Tropical Storm + Running = Wet and Wild Fun

Tropical storm Hermine (seriously, what is up with that name?) finally headed inland last night, and Austin is getting hammered today. Of course, that makes for ideal running weather. As a result of the weather, my morning 1-2 mile shake-out run quickly became a 4-5 mile progressive run. My tempo tonight will surely suffer, but there is no reason not to take advantage of this weather.

In other running news, the US 20K championships were held yesterday in New Haven, Connecticut. Sean Quigley and Lewy Boulet took the men's and women's titles respectively (congratulations to them), but I was especially excited to learn that Stephanie Rothstein, the second-place finisher in the women's race, was diagnosed with Celiac Disease and claimed that the move to a gluten-free diet was key to her recent running success. Since I went gluten-free this spring, I have had a very difficult time adjusting. I have had issues with iron, fatigue, and having enough energy for my runs. I thought that I might have to take it a bit easier on the running side, which I am not really mentally prepared to do. However, after finding out that a number of elite athletes (including Rothstein, Amy Yoder, and Austin's Desiree Ficker) have actually become better with the new diet, I am pretty hopeful that things will get better. And they actually have in recent months.

Blanka Vlasic takes the title of "photo of the week" (or month) with this glorious shot after claiming the world's best women's high jump this past Sunday. She even had the chance to do it in our home country in front of a friendly crowd. Needless to say, she was excited.


Finally, I have taken part in a few conversations with fellow runners over the following question: if Jim Ryun was a miler today instead of 40 years ago, would he dominate the competition? He remains the only person to run sub-4 in a high-school only competition, and he did it virtually on his own. Check out the video here. It's nothing short of incredible, as is the quality of that ancient video.

A Gluten-Free Anniversary Feast!

Today is my fiancee and I's "official anniversary", so I decided to prepare a bit of a feast. The menu: gluten-free chicken enchilada casserole, a gluten-free chocolate cupcake from Whole Foods, and Redbridge, a gluten-free beer. The recipe for the casserole is a slight variation of one found in the Gluten-Free Everyday Cookbook, a wonderful gift Sarah gave me for my birthday this year. The ingredients are simple and can be purchased for around 10 dollars, and it leaves a whole lot of leftovers. As Sarah is in Williamsburg for graduate school (she made a chicken and rice dish for our anniversary, out in Virginia), I should have enough food for myself for the next two days from this casserole =P. I am not much of a cook, so I am pretty proud that I have become quite proficient at making this particular dish. Here are some fun pictures from the feast.

Pre-preparation:















Ready to cook:















Futurama, the entertainment provided during baking:















The finished product, with cupcake and Redbridge:















It turned out to be delicious as always, and I find it to be even better as leftovers. It is too bad that Sarah is not here tonight, but I plan on preparing this dish for her when I see her in October =).

To celebrate our anniversary tonight, we are renting "Zombieland" in our respective locations and viewing it "long-distance style", with Skype chat armed and ready. This will be our first "long-distance date night", so I am quite excited about it. After all, but who could pass up zombies on a such a romantic occasion?

To conclude, I will leave y'all with a lovely song Sarah posted on my Facebook wall. It has been in my head ever since (a good thing), so I figure it appropriate to put it right. I miss Sarah quite a bit but this song brings a smile to my face in her absence.

Edward Sharpe & The Magnetic Zeros - Home [2009]

14:44.76!!!

Molly Huddle gets the 5K AR! It is always awesome seeing people you saw (or competed against) during high school races all the time performing so well.

It has been a couple days...

but it is still amazing.

For the full video of the race, click here.

I popped the question and she said yes =).

Wow. What a display at Monaco.

I am really becoming more and more excited about the state of American mid- and long-distance running. We had an amazing showing at the Monaco Diamond League Meet this past week. Andrew Wheating showed that he truly belonged in Europe with a fantastic time of 3:30.9 and fourth place showing in the men's 1500m. Lopez Lomong came up less than two seconds behind Wheating with a new personal best - not bad considering Lopez has been sick the past few weeks. Alysia Johnson destroyed her competition in the women's 800m with a 1:57.3. Shannon Rowbury finished third with a big PR (8:31) in the women's 3000m. The American sprinters and hurdlers also performed well, exemplified by David Oliver's big win in the 110m hurdles with a fast time despite a bad start and hitting some of the hurdles. The only blight at the meet for the Americans seemed to be Leo Manzano's choke job in the men's 1500m, finishing over ten seconds behind the leaders. Leo seems to be really struggling with a two-face summer as he just recently set a PR in the 800m. Let's hope for the best during the rest of the summer for Leo as well as the rest of the Americans.

Resolving the Isoparametric Concept with Compatibility

Comment: This post was inspired by conversations I have had during the past few days at a workshop I recently attended. I apologize ahead of time for its problem specific nature and overall lack of generality. Nonetheless, it is simply my attempt at resolving some inconsistencies and misconceptions in the field of computational mechanics.

I had the pleasure of attending a workshop in Pavia, Italy this past week entitled "Non-Standard Discretizations for Partial Differential Equations." One of the main focuses of this workshop was the subject of compatible discretizations. Compatible discretizations are ones which preserve certain properties of the underlying partial differential equation such as topology, conservation, symmetries, and positivity structures and maximum principles. The main tools behind the construction of these methods as often quite mathematical in nature (e.g., exact sequences), and they have not quite taken hold yet in the engineering community. Nonetheless, these methods have very nice properties and typically are much more accurate than standard numerical techniques.

In the engineering community, the utilization of the isoparametric concept is pretty much a religious practice. The isoparametric concept simply states that one uses the same discretization for the geometry as well as for the analysis. This is an especially useful property for problems in nonlinear structural mechanics as it allows one to represent exactly all rigid body modes (translations and rotations). However, most compatible discretizations do not preserve the isoparametric property, and many mathematicians argue they should not. Some in fact state the adherence to the isoparametric concept is just a consequence of inertia and misunderstanding. In certain circumstances, I would have to agree with these mathematicians. However, in others, I would have to disagree. In fact, in some important instances, I would contend that the isoparametric concept is one of compatability.

Consider elasticity. Elasticity has many meanings, and we need to respect that. In particular, linear elasticity and nonlinear elasticity are completely different animals. Linear elasticity is a theory of fields. It is a theory of vectors in Cartesian space. In a sense, it is a theory of Eulerian flow. Nonlinear Lagrangian elasticity, on the other hand, is a theory of shape representation. One is not solving for vector fields on top of a given geometry. Instead, in nonlinear elasticity, one is solving for the geometry itself. So many discretizations for nonlinear elasticity are based on simple extensions of those for linear elasticity, but from the compatibility standpoint this makes absolutely zero sense! These two problems have very different geometrical, topological, and symmetry properties.

I would agree that the isoparametric concept has little meaning in the discretization of fields defined on top of a given geometry, as in linear elasticity. After all, in linear elasticity, one is not really changing the surface or volume. However, it has clear meaning in nonlinear elasticity, where one involves a moving geometry. The isoparametric concept preserves the most important geometric invariant of all: conservation of shape under translation and rotation. This ensures there is no energy associated with rigid body modes, an incredibly important conservation law for nonlinear elasticity. This property ensures no spurious modes just as compatible edge elements ensure no spurious modes for electromagnetics. In this sense, the isoparametric concept is akin to compatibility. It is a key component of compatibility of shape.

All in all, I would contend that we should know what we are dealing with before we decide what is compatible or not. If we are dealing with fields, we should worry about compatibility of fields. If we are dealing instead with shape, we should worry instead about compatibility of shape and consequently the isoparametric concept.