Ising the Body Electric

Last week I was in Chicago, visiting my friend Kevin, so I didn't get around to putting up a post, but I did get some material for this week: I've been going to a lot of shows, concerts, and other group events lately, and it got me thinking about crowd dynamics, specifically standing ovations.  I figured there were two factors that determined whether someone would stand up during applause:

• The quality of the performance
• Whether nearby people were standing

These two conditions reminded me of the Ising model used to simulate magnetic materials.  The idea is that in a ferromagnetic material (like iron), we can imagine a bunch of arrows, called spins, that point up or down.  The energy of any particular spin is related to those of its neighbors: +1 for each opposite spin, and -1 for matching spin (remember that low-energy states are preferred).  Here's an example:

In the Ising model, we pick a random spin at each time step, and decide if it should be flipped.  The probability is given by the Boltzmann distribution,

where ΔE is the difference in energy between the current state and the flipped state, and kT is the thermal energy.  For cases where the new state is lower energy, we get P > 1, so a flip is guaranteed.  We can also introduce an overall field, which biases the system in one direction – This could represent a permanent magnet near the iron, for example.
So how does this relate to audiences?  Each person can represent a spin, and their neighbors influence their probability of standing or sitting.  Someone could stand independent of their neighbors for an exceptional performance, so that's the external field.  Temperature relates to how willing people are to switch between standing and sitting.

I wrote up a version of the algorithm in Python, which you can try for yourself – I added a bunch of comments, so I hope it's not too opaque.  Here are the results for a performance not quite up to snuff:

And one that got the pixel people a bit more excited:

The only difference in conditions for these was the "performance quality" (external field): 0.1 for the first one and 0.5 for the second.  If you come up with any interesting settings yourself, be sure to leave a comment!

It's Not the Fall That Kills You

This week, I'd like to get back to one of the mainstays of this blog: Looking at physics in popular media.  A recent favorite movie of mine is the 2015 film Tomorrowland, about a secret pocket dimension where the world's greatest scientists are allowed to do their work in peace.  The central message is that an important part of science is hope for the future, that all is not lost.  Helpful thing to remember after my midweek post.

The opening scene is George Clooney's character, Frank, as a young boy inventing a jet pack.  On his first trip to Tomorrowland, he falls off a ledge, but is able to catch his jet pack, put it on, and stop just before hitting the ground.  Every time I've watched this scene, I've been skeptical that he could survive such a rapid acceleration.

I looked around for human g-force limits, and one of the largest values was for a rocket sled, which had an acceleration of 46.2 g.  A rocket sled sits on a rail, and a rocket at the back propels it (image from Wikipedia):

This is a little different from a jet pack, since it has a seat that can cushion some of the acceleration, so I'm not sure how accurate a limit that is.

In the movie, Frank falls for about 65 seconds before turning on the jet pack.  On Earth, it only takes a person 15 seconds to reach 99% of their terminal velocity, 54 m/s.  Tomorrowland looks to have similar gravity and atmosphere, so Frank is certainly going this fast by then.  When he fires the jet pack, he comes to a stop in about 2 seconds, which works out to 2.8 g, nowhere near fatal!

In case you're wondering what would happen without air-resistance and terminal velocity, even that isn't necessarily fatal: 32.5 g wouldn't be fun, but he would probably get away with only some dislocated shoulders.

A Personal Note

A few days ago, a family friend asked me to make a video for her class of 6th graders explaining what it means to be a physics graduate student, why I chose it, and what I like about it.  That, coupled with the recent election, got me thinking about how I got into physics in the first place.  I took my first physics class in 10th grade, with a wonderful teacher named Ben Bakker.  Something I immediately noticed was that he always seemed to be in awe of the universe.  He would write an equation on the board, step back, and say, "Whew, isn't that beautiful?"

The moment I remember when I really got a clear sense of that beauty was during a lab on projectile motion.  We were given spring-loaded cannons that shot ping-pong balls, and allowed to fire a few times with it pointed horizontally.  Based on the muzzle velocity we measured from that, we determined the angle to fire the ball through a small hoop a distance away.  The ball sailed through the center on the first try.  Even with all the approximations (no air-resistance, limited distance/angle accuracy) the science worked.  To me, that was beautiful, and I've seen so much more since.

Earlier this year, Neil deGrasse Tyson came to speak at the University of Michigan.  His talk was on the value of science to a society.  One of his big examples was that fact that most stars were given Arabic names, because Islamic countries were leaders in science during the middle ages.  In the modern era though, science has been devalued, resulting in the region's decline.

Last night, Tyson was on The Late Show, and encouraged everyone to make an effort to learn and teach for the next four years:

As a scientist, I find the skepticism surrounding issues like climate change deeply troubling.  Even though I have never studied climate science myself, I understand the scientific method, and the vast majority of climate scientists have agreed that there is a causal link between CO2 levels and global temperature.

I hope by writing this blog I can get just a few more people interested in science, and help them understand its value and its beauty.

The Living Daylights

Last weekend, I was doing some research work on a computing cluster in Germany, and the time stamps suddenly jumped by an hour – Turns out the EU changes from daylight saving time on the last Sunday of October, rather than the first Sunday of November.  I had been under the impression (along with many others) that DST was introduced for the benefit of farmers, but they actually lobbied against it.  The original intent was to give more daylight after the work day, to encourage people to shop.  I thought I'd take a look at how this idea lines up with the sunrise/set times from the US Naval Observatory.  Here are the times using standard time all year:

The black lines show my usual wake/sleep times.  Now if we introduce DST:

By using DST, I'm awake during more of the daylight.  This is the rationale behind one of the other arguments for changing clocks – energy savings by reducing light/heat use.  It's easier to see if we look at the overlap between waking and daylight in the two systems:

The idea that DST saves energy is disputed though, and a number of studies have not shown a conclusive benefit, so it's likely a small effect if any.  Seems likely to stay though, since getting rid of DST would take more effort than it costs to keep around.  I'll just have to keep a close eye on my foreign time stamps.