Archive for the ‘Basic Grad Student’ Category

Card Shuffling I

April 19, 2009

Just about anyone interested in mathematics has studied a little probability and probably done some easy analysis of basic card games and dice games. Completely off topic for a second, am I the only one who has noticed that basic probability homework exercises are the only situation, aside from funerals, that anyone will ever use the word “urn?” For whatever reason, probabilists love that word. Anyway, in any real card game, the computations tend to get complicated rather quickly, and most people get turned off from the discussion. With some ingenuity, however, one can answer some pretty cool (but initially difficult seeming) questions without having to go through a lot of tedious computations.

Take as an example card shuffling. In the face of expert card-counters, the natural question for the dealer is how many times he or she has to shuffle the deck before it’s well-mixed. In the case when the dealer is also playing the game — and is a card-counter at the level of a member of the MIT black jack team, say — he or she could drastically improve their odds by using a shuffling method which seems to shuffle the deck well, but actually is very poor at doing so. Anyway, at this point the question is slightly ill-posed, as we have no obvious way to interpret the word mixed, let alone well. In fact, coming up with a mathematical model of what shuffling means is already fairly difficult. What I’m hoping to do is give a framework which makes the problem more tractable.

A Silly Infinite Series

April 5, 2009

A year or two ago, a couple of us were bored and somehow got to thinking about the series

$\displaystyle{\sum_{n=1}^{\infty}\frac{n^k}{2^n}.}$

Fun With Sums

February 22, 2009

It’s been a while since there has been any math on the blog, so I figured I’d share a recent (trivial) mathematical fact I came upon while passing the time. A less noble goal is that I hope some of you will find it interesting enough to think about it for a while. In other words, I’m too lazy to keep working on it but I hope some others will fall into my trap and let me know the answer.
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The new LHC schedule

February 10, 2009

In a meeting at Chamonix last week, CERN, the LHC collaboration, and the LHC experiments came up with a 2009 schedule.  “Second beams” (as opposed to first beams last year) will start a little later than expected: September 2009 instead of July.  Then the goal is to have first collisions at the end of October, making the delay due to The Incident almost exactly one year.

Then after that, the good news starts in earnest.  Instead of having a long shutdown over the 2009-2010 winter, as CERN usually does, the shutdown will be short, and we continue running and collecting data until we have something close to 200 pb-1 at 10 TeV, which will probably take about a year, until fall of 2010.  That’s great, because it’s just enough for some of the basic discoveries: Z’ and W’ above 1 TeV, Higgs -> WW (if the Tevatron doesn’t see it first), the low-mass region of SUSY/mSUGRA parameter space (the “LM#” points), contact interactions in jets, and maybe a very optimistic extra-dimensions model (see my “Early Discoveries at CMS” talk at Dark Matter and the LHC conference).  Running at 6 TeV collision energies was considered, and thankfully rejected, as that would be just below the interesting threshold for a lot of this.  (The LHC’s design energy is 14 TeV, which is scheduled for 2011.)

At the risk of sounding naive, I think it’s really going to happen this time.  The LHC people must know a lot more about the actual behavior of the beams from their real-data test last year, and given how disappointing last year’s setback was, I’m sure they’ll do everything they can to avoid anything like it.  In other words, the argument is based on social reasons, not technical ones, but guessing when we’ll have data is a social science.

Pictures from the LHC incident

December 11, 2008

A few days ago, CERN released pictures from the LHC incident.  Here’s one from the DG’s talk.  There are a few more, plus a video of the repairs, in their press release.  This interconnect between two magnets is normally straight.

If you add up the energy stored in the magnets during the 5 TeV test, it comes to about 6 MJ, of which 4 MJ was dumped into a system designed to absorb energy on a rapid demagnetization.  Unfortunately, 2 MJ is the amount of energy a 3-ton SUV has when it crashes at 90 miles per hour.  Twenty-nine magnets need actual repairs, which is not too bad of a load for a factory that built over 1,600 in the past 7 years.  A lot of the talks about this focus on new preventative measures to identify spots of high resistance (several more have been found, though they were all within specifications, unlike the one that caused the accident) and to absorb more energy in the case of future accidents.

The new start-date for powering tests is the end of June, 2009, with beam again in July (a 10-month delay).

From a personal perspective, though, it turns out that the beam collected last September was exactly enough for the tests I needed to do.  (Whew! for me, at least.)

CERN releases report on LHC incident

October 16, 2008

If you’d like to know the details, you can find a summary on the CERN Press Release site and a technical report on their document server.  Some things I found interesting:

• Confirmation that the cause was an electrical fault, rather than a magnet quench.  When temperatures rose, the magnets certainly quenched in response, but the initial cause was “an electrical arc which punctured the helium enclosure, leading to a release of helium into the insulation vacuum of the cryostat.”
• Sentences that begin, “After 0.39 seconds”, “at 0.46 seconds”, and “at 0.86 seconds…”
• At most 5 quadrupole and 24 dipole magnets will need to be repaired, though more may need to be removed to clean off “contamination by a soot-like dust.”  There are enough spare magnets and components for all of these repairs.  (Whew!)
• In all, 6 tonnes of helium were lost out of the 15 tonnes that were in that sector.  The last 4 leaked slowly, before the enclosure could be closed.

Again, I’m not a CERN representative, I’m just very interested in the outcome of this project, as may be some of the readers of this blog.

“Live” video of LHC particles

October 15, 2008

A few days after the first LHC collisions, I dug into our growing dataset and made an animation from the signals we captured in the CMS detector of muons from LHC beam-halo events.  The result looks like a computer simulation, but these are real measurements from the detector, observations from 10:33-10:42 PM Geneva-time on September 11, 2008.  In that sense, it’s a live video.  During this period, LHC beam #2 circulated for 9 minutes, 6 million times around the ring without getting off track.  All the cheering on September 10th was about getting the beam to go once around the ring without getting off track.

The animation can be found at the bottom of the CMS Media page.

Red dots are the signals in the detectors, yellow lines are the best-fit curves through them, representing the path taken by the muons.  Notice that the muons are more often vertical when the beam is off (because they’re cosmic rays) and horizontal when the beam is on (because they’re from proton collisions with gas atoms and collimators far upstream in the LHC).  The rate also increases dramatically.

This is not sensitive information!

September 24, 2008

After yesterday’s post, the first comment was actually a ping from the Not Even Wrong blog, quoting my paragraph describing the electrical failure in the LHC.  Peter Woit used it as an example of a leak (information, not helium) through a CERN policy discouraging the blogging of sensitive information.  It is not sensitive information, and it does not go substantially beyond what is given in the press release, which reveals the basic cause of the accident as it’s currently understood and the decision that there must be significant down-time to repair the damage.  (And most of that down-time is for re-cooling, not the repairs themselves.)

My description is more colorful than the press release because I am not the official face of CERN.  As described in a much-earlier post, I am not even an LHC person, but a member of the CMS collaboration, so for LHC news, I’m an “outsider” who happens to live close to the source.  That is what I thought would be valuable about this blog: it would give people who are interested in the development of the LHC (namely, mathematicians who have heard of field theory), the same kind of closeness that the experimenters down the hall have.  It is not a conduit for collaboration secrets, and I have been extremely pedantic in what I have revealed.  (I started by reading the CMS Constitution, and I have checked everything I say to make sure it’s on a public website somewhere, however obscure.  If I’m not sure about the internal-versus-external status of a website, I check it in my iPod, which doesn’t know any of my passwords.  Veeery pedantic.)

It is quite reasonable for scientific collaborations to have private information, because they are the kinds of social organizations for whom it would be best for everyone to reveal well-digested information at a late time, but better for an individual, worse for the group, to release exciting information early.  We need to control that, with our own good-will preferably, and that’s how it’s currently instituted.  The world interest in the LHC, the unprecedented size of the collaborations, and the new existence of blogging introduces a temptation for individual scientists to be self-proclaimed Promethei, and that’s a problem, not a good thing.

To illustrate what I mean with a perhaps not-applicable example, do you remember five to ten years ago when large extra dimensions were a new idea?  People first started thinking that maybe the hierarchy problem doesn’t exist, and maybe the Plank scale is actually just a few TeV (those of you who are physicists or part-physicists)?  Then someone went one step further and said, “well if so, maybe the new particles we’ll see at the LHC will be black holes.”  And physicists thought about that and how they would Hawking-radiate in fascinatingly spherical patterns and how that would be cool, but in the end, not consistent with existing observations.  Of course no attempt could or should be made to keep scientific discourse like that secret, but when it left the physicists, it became the headline “LHC to Make Black Holes, Eat Earth (page C-1)” and a frenzy that even lead to a death.  Somehow that sort of thing happens to ideas and information, and there is strangely no way to reign it in; no amount of truth mops it up.  It is utterly reasonable for the LHC collaboration to want to do an investigation before they let their members speak openly about it.

I don’t want to be responsible for “LHC Explodes, Experts Say (page E-13).”  Given what I know as a nearby outsider, the problem is exactly as bad as the press release says it is: a broken electrical connection, a huge helium leak, and possibly some damage to the magnets.  The extent cannot be known until it is investigated.  Why is it taking so long?  I can guess: a helium-rich environment is an oxygen-poor environment, and the moment they switched on the beams, they turned the tunnel into a radiation zone that will need to be mapped before it can be safely traversed.

Of course, I’m also disappointed and nervous, because I have a lot at stake.  So do the LHC people.  And we all have an interest in carefully-evaluated information; I mean, we’re scientists after all!

No LHC beams until next year

September 23, 2008

(If you read this, you are hereby obligated to read the next post.)

Nope, the verdict is in: the LHC will not be turned on again this year, even for a shortened 10 TeV run.  The restart has been scheduled for early spring of next year, so I’ll probably get very familiar with these 14 minutes of data!

I was in a meeting at CERN when someone ran to the front of the room with a computer, then after letting the speaker finish and setting up the computer to project the press release/e-mail (agonizing moments: it was a Mac), they let us know.  I was worried that the sector with the helium explosion had collapsed like an old mine— there were rumors going around that this is a weak point in the tunnel.  (Of course there would be such rumors.)

I have learned a few more graphic details about the event in the last few days.  First off, it was two tonnes of helium, not one.  But I’ve also learned that this was a more explosive and dramatic event than I had imagined— helium is fortunately an inert gas, but the temperature gradient caused it to explode violently, probably causing physical damage to the nearby components.  And now that section of the LHC is an ice tunnel, maybe with stalagtites hanging down and a Yeti moaning in the distance.  (A Yeti may well replace Big Bird on my diagrams.)  There was enough helium released to replace all the air in a kilometer-long section of the tunnel.  The full tunnel is 27 km long, so I imagine it’s dilute enough to breathe, possibly with a squeaky voice.  (Okay, a high-pitched Yeti.)

One point that I want to set straight is that as far as I understand the term “magnet quench,” this wasn’t a quench.  It was an electrical connector between two magnets which failed under the load of 8,500 Amps of current.  When a superconducting magnet quenches, a small patch of the superconducting coils heat up over the critical temperature, making it no longer superconducting.  It gets warmer, heating up more of the surrounding region, until a runaway effect dumps all of the magnet’s energy into heat and throws things around because strong magnetic fields have just been turned off.  This was less exotic: more like a broken fuse or bad wiring (operating at hundreds of times the normal electrical consumption of a household, but still).

So that’s probably it for the regular (irregular) posts, at least until “spring.”  I should probably sit down and calculate when I’ll next be able to publish a scientific paper.  Hmm.  How tall do you think a Yeti is?

Two-month delay for the LHC

September 20, 2008

(If you read this, you are hereby obligated to read the next-to-next post.)

Bad news: a connection between two magnets in the LHC will need to be repaired due to an electrical fault, and this repair requires at least two months of down-time, because the sector will warm to room temperature in the process.  (It takes months to cool the LHC to its 2 Kelvin operating temperature.)

Here’s what happened: as a dry-run for storing a 5 TeV beam (there was no beam in the machine at the time), the dipole magnets which would hold it in its trajectory had to reach a field strength of 6 Tesla.  This is an extremely high field, about twice what someone would get in an MRI, requiring huge electrical currents.  For some unknown reason (the subject of an ongoing investigation), a connector somewhere shorted, breaking a coolant duct which then sprayed a metric tonne of liquid helium everywhere.  When the proverbial smoke cleared around mid-day yesterday, the sector was 80 degrees Kelvin.

The delay will take a rather large bite out of the 10 TeV collisions run planned for this year, but it won’t necessarily push back the start of 14 TeV collisions in 2009, since the commissioning of the magnets for full field (8.3 Tesla) is something that has to be done while the beam is not running.

Meanwhile, we have collected about 14 minutes of single-beam data since the grand opening ten days ago (that’s impressive for the early-early phase of an accelerator).  Strangely, the delay of the LHC seems somehow distant, since there are so many detector studies we need to do with these millions of events, and the presentation deadlines are so soon…