Showing posts with label randomness. Show all posts
Showing posts with label randomness. Show all posts
Thursday, October 13, 2011
Wednesday, November 11, 2009
Notes for today's lecture
It won't be on the exam, but if you are curious to go through today's material on fluid dynamics at a bit more leisurely pace, I've written up some notes.
UPDATE: I did some cleaning up of the notes. I added quite a bit on fluid rotation (like what curve describes the shape of water going through a drain), and also added a few examples. Specifically, I showed how the Hall effect (current flow in the presence of a magnetic field) requires a tensor conductivity, and treated the case of steady flow through a cylindrical pipe. The latter is a rare example of an analytical solution to the Navier-Stokes equations (given a good number of reasonable assumptions), and quite practical.
The updated notes are in the same location linked above.
No, it is still not going to be on the final, it is just cool. ;-)
UPDATE: I did some cleaning up of the notes. I added quite a bit on fluid rotation (like what curve describes the shape of water going through a drain), and also added a few examples. Specifically, I showed how the Hall effect (current flow in the presence of a magnetic field) requires a tensor conductivity, and treated the case of steady flow through a cylindrical pipe. The latter is a rare example of an analytical solution to the Navier-Stokes equations (given a good number of reasonable assumptions), and quite practical.
The updated notes are in the same location linked above.
No, it is still not going to be on the final, it is just cool. ;-)
Friday, October 16, 2009
Randomness
Since we're about to finish up relativity, I've been thinking a lot about what I think is the 'correct' way to cover mechanics, E&M, and relativity. In doing some reading, I ran across this quote, which made me think even more that our usual approach is severely lacking:
Just something I find interesting: despite what you might hear in intro courses or popular accounts, E&M played a big role in inspiring relativity, it was not merely the speed of light and the aether.
Problem is, the history is in a way conceptually out of order, and harder to teach (IMHO). My evidence being how relativity is often presented in intro-physics sequences: as a total non sequitur, just sort of shoved in there. Moreover, in spite of the preserved historical ordering of topics, the motivation given usually starts out with the Michelson-Morley experiment and the aether, and quietly ignores EM forces in different reference frames. Thus, we keep the historical ordering, but throw out crucial parts of the original (and exceedingly insightful) motivation!
I prefer to follow the Mechanics -> Relativity -> Electromagnetism ordering, which I guess I've made obvious now. Relativity is hard conceptually, but I find students have a harder time with electromagnetism at first, particularly magnetism. Having relativity under your belt at least makes the magnetic field seem less arbitrary, which is reassuring I think. Introducing relativity after mechanics and E&M, while historically accurate, sometimes makes it seem like an ugly hack, which it wasn't at all. If you are going to do relativity after E&M anyway, why not cover the E&M aspect too? Purcell's book does a wonderful job.
On the other hand, doing relativity after mechanics is harder to motivate sometimes, and one has to resort to strange little thought experiments to find anything wrong with Newtonian physics. Thinking about relativity right after a mechanics course, though, has your brain in the right mode and the kinematics fresh in your mind.
Of course, I suppose it is just difficult either way, reality is a harsh mistress. And Poincare probably deserves more credit than he gets.
"The influence of the crucial Michelson-Morley experiment on my own efforts has been rather indirect. I learned of it through H.A. Lorentz's decisive investigations of the electrodynamics of moving bodies (1895) with which I was acquainted before developing the special theory of relativity . . . What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body moving in a magnetic field was nothing else than an electric field. - Albert Einstein
Just something I find interesting: despite what you might hear in intro courses or popular accounts, E&M played a big role in inspiring relativity, it was not merely the speed of light and the aether.
Problem is, the history is in a way conceptually out of order, and harder to teach (IMHO). My evidence being how relativity is often presented in intro-physics sequences: as a total non sequitur, just sort of shoved in there. Moreover, in spite of the preserved historical ordering of topics, the motivation given usually starts out with the Michelson-Morley experiment and the aether, and quietly ignores EM forces in different reference frames. Thus, we keep the historical ordering, but throw out crucial parts of the original (and exceedingly insightful) motivation!
I prefer to follow the Mechanics -> Relativity -> Electromagnetism ordering, which I guess I've made obvious now. Relativity is hard conceptually, but I find students have a harder time with electromagnetism at first, particularly magnetism. Having relativity under your belt at least makes the magnetic field seem less arbitrary, which is reassuring I think. Introducing relativity after mechanics and E&M, while historically accurate, sometimes makes it seem like an ugly hack, which it wasn't at all. If you are going to do relativity after E&M anyway, why not cover the E&M aspect too? Purcell's book does a wonderful job.
On the other hand, doing relativity after mechanics is harder to motivate sometimes, and one has to resort to strange little thought experiments to find anything wrong with Newtonian physics. Thinking about relativity right after a mechanics course, though, has your brain in the right mode and the kinematics fresh in your mind.
Of course, I suppose it is just difficult either way, reality is a harsh mistress. And Poincare probably deserves more credit than he gets.
Thursday, October 1, 2009
Homework
Maybe I'm just loopy from preparing my tenure dossier, but here are some thoughts on homework.
1) By way of Drew: "Problems worthy / of attack / prove their worth / by fighting back."
2) I showed some grad students and faculty your homework, and they now fear you. You will be rocking PH331 and ECE340 when the time comes, because you're doing their homework already ;-)
1) By way of Drew: "Problems worthy / of attack / prove their worth / by fighting back."
2) I showed some grad students and faculty your homework, and they now fear you. You will be rocking PH331 and ECE340 when the time comes, because you're doing their homework already ;-)
Wednesday, September 30, 2009
Friday, September 25, 2009
Some notes on electrical measurements
This is an unfinished document that is part of another project - the start of some notes on how to perform electrical measurements in general, and specifically on samples of real, live materials. After our next meeting, it might be of interest.
Basically, the more interesting part at the end shows you how to calculate the resistivity (or conductivity) of a conducting material from experimental data, the so-called 'four point probe' technique. Moreover, you can figure it out for conductors of various interesting shapes, like thin films, using very general symmetry-related arguments. We'll cover the necessary background in Friday's recitation.
If you're studying or planning to study anything materials- or device-related, you will see the four-point probe technique again. It is not hugely difficult, but not commonly covered in any depth, and usually just taken on faith. So, when you do see the four-point probe expressions again, you can smile and know that they are not, in fact, magic.
Basically, the more interesting part at the end shows you how to calculate the resistivity (or conductivity) of a conducting material from experimental data, the so-called 'four point probe' technique. Moreover, you can figure it out for conductors of various interesting shapes, like thin films, using very general symmetry-related arguments. We'll cover the necessary background in Friday's recitation.
If you're studying or planning to study anything materials- or device-related, you will see the four-point probe technique again. It is not hugely difficult, but not commonly covered in any depth, and usually just taken on faith. So, when you do see the four-point probe expressions again, you can smile and know that they are not, in fact, magic.
Saturday, September 19, 2009
Using analogies on the internet is like ...
I thought this was a nice read. My own personal data suggests it to be true.
Thursday, September 10, 2009
Friday, September 4, 2009
Thursday, September 3, 2009
Wednesday, September 2, 2009
It could be worse.
A truly pathalogical function. Continuous everywhere and differentiable nowhere.
A nice quote:
I have an image of rogue mathematical symbols ganging up on me now. Great.
A nice quote:
While it's not very common that badly-behaved functions arise in physics, there are functions which at least don't always remember to say please and thank you. They have to be gently corrected, but they're good at heart. The mathematicians are the ones who have to deal with the truly shady functions, the ones who form prison gangs and don't play by the rules and obey the laws. Or theorems.
I have an image of rogue mathematical symbols ganging up on me now. Great.
Subscribe to:
Posts (Atom)