Thursday, September 29, 2011

wksht1

The first set is fun.
If you're reading this and not in the class, take a look at this "street-fighting" mathematics ;)
http://www.astro.caltech.edu/~jrv/Ay20/ws/ws_collab_sfmath.pdf

Wednesday, September 28, 2011

Melody, a high schooler

An email I received:


Hi!

Thanks so much! I don't know how much Susan told you, but I'm really interested in astronomy, especially planetary science! :) What field of astronomy do you study? At Caltech, is astronomy merged with physics and math? Or are there plenty of astro courses and professors?
I also know that JPL is near Caltech (or it might be in Caltech, haha). Do you get to intern / work there a lot?

Thank you!

Melody

My response:

Oh hello! :D

I'm an astrophysicist, so that means a bunch of straight up physics with different elective classes and sequences we take. It's half physics, half astronomy classes based very heavily on physics and some coding/math.

It's Caltech's only astronomy program; there is a Planetary Science major (we call them options) in the GPS (geological, planetary science) division, where astro is in the PMA (Phys, math, astronomy/physics) division. So Astronomy is actually astrophysics at caltech, which is really mostly physics, which involves lots of math! :D It's fricking amazing!

But you don't have to worry; there are so many astro courses. And so many more professors. we have a building, Cahill: http://morphopedia.com/projects/cahill-center-for-astronomy-and-astrophy which rocks everyone's socks off. The profs are great - about a third are pretty old and super, super smart (whereas the geo/gps profs are either a bit boring or ridiculously awesome - mostly the latter) and about half are young, new, and in love with their subject, whether its exosolar planets or black holes/agn (active galactic nuclei) or any of a list of extraordinary astrophysical phenomena that are way over my head.

This is the course requirements: 
http://catalog.caltech.edu/pdf/catalog_11_12_part3.pdf (search astrophysics option to get to the right page)
A list of courses at caltech:
Courses this term (we're on a trimester schedule): 
http://regis.caltech.edu/schedules/FA2011-12.html

So JPL is a 15min drive away, so there's not much interaction. There is, I think, if you're a postdoc or professor who does planetary science stuff. If you want to work there, I believe it's more of an engineering thing. (Mars Rover and all that). There's also a lot of computer work done at JPL. I'm sure Susan's told you about her lab/research, so it's viable for you to work for a Summer Research thing there (SURF). You will probably be expected to know some level of programming for JPL, however, so if you want to research there, make sure you know a bit.

I'm having the time of my life. Today I had three classes in the morning: Ay20, the intro astro sequence on the local neighborhood and galaxies, taught amazingly well (almost no lecture and mostly collaboratively working on problems that require ingenuity); Ma2a, a core class on Ordinary differential eqns, and ACM95a, a nice and famously hard intro to computations involving complex variables. I'm learning things, relevant and interesting things, that I had no idea even existed back in high school. That's what Caltech is to me.

Last year, as I had never taken anything related to astronomy or geology, I really wanted to - just cause it sounded awesome (ie I love the subjects haha). I took Ay20, a very heavily lecture-dependent, derivation-based exploration of the universe and the formation of structure. It was my favorite class I've ever had, and also the hardest - I spent at least 15hrs a week on classes, reading, and especially the 10+hr-long sets. It was hard, but totally worth it. I guess this should be qualified by the fact that I don't remember it all, now, as we moved a bit too fast for me, which is really unfortunate.

I also took two intro geology classes, one on the biosphere and the rock record of life/oxygen/geologic events, taught by my favorite professor :) (he was intelligent and engaging and hilarious and fun) and one a geo/astro intro to planetary sciences, which I didn't enjoy as much. We did simple mechanics, looked at the solar system and stuff.

So yeah, hope that was helpful. I love Caltech - the people, the professors and classes and the culture and Astro and geo - but it's not for everyone (like Susan). I guess you have to be okay with a slightly quirky culture, a tiny school with a large population of lone workers, and a lot of hard work. But we also complain too much (it's a lot of work, but it fits the school) so if you're "really interested" like you say, this is the place.  A lot of people are bitter - perhaps I'm still too young - a lot more than other schools, I think. But then, we skip out on crazy dramatics and stupid frats as well, so it's your pick.

Cool. You should definitely apply - if the opportunity presents itself, you can always say no upon reflection.

I guess as a final say, you should decide for yourself. You need to be sure - and I mean sure - that you love science/engineering/math, or else you will be disappointed  You can't just quit planetary science and do history, at least not that good of a program, so if you're not sure, go to Harvard or Princeton or  Berkeley or JHU or any number of other schools (and for state schools, any UC, and UW in seattle and madison that I've heard of) that are also amazing for astro - for undergrad science, I think it matters most how much you put into your classes, not the name of the school.

I come from a family that really didn't want me to do astro or geology, and tried to push me towards medicine and (when I refused) econ. I come from a tiny midwestern high school that only taught me a bit a physics and math and a lot of how to interact with kids to whom graduating hs was tricky and getting a PhD literally means nothing to them. As in, under 20 kids had heard of MIT. It is so much more nerdy here, and (although I loved, loved high school) coming here has expanded every horizon imaginable.

You'll probably love college wherever you go (at least I hope!). If you are passionate about astro/science, you can go anywhere for a wonderful education.

Yeah, that was very long ;) bye!
Monica

If you read that all, i) I'm impressed with your patience, cause no way would I have, and ii) any suggestions are good. Although it's probably way too much info already. If you haven't noticed, I'm long-winded.

Tuesday, September 27, 2011

Notes

Just a few things:

Poynting–Robertson drag: solar radiation will cause dust grains to spiral inward.

From the perspective of the dust grain, solar radiation appears to be coming from a slightly forward direction. This is the aberration of light; at the instant of any observation of an object, the apparent position of the object (the sun) is displaced (see figure below). Absorbing this light leads to a force component against the direction of movement.

From the perspective of the solar system (the other reference frame), the dust absorbs sunlight in only the radial direction and its angular momentum is unchanged. However, by absorbing the photons it gains mass, and to conserve angular momentum L = r x mv, the dust must drop to a lower orbit.
Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light, a phenomenon known as the aberration of light.

Paucity of intelligent life: part of this
We've highly overestimated intelligent, technologically advanced life (they would have come knocking). Why? One reason is that there is no evolutionary pressure to gain technology; another is that the lifespan of an 'advanced' civilization is perhaps on a very small order, and that they die out quickly.

Heliosphere map and IBEX: listen to this short 2009 broadcast

The sun's corona boils off into space, producing the solar wind of hot ionized gas, flowing out at a million miles an hour. This inflates the bubble of the heliosphere. IBEX, the interstellar boundary explorer, measures neutral particles that propagate in from the outer reaches of the heliosphere, about 10 billion miles out. In the space between the termination shock and the ISM, the gas becomes heated and slower. The neutralized particles are produced in this interaction region between solar-material and outer-space material. IBEX took 6 months to map these particles.


It was expected to see a variation in the particle flux, relatively small (tens of percent) and to vary over  large angular ranges. Instead, there is very narrow 'ribbon' in the sky, where the flux is two or three times of anywhere else. The ribbon appears to line up with the external magnetic field (outside of the solar field) where it drapes around and squeezes hardest on our heliosphere. Most likely, the ribbon of incoming particles is correlated to the higher density of particles outside.

Pretty awesome stuff. :P

Hello.

Why, hello!

This isn't really relevant to astronomy, and it's not exactly an introduction of myself. Instead, this is more a sorta collapsed version of both in the form of a little question! I was reading up on some astrophysics things over the summer, to better understand my SURF with our Professor ;) and I came across this wonderful class, the results of which are here. One project, by an Aaswath Raman, was really helpful, and there are many others that I plan on reading and blogging about :)

But that's not the point. Earlier - maybe a day or so ago, one of my fellow Lloydies and I were fiddling around the piano when he asked a question that was amazingly simple but that I had no idea of how to answer. How, indeed, does a piano create sound? On the first order it's hitting a key with your fingers, and it's obvious from glancing in any piano that this movement depresses a lever that in turn hits a string; the string vibrates, and sound is produced.

We're taking Ph12 right now, and just took our first class today. It's a class on waves. So when that hammer hits the string, how does the string vibrate to create sound? We determined it's probably not a torque driven oscillation, that the string must vibrate either up-and-down or side-to-side, or some combination of both.

Then again, the sound waves coming towards us are longitudinal waves. which compress the air and (with help of a search engine) the opposite, which is a process you might recall as rarefaction.

The motion of the strings is (mostly) transverse. This is a wave where oscillations move perpendicular to the energy being transferred (like our light waves). The string vibrates so that the energy associated with that note being struck is transferred through a wooden bridge to a soundboard, and it is the velocity of the soundboard, in turn, that actually produces the sound waves.

Interestingly, the string vibrates both in a transverse and longitudinal mode, which is, in retrospect, perfectly reasonable for something being struck. There's a nonlinear coupling of the transverse string modes to longitudinal modes (the strings are damped, as well as stiff), but in the strings of the piano the longitudinal speed of sound in piano strings are ~20 times that of the transverse oscillations (i.e., their frequencies are therefore too high to hear most the time).

See also
A piano waveform (a chord)

  • Modeling a piano here, effectively on the basic wave equation for strings in one dimension. This was my foremost reference
  • This is an artistic thingy centered on burning pianos :( sad, but interestingly epic for a short while
  • Strings have very pretty sounds: listen to this gorgeous piece! Heartbeat, by Jake Shimabukuro
  • This page is nice: it has a simple explanation of the math of music (with really cool stuff on the waveforms of instruments)
  • Numerical simulations of piano strings, an article written back in 1993 that describes the vibrations of a string by a set of differential and PDEs. Another useful reference.