipa ballet. The only new work was Ratmansky’s reconstruction of Harlequinade. More details on each performance I saw are below the fold. Continue reading

#MathStatMonth Day 29: Periodicity and Chaos

There is a famous paper in the field of dynamical systems titled “Period Three Implies Chaos.” The result in this paper by Li and Yorke is actually stronger than the statement in the title, but that’s the cleanest and flashiest part.

The systems the paper considers are difference equations. We can think of measuring some quantity x at discrete points in space or time. I’ll use time here for simplicity. This could track things like a population in an ecosystem, the position of an object, or the concentration of some part of a solution. Continue reading

#MathStatMonth Day 28: Snarks

You may seek it with thimbles — and seek it with care;
You may hunt it with forks and hope;
You may threaten its life with a railway share;
You may charm it with smiles and soap…
From Lewis Carroll’s “The Hunting of the Snark”

A snark (of the mathematical variety, at least) is a type of graph that comes up in a number of important questions in graph theory but about which we know relatively little. We don’t even know of many examples of snarks beyond a couple of infinite families. Continue reading