Large Hardon Collider

[Woozie]

I'm pretty sure my prof. just wrote the problem wrong since when he referenced it today it was more logical. I'd explain better but I just got out of my exam and I'm exhausted, lol.

The limits of sequences make ZERO logical sense unless I just don't understand them enough yet. We've only done the very first section of intro to sequences so I know there's MUCH more to learn but one of the problems on my test was like discuss the properties of the sequence n+1/2n-3 and find the limit. I did all the math correctly (checked a few min ago on wolfram since I remembered the problem) but when I graphed the function and looked at the values in a table it didn't make sense to me. I keep seeing the discontinuity of the function at 3/2, the table gives error at 3/2, the derivative of the sequence when turned into a function approaches 0 from like -5 or something? and the limit is 1/2.

I'm just honestly confused with the concept I guess. The derivative test is like it was in calc 1 I assume? Just to test increasing or decreasing (or concavity?), but how is the function increasing when the sequence appears to be decreasing towards 1/2?

I'm doubting I'll get full credit on the problem since I feel like I did something wrong, but looking again at the derivative of the function the lowest boundary (for all x > 1) is -5 and it approaches 0. So, I don't know. I'm splitting hairs over what will probably be ~5 points of the total test, but I'm kinda raging over it too.

tl;dr: so far, fuck sequences. I need to learn more about them.

You're refering to the limit of a sequence, right? Not a series? The derivative test is for series (i.e. when you're adding the terms of a sequence). If you have just a sequence, you just take the limit as n approaches infinity. You can treat the sequence in the same way you'd treat functions as x goes to infinity. Last semester when you were given f(x)=(x+1)/(2x-3) limit as x approaches infinity, how did you solve it? For a sequence, you solve it the same way because a sequence is just a function who's domain is restricted (usually) to the natural numbers (or perhaps starting at some other integer and going to positive infinity). It's only for series that things get different and you have to start using tests to see if it converges. In this case, since it's a sequence and not a series, the limit is simply 1/2 for the same reason you got 1/2 when dealing with f(x) last semester.

Yes, there is a discontinuity at n=3/2, but n can never equal 3/2 because sequences only run over the natural numbers and 3/2 is not a natural number.

Also, the derivative of that function is always negative, so the function is always decreasing.

[Ferion]

The limits of sequences make ZERO logical sense unless I just don't understand them enough yet. We've only done the very first section of intro to sequences so I know there's MUCH more to learn but one of the problems on my test was like discuss the properties of the sequence n+1/2n-3 and find the limit. I did all the math correctly (checked a few min ago on wolfram since I remembered the problem) but when I graphed the function and looked at the values in a table it didn't make sense to me. I keep seeing the discontinuity of the function at 3/2, the table gives error at 3/2, the derivative of the sequence when turned into a function approaches 0 from like -5 or something? and the limit is 1/2.

I think you're just over thinking things and making it more complicated than it actually is. Once you get more comfortable with the notation, everything becomes a lot clearer. Your biggest problem is that you're treating the sequence as a function with the domain set in the real numbers instead of the natural numbers. The definition of a sequence is it is a function whose domain is the set of positive integers. So when you're talking about discontinuity at (3/2) I'm guessing you mean when n = (3/2) since that makes the denominator equal to 0. However, since we're talking about sequences it is impossible for n ever to equal (3/2). When trying to look at the graph of the sequence, you need to be very careful to make sure you're only looking at natural numbers as the inputs. I'm not sure if I'm doing a good job at explaining this, but to put it bluntly, if you said (1/2) was the limit you're right.

Edit: Woozie beat me to it.

[BerenTebogo]

You're refering to the limit of a sequence, right? Not a series? The derivative test is for series (i.e. when you're adding the terms of a sequence). If you have just a sequence, you just take the limit as n approaches infinity. You can treat the sequence in the same way you'd treat functions as x goes to infinity. Last semester when you were given f(x)=(x+1)/(2x-3) limit as x approaches infinity, how did you solve it? For a sequence, you solve it the same way because a sequence is just a function who's domain is restricted (usually) to the natural numbers (or perhaps starting at some other integer and going to positive infinity). It's only for series that things get different and you have to start using tests to see if it converges. In this case, since it's a sequence and not a series, the limit is simply 1/2 for the same reason you got 1/2 when dealing with f(x) last semester.

Yes, there is a discontinuity at n=3/2, but n can never equal 3/2 because sequences only run over the natural numbers and 3/2 is not a natural number.

Also, the derivative of that function is always negative, so the function is always decreasing.

That actually makes much more sense now. Going to get like -3 or 4 points off because I put increasing (hurrr) but I'm pretty sure I got everything else on the test right. I'm pushing myself to maintain a 4.0 for this entire semester and it's driving me nuts ~_~ I find myself agonizing over every possible missed half point on shit these days.

Thanks a bunch :Q

[Ferion]

A better way to look at how a sequence behaves is to plot it on a number line rather than graph it like a normal function. This will still show you the behavior of the sequence without confusing yourself about the inputs. At least that's what I find to be a lot easier to look at.

[Lhyet]

Cumbria 'still suitable' for nuclear waste storage

West Cumbria is still in the running as a location for deep geologic storage of nuclear waste, according to a report.

...

Greenpeace senior energy campaigner Ben Ayliffe said: "This report means that almost anywhere in the Lake District could become a dump for the UK's radioactive waste.

"It's hard to imagine a more tragic legacy to Britain's nuclear folly than vats of lethal nuclear waste being stored around Keswick or Scafell Pike.

"It's certainly not the sweeping vistas that would have inspired Wordsworth or Coleridge."


You heard it here first! Burying nuclear waste deep underground will instantly cause all surrounding land to look like this:
http://cache.kotaku.com/assets/resou...aser-thumb.JPG

[foopy]

http://www.bbc.co.uk/news/technology-11644252

The title has gone to China's Tianhe-1A supercomputer that is capable of carrying out more than 2.5 thousand trillion calculations a second."
"I would say it's 47% faster than the Oak Ridge National Laboratory's machine, 1.7 Pflops (ORNL system) to 2.5 Pflops (Chinese system)."

[Eliseos]

It still can't make me coffee.

[Psion]

Don't worry, maybe in time a supercomputer's sheer calculation power could influence the quantum level to materialize one for you. :O

[Altariel]

Wasn't it shown that the universe was "flat" (as opposed to open or closed) some time ago? Or has that changed? It's one of the few things I remember from last time I watched Lawrence Krauss's lecture on the Universe.

Actually that's quite a good talk, thanks for posting it. I don't know why I never subscribed to Dawkins' youtube channel until now... The method that Krauss explains to measure the curvature (or lack thereof) of the universe is pretty ingenious. To my knowledge the "flatness problem" was still an open question but most of the cosmology books that I've read were written in the early part of the decade.

However, maybe someone can help me understand better. Isn't the "shape" of the universe a different issue than it's curvature? Maybe they are one in the same and I just don't understand the geometry very well; I always had a problem visualizing that the universe isn't expanding "into" anything.

[Max™]

Oh, don't worry, most people have trouble visualizing this stuff.

http://agnesaviiki.tumblr.com/photo/...6loA6LO1qzz425
http://map.gsfc.nasa.gov/media/factcards/UniShape_b.jpg
http://map.gsfc.nasa.gov/media/030639/030639_1_320.jpg

"So what you think you just explained is...?"
http://t1.gstatic.com/images?q=tbn:T...th-box.jpg&t=1
'Correct! This box contains our OWN UNIVERSE!'

[Kaylia]

http://www.sciencedaily.com/releases...1028141430.htm

Nearly one in four stars similar to the sun may host planets as small as Earth, according to a new study funded by NASA and the University of California.

The study is the most extensive and sensitive planetary census of its kind. Astronomers used the W.M. Keck Observatory in Hawaii for five years to search 166 sun-like stars near our solar system for planets of various sizes, ranging from three to 1,000 times the mass of Earth. All of the planets in the study orbit close to their stars. The results show more small planets than large ones, indicating small planets are more prevalent in our Milky Way galaxy.

"We studied planets of many masses -- like counting boulders, rocks and pebbles in a canyon -- and found more rocks than boulders, and more pebbles than rocks. Our ground-based technology can't see the grains of sand, the Earth-size planets, but we can estimate their numbers," said Andrew Howard of the University of California, Berkeley, lead author of the new study. "Earth-size planets in our galaxy are like grains of sand sprinkled on a beach -- they are everywhere."

The study appears in the Oct. 29 issue of the journal Science.

The research provides a tantalizing clue that potentially habitable planets could also be common. These hypothesized Earth-size worlds would orbit farther away from their stars, where conditions could be favorable for life. NASA's Kepler spacecraft is also surveying sun-like stars for planets and is expected to find the first true Earth-like planets in the next few years.

http://www.sciencedaily.com/images/2...1430-large.jpg

Howard and his planet-hunting team, which includes principal investigator Geoff Marcy, also of the University of California, Berkeley, looked for planets within 80-light-years of Earth, using the radial velocity, or "wobble," technique.

They measured the numbers of planets falling into five groups, ranging from 1,000 times the mass of Earth, or about three times the mass of Jupiter, down to three times the mass of Earth. The search was confined to planets orbiting close to their stars -- within 0.25 astronomical units, or a quarter of the distance between our sun and Earth.

A distinct trend jumped out of the data: smaller planets outnumber larger ones. Only 1.6 percent of stars were found to host giant planets orbiting close in. That includes the three highest-mass planet groups in the study, or planets comparable to Saturn and Jupiter. About 6.5 percent of stars were found to have intermediate-mass planets, with 10 to 30 times the mass of Earth -- planets the size of Neptune and Uranus. And 11.8 percent had the so-called "super-Earths," weighing in at only three to 10 times the mass of Earth.

"During planet formation, small bodies similar to asteroids and comets stick together, eventually growing to Earth-size and beyond. Not all of the planets grow large enough to become giant planets like Saturn and Jupiter," Howard said. "It's natural for lots of these building blocks, the small planets, to be left over in this process."

The astronomers extrapolated from these survey data to estimate that 23 percent of sun-like stars in our galaxy host even smaller planets, the Earth-sized ones, orbiting in the hot zone close to a star. "This is the statistical fruit of years of planet-hunting work," said Marcy. "The data tell us that our galaxy, with its roughly 200 billion stars, has at least 46 billion Earth-size planets, and that's not counting Earth-size planets that orbit farther away from their stars in the habitable zone."

The findings challenge a key prediction of some theories of planet formation. Models predict a planet "desert" in the hot-zone region close to stars, or a drop in the numbers of planets with masses less than 30 times that of Earth. This desert was thought to arise because most planets form in the cool, outer region of solar systems, and only the giant planets were thought to migrate in significant numbers into the hot inner region. The new study finds a surplus of close-in, small planets where theories had predicted a scarcity.

"We are at the cusp of understanding the frequency of Earth-sized planets among celestial bodies in the solar neighborhood," said Mario R. Perez, Keck program scientist at NASA Headquarters in Washington. "This work is part of a key NASA science program and will stimulate new theories to explain the significance and impact of these findings."

NASA's Exoplanet Science Institute at the California Institute of Technology, Pasadena, Calif., manages time allocation on the Keck telescope for NASA. NASA's Jet Propulsion Laboratory, also in Pasadena, manages NASA's Exoplanet Exploration program office. More information about exoplanets and NASA's planet-finding program is at

More of the same, but we are actually getting close to a real number this time, and this number match the most optimist guess we made.

[Max™]

Anyone heard about an apparent falsified prediction from Cosmological Natural Selection recently?

Mentions in here: http://arxiv.org/PS_cache/hep-th/pdf/0612/0612185v1.pdf that a 1.6+ solar mass neutron star would pretty much screw the CNS model, not a total "it's all fucked" exactly, but at the very least, if we're right about very much with star formation, CNS needs to be retooled completely.

http://www.sciencedaily.com/releases...1027133142.htm

The researchers expected the neutron star to have roughly one and a half times the mass of the Sun. Instead, their observations revealed it to be twice as massive as the Sun. That much mass, they say, changes their understanding of a neutron star's composition. Some theoretical models postulated that, in addition to neutrons, such stars also would contain certain other exotic subatomic particles called hyperons or condensates of kaons.
"Our results rule out those ideas," Ransom said.

[Kaylia]

^
Stellar model works under so many hypothesis I'm not really surprised. However, it's always nice when they find something that destroy the current model

Spoiler: show

How the fuck do I solve the lamda in this systems? I've been trying for 2 hours and keep getting monstrosity (that also happen to be different everytime). I'm curious to see if there is any trick I'm missing, or i have to do it the hardway (evaluate every integral )
http://img683.imageshack.us/img683/2227/mathse.jpg

Is there any way to solve it easily with mathematica?

[edit]
Found a way to solve it manually after many hours of labor. I could never make it works in mathematica.



Also, fucking entropy, how does it works? I'm not even sure the equation above are correct in the first place (should be close though)

[Kryssan]

A bit late but here you go: LLNL Press Release NiF Activation

WASHINGTON, D.C. – The National Nuclear Security Administration (NNSA) and Lawrence Livermore National Laboratory (LLNL) today announced that the National Ignition Facility (NIF) recently completed its first integrated ignition experiment. In the test, the 192-beam laser system fired 1 megajoule of laser energy into its first cryogenically layered capsule, raising the drive energy by a factor of thirty over experiments previously conducted at the Omega laser at the University of Rochester. With the completion of this test, NIF is beginning its next phase of the campaign to culminate in fusion ignition tests.



Before the shot: The target is mounted in the cryogenic target positioning device. The two copper-colored arms form a shroud around the cold target to protect it until they open five seconds before a shot.
Click for high resolution image


After the shot: The remains of the target assembly.
Click for higher resolution image


“NIF is an example of what the NNSA labs do best,” said NNSA Deputy Administrator for Defense Programs Don Cook. “We are bringing together the best minds in science, engineering and technology to solve some of the nation’s greatest challenges.
With NIF, the nation has a critically important asset that supports our national security priorities, pushes the frontiers of science and discovery, and carries the potential for critical advances in energy security.”
NIF, the world’s largest and highest-energy laser system, is expected to be the first laser system to demonstrate reliable fusion ignition – the same force that powers the sun and the stars – in a laboratory environment. When NIF’s lasers fire, more than one million joules of ultraviolet energy are focused into a pencil-eraser-sized gold cylinder that contains a peppercorn-sized plastic capsule filled with the hydrogen fuel.
The experiment demonstrated the integration of the complex systems required for an ignition campaign. This target was filled with a mixture of tritium, hydrogen and deuterium tailored to enable the most comprehensive physics, a necessary step on the path to demonstrating fusion ignition. All systems operated successfully, and 26 target diagnostics participated in the shot.
“From both a system integration and from a physics point of view, this experiment was outstanding,” said Ed Moses, Director of the National Ignition Facility. “This is a great moment in the 50-year history of inertial confinement fusion. It represents significant progress in our ability to field complex experiments in support of our NNSA Stockpile Stewardship, Department of Defense, fundamental science and energy missions.”
NIF was built as a part of the NNSA’s program to ensure the safety, security and effectiveness of the nuclear weapons stockpile without underground testing. With NIF, scientists will be able to evaluate key scientific assumptions in current computer models, obtain previously unavailable data on how materials behave at temperatures and pressures like those in the center of a star, and help validate NNSA’s supercomputer simulations by comparing code predictions against laboratory observations. Other missions include advancements in fusion energy technology and enabling scientists to better understand the makeup of stars in the universe and planets both within and outside our solar system.
The experimental program to achieve fusion and energy gain, known as the National Ignition Campaign, is a partnership among LLNL, the Laboratory for Laser Energetics at University of Rochester, Los Alamos and Sandia National Laboratories, and General Atomics. Other contributors include the Massachusetts Institute of Technology, the Atomic Weapons Establishment (UK), Commissariat à l'énergie atomique (France) and many others.
Established by Congress in 2000, NNSA is a semi-autonomous agency within the U.S. Department of Energy responsible for enhancing national security through the military application of nuclear science in the nation’s national security enterprise. NNSA maintains and enhances the safety, security, reliability, and performance of the U.S. nuclear weapons stockpile without nuclear testing; reduces the global danger from weapons of mass destruction; provides the U.S. Navy with safe and effective nuclear propulsion; and responds to nuclear and radiological emergencies in the U.S. and abroad.
Founded in 1952, Lawrence Livermore National Laboratory is a national security laboratory that develops science and engineering technology and provides innovative solutions to our nation’s most important challenges. Lawrence Livermore National Laboratory is managed by Lawrence Livermore National Security, LLC for the U.S. Department of Energy’s National Nuclear Security Administration.

Interesting that none of the news agencies picked up on it. I just happened to check the site and noticed they had updated their releases. Maybe if/when they actually achieve ignition?

[BerenTebogo]

Starting to think Woozie has the right idea with the whole majoring in math thing. If Calc 2 is the hardest undergraduate math I'm excited.

[Cantih]

Don't worry, maybe in time a supercomputer's sheer calculation power could influence the quantum level to materialize one for you. :O

Or possibly, a cup of tea.

[Eliseos]

If Calc 2 is the hardest undergraduate math I'm excited.

I'm not a math major/minor, but I don't think calc2 would be the hardest undergraduate math course. Out of calc1/2/3, sure, but I would put money against it being the hardest overall.

[Shiroikage]

Calc. II was actually a fun time.

[Woozie]

I'm not a math major/minor, but I don't think calc2 would be the hardest undergraduate math course. Out of calc1/2/3, sure, but I would put money against it being the hardest overall.

Sath is a physics major. So out of the math courses he's actually required to take (calc1,2,3/diffEQ), calc 2 is usually the hardest for most people. If he was a math major things would be different.

Edit: My bad, i didn't read because I'm an idiot.

Edit 2: As a math major, the hardest class depends on what you like doing. For the students I TA, they seem to unanimously agree that advanced calc/intro analysis is the hardest undergraduate math class (which for the most part is just a higher version of calc 2, or at least it seems that way with how we teach it here). For me, advanced calc/intro analysis was insanely easy, as was every other undergraduate math course. Things didn't start getting hard until I started signing up for graduate special topics classes in group theory.

[Ferion]

Out of Calc I-IV I would definitely say I had the most trouble with Calc II. Not because it was hard, just because I thought learning so many integration techniques was completely pointless and had to force myself to study. And to be honest, since taking Calc II the only two techniques I've had to use were integration by parts and u-substitution. Had a much easier time with infinite series, despite having to memorize all the tests for convergence I thought it was pretty interesting.

Edit 2: As a math major, the hardest class depends on what you like doing. For the students I TA, they seem to unanimously agree that advanced calc/intro analysis is the hardest undergraduate math class (which for the most part is just a higher version of calc 2, or at least it seems that way with how we teach it here). For me, advanced calc/intro analysis was insanely easy, as was every other undergraduate math course. Things didn't start getting hard until I started signing up for graduate special topics classes in group theory.

Being a math major is completely different than even being a math minor at my school. I've talked to a girl who said she managed to get a minor in math without having to take a calc class beyond Calc II, which I thought was a waste. Math majors are much more focused on proof based classes rather than problem solving. I'm actually taking Advanced Calc this semester, and I'm gonna have to agree with your students Woozie. I'm having a pretty hard time with it, mostly because my professor is incredibly rigorous. She'll prove something in class and I'll have trouble understanding her method. Then I'll look at our textbook's logic for the same theorem and it'll make complete sense. The problem is the same level of rigor my professor uses in class, is the same level on her exams.

Edit: I also wouldn't really call Advanced Calc a higher version of Calc II, it could be different at your school though. We spent almost half of the semester working through proofs for convergence of sequences. We're just now getting into convergence of actual functions and delta-epsilon style proofs. The way it's looking I doubt we'll even get to spend more than a week or two on integration, which was at least half of Calc II for me.