Yeah, that's why I think "people seek more physics here" is simply false. People come here to chat. Sometimes about physics, sometimes about the site, sometimes about something totally different. And all that's fine.
It worth noting that I've seen serious physics be discussed by a few users interleaved with social fluff from a different group of users more than once.
It doesn't seem to bother anyone, and it sometimes results in cross-fertilization of the two lines of inquiry.
I suppose that if the fluff was coming many times faster than the physics it would make the serious discussion hard to follow, but that hasn't been what I've seen.
My approach has been basically what dmckee said, that if multiple conversations are interfering with one another, physics discussion gets priority, but that hasn't really been an issue
@Danu The sequence $0\to\mathbb{Z}\to\mathbb{R}\to\mathrm{U}(1)\to 0$ (as constant sheaves on $M$) is exact and applying the sheaf cohomology $H^{\bullet}(M,-)$ yields the long cohomology sequence $\dots\to H^1(M,\mathbb{R})\to H^1(M,\mathrm{U}(1))\to H^2(M,\mathbb{Z})\to H^2(M,\mathbb{R})\dots$. But due to partitions of unity, $H^n(M,\mathbb{R})$ vanishes for all $n$, so $H^1(M,\mathrm{U}(1)) = H^2(M,\mathbb{Z})$. That $H^1$ classifies bundles follows from the cocycle construction of them.
@AccidentalFourierTransform : oh good, a page that does mention physics. Pity it's from 2008.
Note this: "(Actually, this is only half of Maxwell’s equations, but the other half are a consequence of the interpretation (*) of the electromagnetic field as a curvature of a U(1) connection. Thus this purely geometric interpretation of electromagnetism has some non-trivial physical implications, for instance ruling out the possibility of (classical) magnetic monopoles.)"
@DavidZ Your response on (physics.stackexchange.com/questions/253754/…) still doesn't explain why the question is off-topic. It seems perfectly reasonable for a student (e.g.) to wonder why, if the universe is often described as finite (even only for observability reasons), it's 'boundaries' can't be used as a reference frame. The CMB, in many ways, is such a boundary, and it can be used as a reference frame. Valid question w/ valid answer.
@DilithiumMatrix I don't believe what you're saying is true at all. The question shows a complete lack of knowledge of even the basic principles of the subject area being asked about - in particular, I doubt that the asker knows enough to understand a reasonable answer. Those sorts of questions are not suitable for this site.
I could be wrong about the nature of the question, and in that case I trust the community will override my vote.
Great! @ACuriousMind @Danu , so I've been working under the GA framework for EM using constant dielectric constant (assuming non-permeable media, throughout)
This is clear, right, as the transformation between Gibbs' vectors and Clifford's algebra is straightforward
It provides a lot of niceties for the invariants, all of which take obvious and relatively simple forms
Now, the question is, when we assume nonuniform media, we can't perform a lot of the reductions
And it seems that GA in this case is mostly an ad-hoc framework to deal with subtleties like the cross-product
So, I was wondering if anyone had any resource exploring EM using GA in materials with non-uniform permittivity
by nonuniform media do you mean $\epsilon$ is a spatially varying scalar, or it's a spatially constant nontrivial rank-2 tensor, or the worst of both worlds?
@GuillermoAngeris : please ask a question on the main site. Meanwhile it sounds like you're talking my language. But don't forget that it takes two to tango, and if epsilon varies, what you've got isn't an electromagnetic field. Because c = √(1/ε0μ0) and "the curvature of light rays occurs only in spaces where the speed of light is spatially variable". It's a gravitational field.
@JohnDuffield This question is already on the main site. And, it doesn't require having a gravitational field if we make the approximation that the material itself changes the speed of light (which is mediated by non-classical processes, fine, but it's an approximation)
wild factoid: Tao recently is the 1st yr winner of a $3M millenium prize, and (so far) also appears to have said absolutely nothing )( about it in his blog or interviews
My favourite example is here mathoverflow.net/a/17906/38721 you've got your sobolev spaces, $L^p$ norms, quantum mechanics, calculus, other insane spaces, stunning
@bolbteppa Uh, where is the quantum mechanics there, and why do you think that Sobolev, L^p and calculus are worthy of being listed as distinct objects?
@yuggib oh! sorry. freudian slip. its called the breakthru prize and yes a single award is worth (a staggering) $3M ie 3x nobel, abel, or turing prizes alone
(the title is oversimplified, but hey, it is just a title)
I am currently finishing my MSc in computer science. I am interested in programming languages, especially in type systems. I got interested in research in this field and next semester I will start a PhD on the subject.
Now here is the r...
@ACuriousMind re publicity/ awareness, actually it would seem that large segments of the public are not really much aware of the "Big" science prizes eg those just mentioned by me... (not to even say anything about basic science/ math "literacy") & this chat room & SE in general has an extremely wide variance in bkgs... (part of its appeal...) compare this to eg big sports prizes eg world cup etc...
@ramsay No, but you can continuously extend $f: \mathbb{R}-\{0\}\to \mathbb{R}, x\mapsto \frac{\sin(x)}{x}$ to a function $\bar{f} : \mathbb{R}\to\mathbb{R}$ by setting $\bar{f}(0) = 0, \bar{f}(x) = f(x)$ for $x\neq 0$.
@ramsay Yes. My point is that the limit $\lim_{x\to 0}\frac{\sin(x)}{x}$ exists, which is the closest you can get for a value of that fraction at zero.
However, you might ask whether the extended function that is zero at zero and $\frac{\sin(x)}{x}$ everywhere else is differentiable at zero. That's probably a nice exercise to figure that out.
@vzn , it was a speaker who came to talk at my department. I am trying to find a general description of methods like this. Here he introduced Bloch oscillations to suppress phase shift, in conjunction with a PI control loop. I am basically looking for a starting point on understanding how this improves sensitivity.
If I get a good grasp on the idea, I want to try implementing similar ideas in other systems
