@Danu Says the guy who answers QFT questions ;)

Once again, I am mystified by a statement in Reed & Simon.

After proving that the compactness of a space is equivalent to every net having a convergent subnet (a generalization of the usual Bolzano-Weierstrass theorem on $\mathbb{R}$, if I'm not mistaken), they state the following:

Example 1: The unit ball in $\ell_2$ is not compact in the metric topology. No subset of a sequence of orthonormal elements can converge

Is there any way anyone can enlighten me as to what this means?

Well, the space of sequences is infinite-dimensional

$\ell_2$ is the 'discrete version of $L^2(\mathbb{C})$' (i.e. a Hilbert space)

Okay..

So, if you look at the sequence of its basis elements it goes: $(1,0,0,\dots),(0,1,0,\dots),(0,0,1,0,\dots),\dots$

right

so it never converges

Surely, this sequence of sequences never converges

awesome

okay

and what about a finite dimensional analog of $\ell_2$? (what is this called/does it exist?)

can we construct an infinite sequence there which does not converge?

@Danu Hmm...since all finite-dimensional vector spaces of the same dimension are isomorphic, and the unit ball in $\mathbb{R}^n$ is compact, the unit ball in all finite-dimensional vector spaces will be compact

or rather, has no convergent subset

Oh, are they? Nice haha

In $\mathbb{R}^n$, compactness means being closed and bounded, which the unit ball is.

I feel like I lack so much knowledge, it ain't even funny no more

yeah, I know that for $\mathbb{R}^n$

but not that same dimension = isomorphic

The isomorphism is "obvious": Take the $n$ basis vectors of your space and send them onto the standard basis of $\mathbb{R}^n$.

It is clear at least that the basis element argument cannot work with finitely many dimensions because it ends up being cyclic and even if you 'perturb' it so it doesn't actually repeat itself you do end up getting infinitely many infinitely close elements of the sequence

oh yeah

Sorry - I still associate isomorphisms with iso-metries which are, I think, more difficult generally

but a bicontinuous bijection isn't that difficult, I guess (to set up)

@Danu That's true, and the reason why vector spaces are boring ;)

Do you mean finite-dimensional ones?

Yeah, but even for the infinite-dimensional ones, the Hilbert spaces at least are also relatively boring: If they have a basis indexed by a set $B$, then they are isometrically isomorphic to the space of sequences $l^2(B)$ (see Wiki).

I saw the proof of that statement in R&S too

So, even in the infinite-dim case, we kinda have that the spaces of same "dimensions" (rather, cardinality), are the same

only if they have a countable dense set though

Not that I don't absolutely love the both of you, <3, but this kind of chat does seem better suited for a separate chat room given that it's been going on for weeks

How can one claim to be doing diffusive shock acceleration without actually accounting for diffusion?

@Jim If you think it shouldn't be here... I honestly prefer having some chat going on rather than just silence (see also my extended discussions on chess with @Phonon)

(not trying to say you're wrong)

Ahh, your filling the silence. Since I hate libraries, I must say, carry on then

@KyleKanos Um...by not knowing what they are talking about? :P

The claim In order to track the evolution of the electron distribution in the downstream we follow the method of <someone>, where the electrons are assumed frozen to the flow (i.e. diffusion is neglected)

I'm not sure I buy it right now. I'm going to have to go and read <someone>'s paper

I've not really any expertise there, but Wiki says that any kind of Fermi acceleration might be (erroneously) called "diffusive shock acceleration"

$\partial_t\psi+\mathbf u\cdot\nabla\psi = \kappa\nabla^2\psi+p\left(\nabla\cdot\mathbf u\right)\partial_p\psi$ is the general transport equation used in diffusive shock acceleration

They took $\kappa=0$, basically

@ACuriousMind Diffusive shock acceleration is the mathematical model to the physical model of Fermi acceleration

It's more of DSA is FA but FA is not necessarily DSA type relation

Ahhh...and they're just throwing away the diffusion term and still say they're doing DSA. That sounds...odd

(Random fact: DSA is also the abbreviation for a "well-known" German P'n'P RPG)

Definitely odd....but in reading the <someone>'s paper, I hope to figure out why they make this assumption

Let's drop the politeness here. Which paper is this? I'm curious now too

@ACuriousMind do you mean PvP?

Duffy 1995

Sorry that's the old one

arxiv.org/abs/1409.4068

That's the new one

@Danu No :D P'n'P = "Pen and Paper", i.e doing it the old-fashioned way by rolling dice and shouting at each other ;)

OH haha

So DSA = some form of Dungeons & Dragons?

@KyleKanos Yes, it's "The Dark Eye" in its English version, but it is originally German and was more - or at least equally - popular than D&D here

Das Dunkle Auge?

no

what's the S

Yours would be the literal translation of the English indeed, but it's "Das Schwarze Auge"

ah

The Black Eye didn't seem to appeal to English speakers well, I guess :P

Yeah, The Black Eye sounds like a boxing movie

Hmm, it seems like the argument is that since SNR 1987 is still in the free expansion phase, the ejecta is being pushed faster & further than the diffusion rate. That it's not until the remnant ages into the Sedov phase that the diffusion becomes necessary.

I think I'll need to think about this some more.

hi peeps

hi

hi

anyone saw Ben's new question? physics.stackexchange.com/questions/135716/… :))

it is funny^^

@ACuriousMind don't tell me you forgot to apply for your masters... or has it started already?

Master's only start in October in Germany

(the academic year in general)

@Phonon Why would you think I forgot to apply? Don't worry, all is well (though, due to some technicalities, I might only formally be studying as a master in the coming summer term)

I'm currently unoccupied by academic matters though - sweet, free time :)

ahh

...my courses already on way... been a week now

nice then, enjoy the **** out of the remaining days :D

@Danu then you don't have an excuse not to play chess these days :D how's it going btw?

@Phonon Thanks, I will :) (It's still about a month before it's back to regular courses)

@ACuriousMind (technicalities).. what happened man?

@Phonon The dreaded lab courses we have to take have a idiotic booking system that prevented my team from booking and completing all the required ones this semester

And since these are required, you don't get your BSc until they are done

Lol, of course the lab courses! I only took a single one, and broke four things in a few weeks

But it's not really a problem, they do not care what you are studying, you can visit (and take exams) in the master courses no matter what.

@Danu If only we had been to fault for breaking something, but it happened twice that we arrived, worked for some hours only to find out it had been broken all along

My penchant for theory may in not a small part be influenced by the terrible organisation of these courses.

On an unrelated note: I second @Jim in asking Is this a joke?.

@ACuriousMind thank you

I mean sure, we all know the sun's energy grabs the clouds, but it's kind of a taboo thing to outright say it

@ACuriousMind sry was afk for a bit, ah ok I see then, c'mon guys that's nothing...I have 5 hours of lab per week LOL (starting with transmission electron microscopy...)

but good to hear you're still admissible to exams and all

@Phonon I'm not sure I could deal with 5 hours of lab every week :D

@ACuriousMind same...

that depends, teaching labs or are you the student?

@ACuriousMind btw any new fav comics? :) give give

I'm the student Jim

that's awful

the guy teaching almost fell asleep talking today...

I love teaching my labs. Students say the darndest things

:DD

"Mr. TA, I can't do this problem, my calculator isn't powerful enough"

hahahaahha :DD stop it

@Phonon None I could remember right away. But I'm better at throwing them as irrelevant comments into ongoing discussions anyway ;)

@ACuriousMind :D ok, yeah

@Jim Well, the TA aren't always in top form either ;)

I had one run out one hour before the end of the session after shouting "Oh god, my train!"

hahaha

:DDDDD

Another was like "I hope you guys know what to do, because I'm too hungover right now to remember".

Yes, that happens

At least that one gave good grades

xD

"wait, how am I supposed to find the slope if all I'm given is a straight line on the graph?"

My response: I'm going to let you think about what you just said

That's just...priceless

@Jim: What semester are these students in?

They were first year physics students, some were 2nd or 3rd year

But this was halfway through the year

"Sir, my oscilloscope isn't showing me anything" "Is it turned on?" "No, but I thought the measurement powered it" "Yes, that's why they provide a giant, useless ON button and a power cord"

It didn't happen with oscilloscopes, but I have to admit that I have overlooked more or less obvious buttons like "ON" or "REPEAT" or something like that multiple times

Something about studying does not prepare you for noticing buttons, it seems

Well, enough of this reminiscing, I'm off for most of the rest of the day. Ciao

@Jim Cya

hahahah Jim :DDD good ones

cya man

@Jim Ah, how I love good old theory classes, where calculators aren't ever allowed :)

What is the name of the phenomenon where you illuminate a film at varying incidence angles, until at some angle the light couples and makes surface plasmons on the film?

You mean SPR surface plasmon resonance??

ahh, yes, thank you @pho

@Phonon

np

Know any good texts on it? Jackson, Griffiths, and Hecht don't seem to have anything

I've heard Plasmonics: applications gives a good intro to it, with further advanced discussions, springer.com/materials/optical+%26+electronic+materials/book/…

other useful links: iopscience.iop.org/1367-2630/10/10/105001 and astbury.leeds.ac.uk/facil/SPR/spr_intro2004.htm

Ummm....what: physics.stackexchange.com/review/suggested-edits/55585

Actually, I was talking about the fact that someone actually approved this edit

Fortunately BMS & I are rational people and said no

Yeah, maybe

It's also interesting to know that I've rejected over 25% of the edits proposed that I've reviewed

physics.stackexchange.com/review/suggested-edits/51703

You need to check your last reviewed suggested edit

(the above link is for one of your last reviewed edits)

Then click the "(more)" button

You've voted on 216 edits and rejected 40 of them

Whoops

I'm very active in reviewing

#2 in close votes (by 600 votes!)

Hahaha

npr.org/blogs/health/2014/09/16/343539024/…

Might be worth the quick read

Different fields though

Medical vs Physics

Someone told me that to get a Professorship at a PhD granting institute, 3 post-docs actually looks good

@ChrisWhite If they're talking about a faculty position at a PhD granting institute, that might be true. If they're talking about any university, they're probably wrong

I think our faculty has one guy making 6 figures

See ya!

@KyleKanos Yeah! The review queue doing what it is supposed to do!