Winter Semester MUAS

My courses have been finalized for the winter semester at "Hochschule Munchen" (Munich University of Applied Sciences). See here for a listing of all the course offerings in English. I'll be teaching a Modern Physics course, based on my course that I teach at Embry-Riddle. And I'll teach an Orbital Mechanics course, using Howard Curtis's excellent textbook.

Finally, I'll be helping with a project course for students interested in participating in a NASA design competition. I don't know if the design specifications have been released yet, but last year it was to simulate a mission to the moon.

I'm looking forward to having a lot of fun!

What is a quasicrystal?

My post on 01.09.2014 about quasicrystals didn't answer the question of what exactly they are. I thought I'd remedy that now.

The atoms of most metals are arranged in a regular array, often called a crystal array (or a crystalline array), that is periodic. This simply means that if you move the array a certain distance in a certain direction, it will look the same. This is called "translational symmetry." In addition, if you rotate the array by a certain angle, it will also look the same. This is called "rotational symmetry."

This is easiest to think about in only two dimensions. That is, you can completely cover a flat space (i.e., a plane) with identical, equilateral triangles.

This called a "tiling" or a "tesselation" (not to be confused with "tesseract," a four-dimensional hypercube, or the tesseract from A Wrinkle in Time). A triangle is one of three shapes than can completely tile the plane. The other two are squares and hexagons.

(The connection with crystals comes when you imagine placing an atom at each vertex. Most crystals are in some form of cubic symmetry, but a few have hexagonal symmetry.)

In addition to translational symmetry, the triangular tiling has three-fold rotational symmetry. That is, if you rotate the triangular pattern by 120, 240, or 360 degrees, you obtain the same pattern. And, as you might expect, a pattern of squares has four-fold rotational symmetry, and the hexagons has six-fold rotational symmetry. They all also exhibit translational symmetry.

You don't have to use only one shape, you can use a repeating pattern of two (or more) different shapes.

This pattern can be moved left or right, up or down, and cover itself exactly - translational symmetry. It also has rotational symmetry. Can you see how many fold?

One thing that you CAN'T do (try it) is to completely cover the plane with pentagons, or any set of shapes with five-fold rotational symmetry. Here's an attempt at that:

If you look closely, it appears to have a five-fold rotational symmetry, but it doesn't exactly. To prove this, you'd have to print out two copies and see if you could match them up after rotation. In addition, this tiling is not periodic - that is, it is not translationally symmetric. Again, it's almost periodic, but not quite. This is the loose definition of a quasi-crystal. An array (three dimensional, of course) that has symmetry and periodicity over the short range, but not over the long range.

The picture above is of a "Penrose tiling," developed by Roger Penrose, a British physicist and mathematician. They are extremely fascinating, and I'm working on a post just about Penrose tiles. They are fun to play with, just like Zometools, and I had a lot of fun doing just that at PCMI in Utah.

Baseball (3) - Orioles Park at Camden Yards

Part of my plan for my visit to DC was to go to two more baseball games, an Orioles game and an Nationals game. I knew that my good friend Bill, also a baseball fan, would help me out. So on Tuesday night, we braved the rush hour traffic and went to Baltimore. We had excellent seats, about in the 20th row. 

How did we get such good seats? StubHub! People re-sell their game tickets on this site, and the closer it gets to game time, the cheaper the tickets usually are, since if they don't sell, the sellers get nothing. In fact, one guy we met suggested waiting until a few minutes until game time, because then they get really cheap. Of course, you must have a smart phone, because you can just download the tickets to your phone, show your phone at the gate, and in you go!  It's a brave new world.

My culinary choice in Baltimore was an 'Old Bay sausage,' which was a sausage with Old Bay seasoning, famous in Maryland. It was spicy and quite good. The only down side was that it had been raining for about an hour prior to the start of the game, but they had the infield covered, and it ended up starting about 20 minutes late. The above photo is the first pitch, and if you zoom in, you'll see a white streak just to the left of first base. That's the ball.

Of course, during the second hitter's at-bat, it started raining again, and we had to suffer through a two-hour rain delay this time. Below is the grounds crew putting away the tarp and spreading more dry dirt on the infield.

You can also see beyond right field a large warehouse. Between the park and this building was a long "alley," where much of the food was sold. It gave the park a nice feel, similar to Wrigley, being in the middle of the city.

After about the 7th inning, since there were so few people at the game, and so few left, they invited all the fans to move to any seat that was empty. So we moved down to about the 8th row, just behind home plate.

During some pitch, it could have been this one, the batter hit the ball and broke his bat. The top half of the bat flew into the stands right toward us! It hit one of the guys in the orange shirts a few rows ahead of us, bounced off, and was caught by a kid a few seats to the left. Luckily nobody was hurt. The bat was sharp. 

Finally, the game ended at 12:20am, with a 5-4 win for the Orioles over the Reds, and we drove back to DC. A long (but fun) night.

Baseball (2) - Wrigley Field

Our second stop on this baseball pilgrimage was the 100-year-old, "jewel-box stadium," Wrigley Field. It was my best baseball experience so far. There are several neat things about Wrigley, the first of which is that it's smack in the middle of the city, with no parking. You are just driving along a city street, and then suddenly there it is.

It's a really neat feeling. There are tons of people on the street (of course, it's a game day so there would be), and the atmosphere is festive. There are several ways to get to the park, probably the best is the 'L' train (or elevated train). There's a stop right at the park. We decided to drive and park in one of the local parking spots, proffered by residents to make some money. They were charging between $20 and $30, the closer to Wrigley, the more expensive. We ended up in a church parking lot, so out $20 went for a good cause.

This photo show how close the fans are to the foul lines. This spot is where a fan deflected a catchable ball in 2003, and sent the Cubs on a downward slide in the playoffs. It's an infamous spot in Cubs history.

They also sell a very good Chicago dog. I try to eat the "local cuisine" at each park, following the Polish Kielbasa from Miller Park. I recommend catching a game at Wrigley. It's a great experience.

Baseball (1) - Miller Park

One of my fun trips this summer was to go with my good friend Jeff to see the Dodgers play the Brewers at Miller Park in Milwaukee. It's a neat stadium because it has a high tech retractable roof. We had a good time, ate some Polish Kielbasa, and had some good beer. Fact: Miller Park is the only major league stadium that sells more sausages than hot dogs.

Unfortunately, the Dodgers lost 9-3, but the hero of the game was the Brewer's first baseman: Mark Reynolds!

He's been playing very well lately for the Brewers. I wish I made his salary!

Quasicrystals

One of the undergraduate series of lectures that I attended at PCMI was on Geometry and Quasicrystals, given by Marjorie Seneschal, math professor at Smith College in Massachusetts. She's written a book on the subject, "Quasicrystals and Geometry".

We even built a quasicrystal out of Zometools at PCMI. The largest quasicrystal ever built - according to Marjorie Senechal. One evening after dinner we got into several groups. Each group built the following piece. It consists of a green tetrahedron hanging in the middle, surrounded by a blue icosahedron, and finally a red rhombic triacontahedron.

Here is a view of just the outer polyhedron almost finished.

Finally, some of the undergraduates, who were experts at Zometools, put all these building blocks together in a large quasicrystal.

And this was the result

This is a model of a "binary icosahedral Cd-Yb quasicrystal." The amazing thing is that anyone was able to figure out this structure. Here is a short description of how they did it.

Zometools are a lot of fun, and I recommend getting a set and having fun.

PS. For those of you who have been wanting to know: a soccer ball is a truncated icosahedron.

Update: Of course, an excellent source of information about quasicrystals is at the Nobel Prize website, since Dan Schechtman won the Chemistry prize in 2011 for his discovery of quasicrystals back in 1982. On that site there is a link "Popular Information," which leads to a nice 7-page paper with excellent graphics explaining crystals and quasicrystals.

Update 2: More information here.