Friday, October 24, 2008

First Tests

This week I had my first two tests at graduate school, one in Classical Mechanics and then one in Statistical Thermodynamics. Now, Stat. Mech. is an undergrad course, so I suppose that it probably doesn't count in most people's minds as being a real "test" at the graduate level, but the course material can be tedious to remember. There are a lot of variables floating around and you really have to have a good understanding of the material to expect to even do remotely well. Some courses you can just memorize equations and then, bam, you have your solutions... not for this class! But having just finished it, literally just 12 minutes ago, I feel entirely confident that I aced the test. Now I do not want to jinx it, but I flew through it and only stumbled a couple times, just to pick myself up and complete every part.

As for classical mechanics... well, that's a different story. The test was hard, not to the point of not being do-able, but it was hard none the less. My derivations were solid, all except for the derivation for the reduced mass of a multi-body system; it escaped me once I sat down at the table with the test in hand despite having just had looked at it no less than 20 minutes prior to the test. I knew the definition of a reduced mass, so hopefully that will suffice seeing as we had to describe how to take a 6 dimensional system down to 1 dimension and the reduced mass kills three dimensions all on its own. I'm feeling somewhat confident... I think... which means I'm not at all, but all of the other students seemed to have gotten the same solutions as I did; we'll see how that goes. There was one question, though, that she puts on every year and no one can answer... well, she doesn't really have the answer, it's a conceptual question that the professors here can not even seem to answer - so I think that not answering that one won't count against me.

So here's the breakdown in my head:

Statistical Mechanics: Success
Classical Mechanics: Who Knows...

Well, off to do Classical Mechanics homework due this evening.

Wednesday, October 22, 2008

Physics Question #2

This problem has come to be known as Olber's Paradox, something familiar to those involved in astrophysics:

Suppose that the Universe is infinitely large and would then contain an infinite number of uniformly distributed stars. This would indicate, then, that the night sky should not, in fact, be dark, it should be infinitely bright! Even if the stars are at a great distance away, there would be more stars at that distance, and thus a large amount of light. So why then, does the night sky appear dark?

Now, one could easily use Google to find a solution to this apparent paradox, but try not to do that, you won't be exercising your mind if you do. Just take a few moments, think, and then post your proposed solution. If you would like, you can then Google it, but I shouldn't take as long to answer this one as I did the previous.

Stepping Back

As I sit here at my office desk, staring at my math and mechanics homework, I can't help but think to myself, gee, I should really be doing that and not writing on my blog. It just seems to make more sense that way. But after careful consideration, I realize that at times you have to step back and take a breather. While it means your work does not get done, it does allow you to refocus your mind by clearing away all of the clutter that has been building up over the weeks. I have always found that, sometimes, the best way to solve a problem that you're stuck on, is to leave it alone for at least 10 minutes. This helps clear your mind of the path that you have convinced yourself works... but in the end doesn't. It seems, though, that if you do not step away, then you just keep trying the same process over and over with the same results (usually a deep sigh and a tossing of the pencil).

A great example of how stepping away is good for the mind, this past weekend I travelled to Oswego to visit my girlfriend for my birthday. As much as I was freaking out in my head about not studying for my test in mechanics I had on Monday, it was quite refreshing to be out shopping with her and to get to spend time with her relaxing. It was great, we went to all of our usual stops, Kohls, Walmart, Barnes and Noble, and the Great Northern Mall. We also got pizza at Enzo's which is by far the best and cheapest pizza in the world - one of the good things to come out of Oswego!

As I said, though, I visited for my birthday, so we celebrated with a dinner at Chili's (our usual restaurant, and she gave me lavish gifts. Now, by lavish I don't mean the most expensive in the world - I wouldn't want that stuff anyway - but she got me things that I've been wanting and needing: a thermos for coffee, socks, bed sheets, tons of candy, a lunch bag and slippers. May not sound interesting to the common person, but I'm thrilled with it all, especially the slippers and thermos! I like my feet warm (especially with the temperature of my apartment) and my coffee hot!

Anywho, I'm sure I have just a ton of stuff to write about and thoughts to express, but I don't care to spend that kind of time doing it right now... maybe later, or next week... or who knows when (probably whenever mechanics homework isn't that hard... so never?). And by the way, I have posted the answer to the Physics Question as a comment on that post. I should probably post another one!

Tuesday, October 14, 2008

Packed Day

I haven't done this in a while, but I felt that I needed to elaborate on a dilemma which has presented itself to me this morning. I thought I had my day all planned out, work on my Statistical Mechanics homework... well, mainly rewriting it in a presentable form, followed by my two hour Classical Mechanics course. Nothing out of the ordinary here, just my usual Tuesday morning. However, it's in the afternoon that things start to get crazy. At 2pm I have an NSF workshop (which I will most definitely elaborate on later) which is designed to help students present a strong application to the NSF Fellowship Committee in order to obtain outside funding for research over the next 3 years. This is a two hour workshop, thus taking up a large chunk of my afternoon which could be used for finishing up both Statistical Mechanics and Math Methods homework (both due tomorrow).

Now, there is also a public lecture tonight at 7pm by a NASA astrophysicist dealing with our Sun and it's impact on near-Earth space. Should be interesting. But, unfortunately, this is also the time allocated by my Math Methods TA for office hours which I may or may not need to attend. Hopefully not! Finally, this morning, I got my usual D2U email which is a daily Dartmouth email about the events going on everyday. Well today, General Abizaid, a retired Four Star General will be giving a talk at 4:30pm on US-Middle East relations, which should be a very interesting talk... but that's during my dinner hours! Oh Lord... I wonder if General Abizaid would mind if I ate during his talk? I don't know, we'll see. I'll let you know what my chosen course was later, as well as answer the Physics Question I posed!

Monday, October 6, 2008

Physics Question

Here we go, why not throw out an age old physics question:

Imagine, if you will, a plane sitting on a large conveyor belt which is as wide and as long as a runway. The treadmill is designed to match the speed of the wheels, moving in the opposite direction. Can the plane take off?

This question normally stirs up quite a debate, do you think you know without looking it up on the internet? Just think about it, consider the system and the particular physical interactions that are occurring. I'll post an answer to this in a week or so.

Sunday, October 5, 2008

Peanuts & Thermo.

Linus seems to have a firm grasp of Thermodynamics. This was the peanuts comic strip for today, and I thought it was perfect timing.

Now I would relate this, also, to my life... I would be Linus pointing out these issues and my girlfriend would be Lucy...

Saturday, October 4, 2008

Normal Approach

XKCD Comic #55... absolutely hilarious! And now for an XKCD variation which appears on a t-shirt which changes the Fourier transform to a Laplace transform. Pure genius.

Statistical Mechanics

For my first instalment of class descriptions I have chosen to write about the undergraduate course I am taking as a "filler". Now, it's deemed a filler due to the fact that I have taken Thermodynamics already, at Oswego, but have not had Statistical Mechanics (Stat. Mech.), so in order to prepare for my graduate level Stat. Mech. course in the Spring, I need to fill in the gaps.

You may be wondering, if you're not a physicist, which I'm guessing most people aren't, what is the difference between Thermodynamics and Stat. Mech.? Or, for that matter, what about them is the same; how are they related? This takes a little prior background knowledge to explain, so let me teach you a little qualitative physics which explain the two topics. Thermodyanics is the study of energy, and for that part, so is Stat. Mech. Mainly, the conversion of energy and the transformation of energy from one form to another is the primary focus of both topics. For example, heating a cup of coffee in the microwave turns electrical energy into waves which in turn vibrate the water molecules in the coffee, thus increasing the average kinetic energy of the particles. As a result, this increases the temperature of the coffee. During this whole process, though, energy is conserved in one form or another. We know that in the Universe energy can not be created or destroyed, only converted into different forms. So in manner of speaking, thermodynamics is the study of the conservation of energy.

The primary difference between Stat. Mech. and what I had, Classical Thermodynamics, is the treatment of the system which they study. In Classical Thermodynamics, the treatment of the processes are done on a macroscopic scale (large). When working in this area, we are not concerned with the physics of the individual molecules, only the system as a whole. This is great for engineering, but from the aspect of a physicist, we want to know everything that is happening with in the system. We take a look at the microscopic state (microstate) of the system and how that relates to the macroscopic state (macrostate). In order to do this, though, we can't describe each particle or molecule individually, that would be ridiculous considering that one mole of gas contains 6.023x1023 molecules! Also, since we are dealing with microstates and with molecules and particles we have to treat the system quantum mechanically. In order to circumnavigate the difficulties of the shear size of our system, we utilize statistical tools for study the molecules. Molecules and particles don't all act in the same manner, but, they do act similarly based on probabilities. Thus, we may not be able to say exactly what a particle is doing before we observe it, but we can calculate a probability for what it is doing. In this fashion we can evaluate a large number of particles very easily and thus formulate the physics of the macrostate from knowledge of the microstate.

The course, thus far, is fairly straight forward and honestly, rather easy. It helps that the textbooks we are using are very verbose and contain great descriptions of the physics, not only in terms of mathematics (quantitatively) but also in basic words (qualitatively). The two text books for the class are as follows:

"Fundamentals of Statistical and Thermal Physics" by Frederick Reif (1965)
"An Introduction to Thermal Physics" by Daniel Schroeder (2000)

Both are good books, very descriptive - but I find that Reif is the more thorough book. This is mostly because it is clearly meant for upper division undergraduate course work where Schroeder could be utilized for a Sophmore level class. Schroeder, though, is a much better writer in terms of "dumbing" the material down and creating an active reading environment, whereas Reif is a little more dull in his writing but is very thorough and intensive. I personally enjoy reading Reif more (incorporates more quantum aspects). This course is definitely a good relief from the rigor of Classical Mechanics and Mathematical Methods, both of which are intensive graduate courses.


Finally! Three weeks after having moved into my apartment in West Lebanon, NH, I was delivered a router allowing me to set up a wireless network. Now, I say finally as if I had been waiting for a delivery guy for weeks... no, that's not the case at all. In fact, I didn't have to pay for this one! I was waiting until I had a paycheck or two put away before I invested in a router. Luckily, though, I was able to obtain one for free and considerably sooner than I had anticipated. It is such a nice feeling to finally be able to unplug in my own apartment and not have to sit on the floor so that I can reach the modem with my ethernet cable! So hopefully, or so it's the plan, I'll be on my computer more often at home after the long hours in the office at Dartmouth which will in turn, lead to me blogging more often. We shall see!