Large Hardon Collider

[Max™]

Spoiler: show

http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://www.folkalley.com/archives/taylor_swift.jpg
http://1.bp.blogspot.com/_PuZoLkvmBb...Little+Mac.gif

Taylor/Mac series.

Uh, seriously though, Zeno's paradox, where you take an infinite number of steps and only cross a finite distance, that's basically a Taylor series.

[Ferion]

Could you give an example of a problem from your book or something that you're not really understanding. The only things I've really seen Taylor/Maclaurin series used for was to approximate functions.

http://en.wikipedia.org/wiki/Taylor_series

If you look at the graphics on the right hand side of the page, it'll at least let you visualize what's going on as you add more terms to your series and how it helps you approximate functions. I'm sure Woozie will have something much more insightful to say, but I haven't taken Calc II in a while so I don't remember enough to give a general explanation that would be better than your professor's.

[BerenTebogo]

http://img804.imageshack.us/img804/9660/taylor.jpg

#56 is one of the ones that I'm completely stumped on for my homework. I can figure out taylor polynomials if I'm given something in the form of find the polynomial to degree n=whatever of f(x)=whatever centered around a=whatever, but when it's like how it is in 55 or 56 I just have no fucking clue what to do or what I'm really even being asked.

[Ferion]

Ok so, I could be wrong, but I can't see anything else that could be done with this type of problem. Taylor/Maclaurin series is most commonly used to approximate functions. So lets say we're looking at #56. All the homework problem is asking you to do is to approximate cos(x) and e^x using Maclaurin series, and then using those expansions instead of the actual term when computing the limit. So in the Wikipedia page I posted last time, it shows series expansions for both cos(x) and e^x. Since lim(a/b) is the same thing as lim(a)/lim(b), you can look at the numerator and denominator separately. So if we look at the top, if you expand cos(x) out, you get 1-x^2/2!+x^4/4!.... etc. So the numerator now looks like 1-(1-x^2/2!+x^4/4!..). If we take the limit of this as x approaches 0, all the xs go to 0 and we get lim(1-(1-0/2!+0/4!..)=0. The same thing can be done for the bottom, but the numerators 0 so the whole limit will be 0. To be honest this type of problem is completely pointless, but I guess it just kind of helps you understand series expansions. Honestly I'm pretty tired so I could be misunderstanding the problem, but this is the only thing that I can see is going on. I don't know if this is clear enough to help you, but I'd figure I'd at least try to explain it.

[Max™]

Wait, isn't there something you can do if you'd wind up with 0/0 while evaluating a limit?

This thing: http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

I knew I'd seen something about that, need to work with the derivatives if it would be indeterminate.

In calculus, l'Hôpital's rule (also called Bernoulli's rule) uses derivatives to help evaluate limits involving indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit.

[Max™]

Hmmm, anyone heard this shit about Penrose finding circles in the CMB?

http://i341.photobucket.com/albums/o...g?t=1290586377

http://www.universetoday.com/79750/p...fore-big-bang/

Have scientists seen evidence of time before the Big Bang, and perhaps a verification of the idea of the cyclical universe? One of the great physicists of our time, Roger Penrose from the University of Oxford, has published a new paper saying that the circular patterns seen in the WMAP mission data on the Cosmic Microwave Background suggest that space and time perhaps did not originate at the Big Bang but that our universe continually cycles through a series of “aeons,” and we have an eternal, cyclical cosmos. His paper also refutes the idea of inflation, a widely accepted theory of a period of very rapid expansion immediately following the Big Bang.

Penrose says that inflation cannot account for the very low entropy state in which the universe was thought to have been created. He and his co-author do not believe that space and time came into existence at the moment of the Big Bang, but instead, that event was just one in a series of many. Each “Big Bang” marked the start of a new aeon, and our universe is just one of many in a cyclical Universe, starting a new universe in place of the one before.

Penrose’s co-author, Vahe Gurzadyan of the Yerevan Physics Institute in Armenia, analyzed seven years’ worth of microwave data from WMAP, as well as data from the BOOMERanG balloon experiment in Antarctica. Penrose and Gurzadyan say they have identified regions in the microwave sky where there are concentric circles showing the radiation’s temperature is markedly smaller than elsewhere.
These circles allow us to “see through” the Big Bang into the aeon that would have existed beforehand. The circles were created when black holes “encountered” or collided with a previous aeon.

“Black-hole encounters, within bound galactic clusters in that previous aeon, would have the observable effect, in our CMB sky,” the duo write in their paper, “of families of concentric circles over which the temperature variance is anomalously low.”
And these circles don’t jive with the idea of inflation, because inflation proposes that the distribution of temperature variations across the sky should be Gaussian, or random, rather than having discernable structures within it.

Penrose’s new theory even projects how the distant future might emerge, where things will again be similar to the beginnings of the Universe at the Big Bang where the Universe was smooth, as opposed to the current jagged form. This continuity of shape, he maintains, will allow a transition from the end of the current aeon, when the universe will have expanded to become infinitely large, to the start of the next, when it once again becomes infinitesimally small and explodes outwards from the next big bang.
Penrose and Gurzadyan say that the entropy at the transition stage will be very low, because black holes, which destroy all information that they suck in, evaporate as the universe expands and in so doing remove entropy from the universe.
“These observational predictions of (Conformal cyclic cosmology) CCC would not be easily explained within standard inflationary cosmology,” they write in their paper.

Paper: http://arxiv.org/abs/1011.3706

Apparently they're claiming 6 sigma significance, which is pretty impressive if correct.


Also: http://www.sciencedaily.com/releases...1123112835.htm

Early Universe Was a Liquid, Nuclei Collisions at the Large Hadron Collider Show

ScienceDaily (Nov. 23, 2010) — In an experiment to collide lead nuclei together at CERN's Large Hadron Collider physicists from the ALICE detector team including researchers from the University of Birmingham have discovered that the very early Universe was not only very hot and dense but behaved like a hot liquid.
http://www.sciencedaily.com/images/2...1123112835.jpg
By accelerating and smashing together lead nuclei at the highest possible energies, the ALICE experiment has generated incredibly hot and dense sub-atomic fireballs, recreating the conditions that existed in the first few microseconds after the Big Bang. Scientists claim that these mini big bangs create temperatures of over ten trillion degrees.

[Psion]

So wait, that means all those fantasy stories harping about the universe having different ages that come around like a wheel might have a kernel of truth to them? <_<;

Or does this mean that the universe is stuck on repeat mode, where when the end of the clip ends, it starts from the beginning? lol

Although if that's the case, I wonder if it's the same universal timeline repeated over and over again, or each time it repeats it has different outcomes.

[Eliseos]

Your mom has concentric circles in her CMB.

[Max™]

Your mom has concentric circles in her CMB.

Oh yeah?

Yo mama so fat, it took a team of astronomers 2 years using the Hubble telescope measuring the distortion of background galaxies from her gravity well in order to calculate her mass!

[Woozie]

http://www.calamitiesofnature.com/archive/401.jpg

[Eliseos]

Hubble don't gotchur mom.

[Max™]

Yo mama so fat, the bitch has an event horizon!

[Mizango]

http://www.calamitiesofnature.com/archive/401.jpg

rofl

[Max™]

In fact, yo mama's ass is so massive, last time she tried to put on a belt, the act of tightening it caused her to drop below her Schwarzschild Radius, which is how she gave a whole new meaning to the term "black hole", hell, she's so fat, if she spun around she'd develop an ergosphere!


http://i341.photobucket.com/albums/o...g?t=1290629253

[Psion]

I feel special for actually getting about half of these. <_<;

[Kaylia]

So my Calc 2 exam on all the types of series is tomorrow and I'm pretty sure I understand everything clearly except Taylor/Mac series. It's not a huge deal since like 95% of the exam will be on things that aren't the T/M series and I'm sure I understand it enough to get at least most of the problems focusing on them done, but really, it'd only be because I've memorized the process.

I'm having a hard time understanding the nature of the T/M series I guess. I watched a video on youtube that tried to explain really what it is for and etc, and that helped a bit, but I could really use an explanation in common sense terms I guess. It's hard to properly describe my confusion, but if anyone has any tricks they use to really grasp the underlying concept of T/M series I'd be really appreciative.

Taylor (and MacLaurin) series are used to transform a function into a polynomial equivalent around a particular point (this point is x=0 for Maclaurin, and x=a for taylor). If you keep a few terms only, it will be a decent approximation. If you keep the whole series, it will be equal to your original function. This concept is very important in physics and mathematics because it allow you to make the jump from insanely complex functions to a simple polynomial. It also allow you to solve many geometry problems that you will encouter eventually.


Wiki's picture is spot on here (n represent the power of your polynomial and incidently, the number of term you kept in the series)
http://upload.wikimedia.org/wikipedi...Exp_series.gif
http://upload.wikimedia.org/math/d/8...eb74574b40.png

The first term is always a constant given by the function itself. For example, if you're trying to approximate f(x)=e^x around x=0, a solid guess would be f(x)= 1 for any value of x close to 0. While it's not true for any value but 0, it still is pretty damn close if you don't go too far


The second term will be a first order approximation (slope*x) obtained from the derivative around the point of interest. Basically, you're trying to write a more accurate function that sum both the constant and a rough estimation of how the function varies. Using earlier example ( e^x ), we find that f '( 0)= 1. In this scenario, taylor series would become f(x)~= 1+1x in the surrounding of 0.

Up to this point, the argument is very similar to what you learned with derivative. A linear approximation is only true if you look at the value immediatly next to to the point of interest (+/- dx). If you go farther, the linear approximation probably won't cut it.

Because the approximation is still not very accurate away from the point of interest (unless the function was linear), we need to find out how much the derivative varies and add a 3rd approximation that consider that . Since f ' '( 0)= 1, the best approximation we have is f(x)~= 1+x+(1*x²)/2!.

If you keep repeating this, you will eventually obtain a complete polynomial that represent your original function.
f(x)=e^(x) = 1+x+½x²...


I skipped the factorial because it's a bit harder to visualize, but if you want to understand why it appears, it's simply needed to cancel out the effect of the derived exponant (if you derivate x³ three times, you will get 3*2*1 or 3!). If you can, try finding the series that describe f(x)= x³+x³+x+1 around . It takes 2 minutes top, and if done right, it should gives you a decent idea of wtf is hapenning.


[edit]
If you want something more concrete, it's pretty close to what you are doing in mechanics when you try to find the traditional movement equation.
http://www.ugrad.math.ubc.ca/coursed...elocity_17.gif

If I ask you to find taylor series of x(t) = sin(t), x(t)= e^t, or x(t) = t³*log(t)/t!, you will get back the equation right above....kinda. (acceleration would be a function given by the sum of t³ and above terms)

[Kaylia]

Anyone here is able to explain me how to obtain isobaric-isothermal ensemble? I've no trouble understanding how to get the canonical ensemble using statistics physics postulate, but I don't see how to repeat the result when the volume can varies.

[Eliseos]

Do you mean an Ericsson cycle? http://en.wikipedia.org/wiki/Ericsson_cycle

I'm not sure what you mean by ensemble.

[Kaylia]

More like http://en.wikipedia.org/wiki/Isother...baric_ensemble


Probability distribution is very easy to find in literature for canonical, microcanonical and grand canonical ensemble, but every reference I find for isobaric-isothermal ensemble skip the explanation.

What bother me right now is that I don't see how I can use phase space to obtain the result since the density won't be equal for different value of V.

[zoobernut]

http://www.nasa.gov/home/hqnews/2010...robiology.html

Anyone see this? Looks interesting.

Dwayne Brown
Headquarters, Washington
202-358-1726
[email protected]

Cathy Weselby
Ames Research Center, Moffett Field, Calif.
650-604-2791
[email protected]

Nov. 29, 2010


MEDIA ADVISORY : M10-167

NASA Sets News Conference on Astrobiology Discovery; Science Journal Has Embargoed Details Until 2 p.m. EST On Dec. 2

WASHINGTON -- NASA will hold a news conference at 2 p.m. EST on Thursday, Dec. 2, to discuss an astrobiology finding that will impact the search for evidence of extraterrestrial life. Astrobiology is the study of the origin, evolution, distribution and future of life in the universe.

The news conference will be held at the NASA Headquarters auditorium at 300 E St. SW, in Washington. It will be broadcast live on NASA Television and streamed on the agency's website at http://www.nasa.gov.

Participants are:
- Mary Voytek, director, Astrobiology Program, NASA Headquarters, Washington
- Felisa Wolfe-Simon, NASA astrobiology research fellow, U.S. Geological Survey, Menlo Park, Calif.
- Pamela Conrad, astrobiologist, NASA's Goddard Space Flight Center, Greenbelt, Md.
- Steven Benner, distinguished fellow, Foundation for Applied Molecular Evolution, Gainesville, Fla.
- James Elser, professor, Arizona State University, Tempe

Media representatives may attend the conference or ask questions by phone or from participating NASA locations. To obtain dial-in information, journalists must send their name, affiliation and telephone number to Steve Cole at [email protected] or call 202-358-0918 by noon Dec. 2.

For NASA TV streaming video and downlink information, visit:

http://www.nasa.gov/ntv