Tuesday, November 24, 2009

The Rijke Tube or The Gondolo

So apparently the first year professor Gondolo was teaching here at the U he had a demonstration set up in which a wire mesh is heated inside a cardboard tube by a propane burner. The bottom of the tube is obstructed while the mesh is heating up because if an air current were allowed to flow it would blow out the propane. When the mesh is hot enough you turn off the propane and remove the obstruction on the bottom. The mesh causes convection heating of the air and an air current starts to flow through the tube. Standing wave patterns form and the tube becomes a resonator. The demonstration is actually rather an old one and is called the Rijke tube. If you don't know what I am talking about or have never seen it here is a youtube video of a small one being built and put into action. The video is pretty long you can just skip to around 3:30 to see the tube work.

As I was saying our young professor Gondolo (well... younger anyway) had a Rijke tube demonstration all set up but the tube was not like the one in the video it was a tube of more than a foot diameter and 10 feet or so tall. The tube was held by ropes hanging from the ceiling of the extremely large physics classroom. Professor Gondolo made the mistake of starting the propane burner and then teaching the physics of it. He taught the physics of the device for too long though and the wire mesh got rather hotter than it should have. When he was done explaining the physics and unblocked the bottom of the tube the mesh was so hot that the new airflow did a lot more than just allow resonance it allowed the cardboard tube to catch on fire. After that particular disaster when the demonstration was rebuilt it was built out of metal ducting and the name "THE GONDOLO" was painted on its side in red along with some nice decorative flames. Since professor Gondolo is going to hopefully become my research advisor I don't think I shall mention it until after he decides to accept me as his student, but I can't help but wonder how he feels about the giant metal demonstration tube that now bears his name.

Either fortunately or unfortunately I never saw the original demonstration with the cardboard tube. The cardboard tube was supposed to have been even larger and louder than the current metal one but the newer one is still damn impressive. The natural frequency of the tube is lower than you can hear (or at least hear well) so mostly what you hear when the tube goes off is the second and third harmonics. But the vibration is so loud and so low that you can definitely feel it.

Thursday, November 19, 2009

Picking A Research Advisor

Some time ago I talked with Professor Wu about becoming a graduate student under him and he told me to attend their group meetings and seminars. It turns out Wu's group has 3 seminars that they are currently doing. One in quantum computation, one advanced solid state physics one, and one on tensor category theory. I have been attending the solid state and the quantum computation one and somewhat humorously I understand more from the quantum computation seminar than from the solid state seminar. This past Saturday though there was a big meeting where all of the faculty (and in some cases soon to be faculty) who are looking for new graduate students to work under them gave short presentations. The event went from 9:00 to 1:30 though it was only supposed to go to 1:00. There were 17 presentations overall.

About of the presentations weren't really of interest to me. To be clear that is to say that most of the presentations were about research that I would have no interest in doing. Of the seventeen I would give serious consideration to 10. Basically there were two types of research position that were represented solid state physics and astronomy. I find it somewhat of a surprise that I find myself drawn so much more to the astronomers than to the solid state but there we are. I still find myself drawn to being a theorist instead of experimentalist and although there were a number of solid state theorists looking for students there was only one cosmological theorist looking for students, namely Paolo Gondolo.

Paolo spends his time working on theories explaining dark matter dynamics. Through looking at gravitational interactions such as gravitational lensing we have been able to get a very good picture of the density of dark matter in the universe and also its distribution. However the only effects that we know are coming from dark matter are just gravitational effects. We might be detecting other effects of dark matter but simply don't know it. At the moment there are things we are observing which don't fit with the predictions of standard models. For instance we can predict the expected flux of cosmic ray positrons but the standard prediction doesn't fit with the observations. Paolo and a number of other people are trying to think up theories of dark matter interactions which could account for observations like this.

Paolo and company has created a fortran package called dark susy which is used to make calculations for the parameters of SUperSYmetric dark matter theories. Thus dark SU-SY. While I feel more attracted to working on the dark energy problem than the dark matter problem I thought working on dark susy might be just the right thing for me to do. My physics knowledge is nowhere near the level that it would need to be in order to really begin working on dark susy. For one thing I don't even have a good knowledge of the standard model of particle physics much less its supersymmetric counter parts. But of course I would run into the same problem in any field that I decided to start research in.

This morning I took the opportunity to go and talk to Paolo about becoming a grad student of his. He started off the discussion by trying to scare me off. Rather, he said he was trying to scare me off but really he was just trying to make sure I understood that there are major disadvantages to being a theorist. Being a theorist takes more work and longer hours and requires you to know more. As a theorist it is harder to get away from your work since anywhere there is paper and/or you have your laptop you can work. On top of that there is very little money in theory. Theory is cheap but that means theorists are underpaid. As a theory grad student the chances of getting an RAship are almost null so not only are the research hours generally longer as a theorist but you have to keep a TAship and teach in order to support yourself. But I knew all of that already so it wasn't really much of an eye opener.

Friday, November 13, 2009

Black Hole Basics Part 2

First a quick review of part 1.

A black hole is an object with a density sufficient to cause a gravitational acceleration greater than the speed of light.

The point to which all mass is drawn at the center of the black hole is called the singularity.

The surface beyond which light cannot escape the black hole is called the event horizon.

The event horizon is a sphere whose radius is called the Schwarzschild radius which is determined for non rotating black holes by the equation R = 2GM/c2 here G is the gravitational constant 6.77 x 10-11 m3/(Kg*s2) M is the mass of the black hole and c = 299792458 m/s is the speed of light.

For part two we will begin with a more thorough analysis of the Schwarzschild radius. If you ever need to remember the equation for the Swarzchild radius is just remember that you combine the speed of light the gravitational constant and the mass of the black hole in such a way as to give you units of meters and you have the equation modulo a factor of 2.

The derivation of the Swarzchild radius is actually somewhat complicated since it involves general relativity theory. But as often happens a simple calculation using just Newtonian gravity gives the right answer. A Newtonian gravitational well of a spherical object has a potential of -G*M/r where r is the distance from the center of the sphere. This means that it would require at least m*G*M/r joules of energy to completely remove an object of mass m from the sphere of mass M if that object was originally a distance r away. This and the formula 1/2m*V2 give us all we need to calculate the Schwarzchild radius or rather the newtonian estimate of it.

We find that at a radius r we require a certain minimum escape velocity in order to not be trapped by the gravitational potential. Specifically we have

m*G*M/RSchwarzchild = 1/2m*V2escape

therefore RScwarzchild = 2*G*M/V2escape

But the condition we are interested in is the condition that the escape velocity is the velocity of light whereupon we recover our previous formula for the Swarzchild radius. This calculation is just a classical approximation but conveniently gives us the correct answer.

Black holes really are perfectly black. That is to say the event horizon of a black hole is a perfect absorber of light. This of course is not surprising since there is nothing at the event horizon for the light to reflect off of. In physics a body with this property of being a perfect absorber of light is also expected to be something called a blackbody emitter. A blackbody emits light according to a certain characteristic spectra which was discovered by Max Planck. Originally it was assumed that a black hole would not have a temperature and therefore would not emit radiation (meaning light). But careful thought about what might happen at the event horizon gave rise to the idea that the black hole could allow virtual particles to become real. Meaning that black holes really do emit radiation and therefore have a non zero temperature. This line of reasoning was followed by Stephen Hawking who calculated the temperature that a black hole would have to have to correspond to this emission. This leads us to the equation for the temperature of a black hole

T = K/M

where K = 1.227 x 1023 kilograms kelvin. (note this is not the boltzmann constant it is just an accumulation of a bunch of terms I didn't feel like writing out)

K may seem to be an extremely large constant temperatures but when you consider the masses involved it actually predicts ridiculously small temperatures. A one solar mass black hole would have a temperature of about 0.00000006 kelvin. Any natural black hole would have a larger mass than this and therefore have an even smaller temperature. So one can safely ignore the temperature of large black holes. Such small temperatures are virtually undetectable. Even for much smaller black holes say one the size of Jupiter the temperature is about 64 microkelvin.

But for very very small black holes hawking radiation causes them to rapidly evaporate though explode might be a more apt term. A black hole of a mass on the order of a kilogram or less would have a temperature of around 1023 and would essentially evaporate instantly. I bring up such a tiny mass because people frequently worry about cern or some other powerful particle accelerator generating a black hole which eats the earth. While it would be great if it were possible for cern to generate black holes because of some as yet unknown phenomenon if it did those black holes would have energies of at most say 1010 J which is being rather generous. Such an energy corresponds to a mass around a thousandth of a gram. So there could be no danger from such a black hole as it would evaporate as soon as it formed.

Tuesday, November 3, 2009

Exercising at 5:30

I have decided to start getting up at 5:30 AM every morning so that I can exercise before I go to teach my discussion sections at 7:30 AM. This morning I did it for the first time and it was fine though ironically I think the field house is a bit crowded when it opens at 6:00 AM. Of course I have no trouble sharing the running track with other people in fact I really actually like sharing it with a bunch of other people it gives me a sense of pace and I am excited to see if I will recognize regulars who will show up at the same time as me to run.

The weight machines on the other hand are much less sharable and since I have a rather pathetic upper body strength also much more embarrassing. Tomorrow morning I will try and mix up my routine by trying to do exercises on the weight machines first and then going up to run. Hopefully this regime lasts for the rest of the semester and beyond, but I have committed myself to it only for the rest of the week and then I will reevaluate whether or not I want to do it.

Monday, November 2, 2009

Nano Begins Again

November is national novel writing month. NAtional NOvel WRIting MOnth or nanowrimo for short. if you are not familiar with it you should visit www.nanowrimo.org the idea is basically to encourage as many people as possible to write something vaguely novel length over the period of a month. I have been threatening to actually win (winning meaning achieving the goal of 50,000 words) for a number of years now but I each year it seems I make it to about 30,000 words. Rather interestingly 50,000 words is actually not that much in terms of a book. A 50,000 word book is on the edge of a novella instead of an actual novel. In previous years I have tried writing in the far future and or in a fantasy type setting and also in a familiar current time world. But nothing seems to be much better than any of the other options. This year I think I am going to mix things up a bit and try something where I mix those types of realities together.

At the moment the rough plot works something like this Charles and Agatha are strangers living in a city together. Agatha is scientist and engineer with a passion for numbers and artificial intelligence and the workings of the human brain. Charles is a fantasy geek who constantly daydreams himself into fantasy scenarios. Agatha builds some fancy device which monitors her brain activity. There is an accident and Agatha and Charles find themselves trapped in a strange fantasy world generated from the both of their minds. Or something at least vaguely like that.