End of Exams

So I squeezed my way through semester 7. My Quantum Mechanics final exam today came blasting right down the calendar and arrived all too soon. Any time I’ve had to write more than 2 exams back to back one of them often suffers. I think that’s mostly due to the fact that any time you select 3 of my courses at random from the past years your bound to get at least one stickler. I don’t think I really suffered this time though as a matter of preparation or skills with the course. The final was just too long! I probably could have made my way through all the questions in a full 12 hour day of work with some help from a good calculator and a textbook, but to do it in 3 hours with no discussion or help was a bit much.

Anyhow, Christmas vacation has arrived and I’m quite happy to get out of classes for two weeks and do everything other than work hard on school.

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Asymmetric Capacitance…

Here’s the abstract for the latest paper…

Electric Field Properties of Asymmetric Capacitances

Properties of the electric field produced between two parallel charged conducting wires are described and analyzed. A DC high voltage supply is used to charge a capacitive configuration of narrow gauge wire which produces a strong electric field. An electrostatic model of the apparatus is developed and used to describe the observed phenomenon of ionization of atmospheric gasses in this electric field. Measurement of the forces caused by the acceleration of these ions provided a means of ascertaining an approximate threshold for the electric field to cause ionization of atmospheric gasses of 2.8 ± 0.4 MV·m−1 in excellent agreement with the accepted value of 3 MV·m−1. Forces on the order of tens of milliNewtons are observed, sufficient to support the entire weight of the apparatus generating the field.

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Antigravity

For my final Physics 397 lab I’m working with Andrew Burke and Steve Jim, we’re studying propulsion. The idea is that we ionize air in the presence of a strong electric field, accelerate the electrons in one direction and the cations in the other direction. As a result in the mass difference (more than 10000:1 for atmospheric gasses) There is thrust generated according to Newton’s third law.

The magnitude of the propulsion force depends on how much air is being ionized and the electric field that it is going to be accelerated across (remember that the mean free path in air (SATP) is on the order of microns, not meters). Generating an electric field strong enough to strip electrons from air molecules isn’t all that simple when you imagine how strong it needs to be, but there is a relatively simply way of doing it. A very simple application of Gauss’s Law to an infinite line charge shows that the field goes like (lambda)/(2*pi*eo*r) where lambda is the linear charge density eo is the permittivity of free space, and r is the distance from the axis of the line charge. That means that the electric field gets arbitrarily large as you approach a theoretical line charge.

To charge a very thin wire (good approx of line charge) we just need to include it in a capacitor and put a large voltage across it. We’re just suspending the thin wire (42 gauge magnet wire) above a large radius of curvature conductor (piece of Al foil).

To measure the force generated (as the obvious manifestation of the phenomenon) we’re suspending the apparatus on a pendulum and measuring the angle of deflection from vertical.

Prelimiary tests have shown that we’re not completely out to lunch, we’re deflecting our “flyer” by close to 100 with a mass of many tens of grams if not hundred (haven’t yet measured).

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Why I love James

Here’s a high quality musing by James Bell the First:

If an intelligent outside observer is required for a waveform to collapse (and thus for anything to exist), how is the entire universe here? Who is the extra-dimensional intelligent outside observer who makes the waveform of the universe collapse into the form that we experience it in? Is there a God?

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When a Gaussian is not a Gaussian

I’ve been sitting in an ETLC computer lab for quite a few hours here trying to write a computer simulation of the phys 397 lab that Rob Joseph and I have been working on for the last month. What should have ended up being a “straight line” passing through a nice series of 60 data points is actually a straight line passing through a jungle of randonimity. What I believe turned out to be our problem was that when we approximated our “filter function” (the transmission spectrum of the IR filters being used) we just used e as the base of the exponent. Assuming that a bell curve is accurately described by a gaussian distribution is something that loads of people probably do every day. I mean we did it every day for a month in Statistical Mechanics when we use the Stirlings approximation of large factorials. There are situations, and unfortunately our lab turns out to be one of them where a Gaussian just doesn’t describe a bell curve very well at all.

Indeed it’s the difference between something being gaussian and something being a bit wider up top or more triangular that throws our data for a loop. When performing the numerical integration right near the peak of the blackbody curve the filter is much narrower than the peak of the spectrum. This means that the variation from one filter to another across this regions is not
extremly pronounced. When the filter funtion is poorly approximated it makes a big difference!

What really needs to be done is to replicate the bell curve of the filter using a numerically exact model. Since I don’t have any means to do this I’m going to have to switch my beautiful 60 data point set into 10 data sets (ten filters) with only 6 data points each.

I was also going to pursue a reverse derivation of the plank curve using a 3D curve fit of my data array, that would have made my lab something close to a manifestation of sheer beauty on paper. But with these results I think it’s not going to be
worth the effort, I know that the answer will be poor.

I’m not all that worried about poor data, If I can write a blog at 12:50 am on a Friday night about the intricacies of a Gaussian Distribution, I’m not going to have any trouble filling 5 pages in Latex on the topic.

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Quantum Mechanics

Quantum Mechanics is honestly the sweetest course I have ever taken in the history of my life. I’m now checking it off on my list of life goals as complete

Now, anybody else in the course right now might be thinking otherwise as we are all finishing up the largest “weekly” assignment of our lives. Mine totals 16 pages. But by struggling through some ridiculous matheMagic to do those complex integrals and expectation values etc. I’ve developed not only a greater interest in the stuff, I’ve really got a much larger respect for the whole deal.

When you start an integral on one page, and hack your way through it on 2 pages, making reference to another 4 pages of previous results for simplification along the way, and arrive at the finish line with an answer of h|bar*(l^2 + a). You really get a grip on how intricately everything fits together. Having started with an expression that was so long I couldn’t even write it on one line (and couldn’t be reduced from there either!) and can develop such an elegant result I’m beginning to get a bit better grip on how perfectly God has this world balanced out. Whether or not the quantum mechanics aspect of the problem characterizes the real world very accurately, the math itself is something that elicits a bit of awe in me. I can’t help but sit here at my desk and be in a good mood even though the clock now shows “12:50″ because I’ve just seen a few of God’s fingerprints.

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LaTeX

My Phys 397 lab course requires that my lab reports be submitted according to a specific style. LaTeX is strongly recommended as this allows us to use a template provided to develop our lab reports and equations etc. in an efficient, neat and standard manor.

I therefore downloaded the freeware MikTeX distribution of the LaTeX language for windows operating systems. I got a bit of practice thus far, but I certainly have a lot yet to learn. For the most part all I have figured out is that TeX is an extremely powerful tool. The more I read (which is not much yet) the more I realize that I haven’t really made much progress yet. It’s one of those things that once I know it I doubt I’ll be using much else to create documents. The thing I’m interested in is how other people are going to respond to my communication via .pdf for all purposes rather than .doc? If you’re wondering how this is going to work out you’ve got about 1 month to find a solution because I know that once I learn I won’t turn back.

Here’s an Example of what I’ve figured out how to do so far. Focussed mostly on the math aspects of the markup, I’ll learn the other stuff as I go along.

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Days of Physics underway

Tuesday and Thursday this semester are certainly days that will teach me that even great things like physics need to be managed in moderation.

Hopefully this semester won’t turn me against it (I have little doubt that this is impossible) but I’ll certainly get my fill. Starting with Electrodynamics and then Quantum for 3 hours straight each morning I then roll right into 3 hours of labs in the afternoon. It’s a bit overboard but that’s just how the cookie crumbles.

I’m a little worried that I’ll get buried within a few weeks and won’t emerge until May.

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