|
The Awesome Science Thread (pg. 20)
|
View this Thread in Original format
| Halcyon+On+On |
| Are... Are you from my dreams? |
|
|
| zGoogleman |
| quote: | Originally posted by Halcyon+On+On
Are... Are you from my dreams? |
I might be...you ing pedophile. |
|
|
| Halcyon+On+On |
| It's nice to have fans. |
|
|
| Acton |
I already had a good idea of the Earth to Mars distance, but I had no idea that GPS satellites were that far out.
I guess it makes sense to have them that far out if they are in geostationary orbits, though. |
|
|
| margaux8 |
| Amazing! I learned a lot from here :) Keep sharing guys :) |
|
|
| looom |
| quote: | Originally posted by Acton
I already had a good idea of the Earth to Mars distance, but I had no idea that GPS satellites were that far out.
I guess it makes sense to have them that far out if they are in geostationary orbits, though. |
I did a quick calculation, geo stationaries are roughly 36k km away, seems so funny that at that distance the 2nd cosmic speed still applies - I should suit up, get into outer space and leave the ship at 35k km off the earth, I wonder, will the gravity pull me back in :D |
|
|
| zGoogleman |
| quote: | Originally posted by Halcyon+On+On
It's nice to have fans. |
Are you only talking to me cause your wife told you to be nice to me? |
|
|
| Lagrangian |
Amazing how the drama of mathematics unfolds. At first, most progress is done quietly and in solitude; one becomes deluded at times, connections and patterns everywhere; distractions and hardship are a given. Slowly, but surely, 'so close' you tell yourself as you plod away through pages of proof. Everything builds up to that moment of divine intervention--the solution is clear and within reach--everything else takes a back seat.
| quote: | On April 17, a paper arrived in the inbox of Annals of Mathematics, one of the discipline’s preeminent journals. Written by a mathematician virtually unknown to the experts in his field — a 50-something lecturer at the University of New Hampshire named Yitang Zhang — the paper claimed to have taken a huge step forward in understanding one of mathematics’ oldest problems, the twin primes conjecture.
Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic’s current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track. |
https://www.simonsfoundation.org/fe...-the-prime-gap/
Excerpts: "Prime numbers — those that have no factors other than 1 and themselves — are the atoms of arithmetic and have fascinated mathematicians since the time of Euclid, who proved more than 2,000 years ago that there are infinitely many of them.
Because prime numbers are fundamentally connected with multiplication, understanding their additive properties can be tricky. Some of the oldest unsolved problems in mathematics concern basic questions about primes and addition, such as the twin primes conjecture, which proposes that there are infinitely many pairs of primes that differ by only 2, and the Goldbach conjecture, which proposes that every even number is the sum of two primes. (By an astonishing coincidence, a weaker version of this latter question was settled in a paper posted online by Harald Helfgott of École Normale Supérieure in Paris while Zhang was delivering his Harvard lecture.)
Prime numbers are abundant at the beginning of the number line, but they grow much sparser among large numbers. Of the first 10 numbers, for example, 40 percent are prime — 2, 3, 5 and 7 — but among 10-digit numbers, only about 4 percent are prime. For over a century, mathematicians have understood how the primes taper off on average: Among large numbers, the expected gap between prime numbers is approximately 2.3 times the number of digits; so, for example, among 100-digit numbers, the expected gap between primes is about 230.
But that’s just on average. Primes are often much closer together than the average predicts, or much farther apart. In particular, “twin” primes often crop up — pairs such as 3 and 5, or 11 and 13, that differ by only 2. And while such pairs get rarer among larger numbers, twin primes never seem to disappear completely (the largest pair discovered so far is 3,756,801,695,685 x 2666,669 – 1 and 3,756,801,695,685 x 2666,669 + 1).
For hundreds of years, mathematicians have speculated that there are infinitely many twin prime pairs. In 1849, French mathematician Alphonse de Polignac extended this conjecture to the idea that there should be infinitely many prime pairs for any possible finite gap, not just 2.
Since that time, the intrinsic appeal of these conjectures has given them the status of a mathematical holy grail, even though they have no known applications. But despite many efforts at proving them, mathematicians weren’t able to rule out the possibility that the gaps between primes grow and grow, eventually exceeding any particular bound.
Now Zhang has broken through this barrier. His paper shows that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N. No matter how far you go into the deserts of the truly gargantuan prime numbers — no matter how sparse the primes become — you will keep finding prime pairs that differ by less than 70 million.
The result is “astounding,” said Daniel Goldston, a number theorist at San Jose State University. “It’s one of those problems you weren’t sure people would ever be able to solve.” |
|
|
| Lagrangian |
I'm taking a free MOOC from U Maryland on Quantum Mechanics. This week we read bout the geometric adiabatic process; adhering to the time-dependent Hamiltonian: when an electrically charged particle is affected by a time-dependent electromagnetic field.
| quote: | | The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. |
http://en.wikipedia.org/wiki/Aharonov–Bohm_effect
The particle orbits through energies in a geometric phase, like a sphere or torus, under slow perturbations - solving a time-dependent Schrodinger equation under the assumption of gradually changing conditions in the system at hand.
http://en.wikipedia.org/wiki/Adiabatic_process_(quantum_mechanics)
| quote: | | An orbital structure is the space in an atom that’s occupied by an electron. But when describing these super-microscopic properties of matter, scientists have had to rely on wave functions — a mathematical way of describing the fuzzy quantum states of particles, namely how they behave in both space and time. Typically, quantum physicists use formulas like the Schrödinger equation to describe these states, often coming up with complex numbers and fancy graphs. |
| quote: | The First Image Ever of a Hydrogen Atom's Orbital Structure
What you’re looking at is the first direct observation of an atom’s electron orbital — an atom's actual wave function! To capture the image, researchers utilized a new quantum microscope — an incredible new device that literally allows scientists to gaze into the quantum realm. |
http://io9.com/the-first-image-ever...struc-509684901 |
|
|
|
|
