Jewelry and Differential Equations

I'm sure that many jewel thieves started on the road to crime after failed attempts to solve a differential equation.

Wolfram Alpha thinks that I may want to find jewelry, even though I asked it about a differential equation. pic.twitter.com/PpfoFUbEUb

— Mason Porter (@masonporter) December 4, 2018

E. L. Ince and the State of Differential Equations in England in 1926

E. L. Ince, being snarky about the state of the study of differential equations in England, in the preface of his classic 1926 book on the subject. pic.twitter.com/nLPXLv5mNt

— Mason Porter (@masonporter) October 29, 2018

Excellent Notation for Predator–Prey Dynamics

I approve!

LaTeX is so much better when you have emoji. pic.twitter.com/SYxgUXpWYN

— Mike Bostock (@mbostock) June 2, 2018

(Tip of the cap to Karen Daniels.)

Tales from the ArXiv: "Calculating Spherical Harmonics Without Derivatives"

There is a new paper on the arXiv that apparently includes a new way of calculating spherical harmonics.

A part that some of you may find interesting is the pedagogical discussion at the beginning of Section 5, which starts: "Historically, there are five ways that spherical harmonics can be derived."

The one that is easiest (by far) for me to understand is the oldest method, which is by solving the differential equation. But I am mathematically inclined, and people with more physical intuition may prefer other methods.

(People who are more comfortable than I am with Lie manipulations may also prefer other approaches.)

Anyway, I appreciate the discussion in this paper.

In Phase Space, No One Can Hear You Scream.

My students have their ODE (ordinary differential equation) final tomorrow morning, and I’ve got the perfect shirt to wear for the occasion: "In phase space, no one can hear you scream." pic.twitter.com/79hoysL80A

— Mason Porter (@masonporter) December 14, 2017

Quote of the Day: Differential Equations and Star Wars Robots

"You know you're in trouble if the different cases for your differential-equation solutions start sounding like the names of Star Wars robots."

(That is my spontaneous gem from today's lecture. We're doing Frobenius series.)

Infinite-Series Techniques: "A Good Psychological Restorative"

Yes, really—at least as prescribed by Drs. Bender and Orszag. Take two of these and call me in the morning.

Infinite-series techniques: "a good psychological restorative"

Prescribed by Drs Bender & Orszag. Take 2 of these & call me in the morning. pic.twitter.com/RH6gk9jh5k

— Mason Porter (@masonporter) October 4, 2017

Update (10/04/17): PBS is now involved (as you can see below).

We agree... 🙃 https://t.co/3wUoBjaUHU

— PBS Infinite Series (@PBSInfinite) October 4, 2017

What Happens in Edmonton Stays in Edmonton

Today I'm off to Edmonton — home of the Eulers!

I will be giving an invited talk at a (mostly) pure-math conference on differential equations.

Differential Equations and "General Fiction"

Eugenia Cheng's tweet below reminds me that when I was in grad school, a local store (a coffee place that also sold books) once had a certain differential-equations textbook in their section on "General Fiction".

The journey is turning into a book tour in itself: signed Beyond Infinity at O'Hare and How to Bake Pi at LAX...in self-improvement!! pic.twitter.com/KqhdGnvoCR

— Dr Eugenia Cheng (@DrEugeniaCheng) August 13, 2017

An Evans Function: A Wronskian on Crack

Definition: An Evans function is a Wronskian on crack.

I'm pretty sure that this is the official definition that you'll find in many mathematics books.

In case you're interested in these objects, see Todd Kapitula's primer. And here is a new article by Chris Jones that reminded me of the above definition.

Actually, I'm pretty sure I once heard someone — maybe even Chris? — joking call an Evans function "a Wronskian on steroids" during a seminar. I remember thinking that 'on steroids' probably wasn't doing justice to the function.

Flying with Differential Equations

Apparently, solving differential equations on a flight now can raise suspicion. Grrrrr....

In an attempt to try to turn some lemons into lemonade (and to be snarky), here is a tweet I wrote for DynamicalSystemsSIAM.

Let us know if you want us to suggest any differential equations for you to solve on your next flight. #flyingwithDiffEqus

— DynamicalSystemsSIAM (@DynamicsSIAM) May 7, 2016

(Tip of the cap to Physics Girl for the news story.)

14th-Order Differential Equations

The setup of today's SMBC takes a while, but the punchline is worth it --- and, um, way too close to the truth.

Ant Fight Club

In my latest post for the Improbable Research blog, I discuss modeling of combat in ants.

One of the reasons I chose to write about this paper is that it also allowed me to introduce modeling issues (e.g., the choice of a differential-equation model versus an agent-based model).

Next time, maybe I'll even use a Mortal Kombat reference. Finish him!

What Happens in Madrid Stays in Madrid

I have arrived in Madrid for the 10th AIMS Conference on Differential Equations, Dynamical Systems, and Applications.

The internet at this hotel is painfully slow. :(

Laplace's Equation: The Game

Thanks to my Somerville undergraduates for the very nice gift and card that they brought to today's leavers party. (The game is called Squint.)

What Happens in Orlando Stays in Orlando

Tomorrow afternoon, I will be flying to Orlando to take part in a conference on differential equations and dynamical systems. I went to the 2000 iteration of this conference but this is my first one since then. It is a math conference with both pure and applied parts of those two areas represented. Orlando is going to be 95 degrees and humid the entire time I am there, so I'll basically just stay indoors and blast the air con. (Scheduling a conference for Florida for the first week of July is a rather strange choice.)

A couple of Techers from my era (including one of my CS 1 TAs!) are attending the conference, and I am going to hang out with a different Techer (Ben Williamson) who lives in Florida and who I haven't seen since 2007. Also, this is my first trip to Orlando since 2004.

A Differential Equation in the New York Times

Here is Steve Strogatz's second guest article in Olivia Judson's New York Times blog. He lifted some of his discussion from his textbook, but it just warms my heart to see differential equations discussed in a venue like the New York Times and even more to see one (even a simple one) actually appear there.

My guess is that Strogatz's third guest article will be about synchronization and networks.

(Tip of the hat to Samuel Lee.)

Fun with Equation Names

I looked at a very interesting paper today (that I need to read carefully) that refers to a paper called the "modified MKdV" equation, which is called the MMKdV equation for short. Let's unpack this name:

The KdV equation stands for the Korteweg-de Vries equation. In other words, it's named after two people.

The MKdV equation stands for the "modified KdV" equation, which means that the MMKdV is in fact the "modified modified KdV" equation, which I would prefer to called the (modified)^2 KdV equation, although I'd really prefer a different adjective entirely be applied to KdV.

It's not close to as bad as "The Los Angeles Angels of Anaheim" (which means "The The Angels Angels of Anaheim" or (The)^2 (Angels)^2 of Anaheim), but it's not exactly great. I have started to get a little bit of personal experience in how equation names arise. Namely, I wrote a paper and found myself in a paper constantly citing the book of a guy who formulated an equation that showed up in what we were doing, so my collaborators and I decided to name the bloody thing after the guy just so we wouldn't have to awkwardly cite the equation from his book so many damned times. He can thank us later.

The Top 10 Differential Equations of All Time

Now that I know that I am providing endless amusement to the grad students, faculty, and (dare-I-say) postdocs in OCIAM, here's a little survey that I have been meaning to do for a while.

Basically, I want to write (or co-write, if anybody else is interested) an article for a venue like the AMS Notices or American Mathematical Monthly that discusses the "top 10 differential equations of all time" (a la David Letterman). The thing is that I need some sort of survey first, so if I just choose 10 that I like, it would be geared too much towards specific subjects. So, if anybody wants to pipe in here, by e-mail, or by any other venue, I would be greatly appreciative. (List of differential equations written on napkins are particularly encouraged, but toilet paper is right out.)

I'd like to get enough lists from people so that I can take the 10 most popular choices from that list and write the article. For each equation, I'd include some (reasonably brief) discussion of where it comes from and why it's important.

Here is a list that partially reflects my opinion but also reflects how little time I'm going to spend typing up the rest of this entry:

10. Lorentz equations

9. the Nesterenko equation*

8. the Klausmeier equation (because it's named after a former colleague who made a great Thanksgiving turkey)

7. Duffing's equation

6. Einstein's field equations (if for no other reason than because it made a guest appearance in The Triplets of Bellevile, and I got a free book out of that)

5. Navier-Stokes equations

4. the linear Schrodinger equation

3. the complex Ginzburg-Landau equation

2. the cubic nonlinear Schrodinger equation (aka, the Gross-Pitaevskii equation) [notice the correlations from 2-4; that's why I need help writing this list]

1. x' = 0


Honorable mention: That equation I "derived" on my AMa 95b final back in the day. (Actually, I could have mentioned any number of courses here, and I think 95b is one of the few in which I didn't develop my own equation of one sort or another with some misplaced derivation. But it amuses me to attribute this to AMa 95, so I won't let the truth get in the way of a good story.)

* This is the "unnamed" equation in a recent paper of mine (and several upcoming ones!) that my collaborators and I decided to name after the person who first derived it because it makes citing his results less cumbersome for the exposition. I wonder if this is how other equations have gotten named?

I swear I'm going to write my review for Avenue Q in the relatively near future.