@Mithrandir24601 yup

"ignore all torques"

"how am I supposed to know that?"

"the problem cannot be solved otherwise"

@0ßelö7 Wonderful justification, right? :P

@Sid fluid mechanics

the professor just started rambling about laminar flow, external flow, and other stuff and I really have no clue what's going on or what his pictures are supposed to mean

and he keeps telling us how easy the class is compared to the graduate version

I'm taking three graduate classes and they're nowhere as hard as that class

@Sid I recently saw this in the project over summer - people spent years assuming they were measuring one fidelity because it was easy to calculate, then a few months ago, a paper came out showing that it was the wrong fidelity :/

@0ßelö7 laminar flow isn't so bad as it's at least it's the name for a bunch of assumptions and is at least physically reasonable

@MathAminPhysics Yes.

Because each point has a neighborhood diffeomorphic to $\Bbb R^3$

@MathAminPhysics Because you can e.g. use the three Euler angles as local coordinates

What's annoying is when they give you a bunch of assumptions that make no sense, use that to come up with an answer, then say that this was proved wrong over 30 years ago :/ Having said that, making the right assumptions is a big part of physics and often what can make it hard

@Mithrandir24601 If a math professor taught the way some engineering professors taught, they would be shamed. It's not like this works for the students either

Unless you get more specific what you don't understand about SO(3) being a 3-manifold, it's difficult for us to tell you something more helpful

It's some weird form of academic hazing, probably because people in the nuclear business can kill many people if they mess up

@ACuriousMind That's actually a really poor proof, imo. It's better to argue that $\mathrm{O}(n)$ is a manifold, which it is because it's a preimage.

Then $\mathrm{SO}(n)$ is a closed submanifold.

@0ßelö7 The average physicist will not know the theorem that regular preimages are submanifolds, so when I'm asked about whether something is a manifold in a physics chat, I will first respond with the way the average physicist would "show" that.

Of course you can imagine I actually hate using coordinates ;P

I gave you the formal proof

@MathAminPhysics In that case, @0ßelö7 has given the correct hint/answer

@ACuriousMind In my mind you are the average physicist

certainly the physicist I have interacted with the most

@0ßelö7 I...am not sure how to react to that :D

@ACuriousMind Ah, your programming wasn't prepared for that?

@0ßelö7 You think the average physicist is an AI?

Hmm

Or that I am an AI intended to model the average physicist?

@ACuriousMind That sounds plausible.

@ACuriousMind I bought a book for \$1.97 today, not even you can argue with that!

@0ßelö7 A completely new one?! :o

@Sid used

@ACuriousMind Should I read ASOIAF or will I become bitter like all those who have read it?

@0ßelö7 What is an average physicist? ACM seems to be more of a 'mathematical physicist' than a 'physicist' though

@0ßelö7 That's still remarkably cheap. I got a used one in Physics for 6$

@Mithrandir24601 Nothing against physicists, but mathematicians have a tendency to vastly underestimate how much they know/care about math

@0ßelö7 Do you enjoy reading fantasy books?

I have observed this many times

@ACuriousMind Who doesn't?

@Blue Agreed

@0ßelö7 I don't recall you being a fantasy reader, that's all

Mathematical physicist means something different to me

But, yeah, if you like fantasy ASOIAF is not a bad read

@ACuriousMind I haven't read a fiction book in a while, true. Been busy reading other things

Like those god damn sermons in my literature class

@Blue Actually, the seminar of my group is called "physical mathematics" because "mathematical physics" was already taken...

@Mithrandir24601 speaking of fluids,

We study the long-time behavior of solutions to the three-dimensional incompressible Navier-Stokes equations with periodic boundary conditions. The body forces decay in time either exponentially or algebraically. We establish the asymptotic expansions of Foias-Saut-type for all Leray-Hopf weak solutions.

cool sounding talk on Thursday

If the force has an asymptotic expansion, as time tends to infinity, in terms of exponential functions or negative-power functions, then any weak solution admits an asymptotic expansion of the same type. Moreover, when the force's expansion holds in Gevrey spaces, which have much stronger norms than the Sobolev spaces, then so does the solution's expansion. This extends the previous results of Foias and Saut for the case of potential forces in Sobolev spaces.

@0ßelö7 hmm... You might be thinking of what I know of as an applied mathematician?

@Mithrandir24601 No

@0ßelö7 Um... you are a Nuclear Engineer?

@Blue I never said that

@Sid I've been paid for engineering and mathematical physics, so it's anyone's guess

@Blue It does, but it isn't what I thought it would be

@Mithrandir24601 I think he's thinking more of the rigorous analysis people like Glimm and Jaffe, while my sort of mathematical physics is closer to the not-entirely-rigorous and more algebraic work of people like Witten, Weyl or Nahm

@ACuriousMind I was thinking about Reed and Simon actually

Glimm and Jaffe is too specialized

Yeah, same category as G/J for me

@0ßelö7 I know the feeling

@ACuriousMind Oh and GR of course :P

?

@EmilioPisanty I am writing a talk on heat flow, @ACuriousMind can confirm it has many applications to GDP

@0ßelö7 GDP as in the econometric thing?

@EmilioPisanty I don't see entirely how that's related to what I said, but "heh :P" anyway.

GDP as in useful applications that grow the economy

analysis is often called applied math in Europe

@0ßelö7 Ah, you finally admit GDP is a joke, very good!

@0ßelö7 "applied"?

@ACuriousMind No.

@EmilioPisanty blame the Europeans

analysis is the idlest of daydream fantasies

@EmilioPisanty Really?

More so than category or model theory? Infinity topoi?

@0ßelö7 well, not the idlest

@EmilioPisanty I like how I have applied math books that are still completely abstract

Kato is a good example

@0ßelö7 perturbation theory for linear operators?

people call that "applied"?

yes

that's preposterous

@EmilioPisanty it has a lot of wisdom in it, even if you're not perturbing things

they should be sent to mechanical shop class to build things with their own hands and see what the real world looks like

It's definitely on the applied side of pure math

so.... it's pure math, then

@EmilioPisanty Applied pure math

@0ßelö7 as opposed to the rest of applied math that only applies non-pure math?

amazon.com/gp/product/0387908455/…

See, applied math. Applied to PDE.

My laptop ran out of power and the photo I took is a bit blurry is the shorthand for a partial derivative $\frac{\partial \phi}{\partial x^\mu}$ equal to $\phi,_\mu ,$

@0ßelö7 that's like saying your work has applications in the study of finite fields

@EmilioPisanty I am joking

A jest, comrade

@0ßelö7 I'm not making fun of you

I'm making fun of the weirdos at Springer who thought 'applications to PDEs' make things 'applied math'

@EmilioPisanty I wasn't kidding when I said that many consider analysis of PDEs to be applied math.

@0ßelö7 I believe you

I still think it's preposterous

but here, have another cartoon

@EmilioPisanty from one of the books useful for my research:

@EmilioPisanty This is very good.

@BalarkaSen yeah, I'm a newly-minted mathwithbaddrawings fan

@0ßelö7 Bahahaha! That's a good one

@Mithrandir24601 it's applied math, I swear

ah, some people

@dmckee do authors get more money if they write some shitty intro chapter and then slap "no experience in X needed" on the back

@0ßelö7 authors get more money if more people buy the book. So, presumably, yes.

@0ßelö7 Authors of textbooks don't get enough money to matter. Look to other incentives to understand their motivation.

@EmilioPisanty I guarantee the people who read this book are very familiar with Riemannian geometry

writing 5 pages about it does not make it appeal to a larger audience

@EmilioPisanty It is typical for a good selling textbook to net an author a few thousand dollars a year for a few years and then trial off to nothing. A so-so selling text might generate enough to take your SO out to a fine restaurant once a year for a few years.

@dmckee oh, I'm aware of that.

I suspect that these chapters are genuine attempts to make the book more suitable for use the in the classroom because having your book adopted for a course lets you know the ffort was worth it in the grand scheme of things.

The extra chapter might make an extra person but the book

Ego service.

I said nonnegative, not nonnegligible =P

@dmckee Then it would make sense for the authors to upload a copy to libgen (serves better their other purposes)

@lılostafa Most books are on libgen anyway

The worst thing an author can do is publish under Elsevier

@lılostafa A published book gets you tenure. A manuscript uploaded to some server gets you .squat with the tenure committee.

@0ßelö7 I would suspect that that kind of chapter is most often there just to fix notation

I really want Reed and Simon but I can't justify the $640 price for the set

@EmilioPisanty I agree, but then why does the back cover say that the intro chapter serves as complete background

Editor's liberty?

@0ßelö7 plausible explanation

@0ßelö7 is it available on libgen?

@lılostafa yes

I have a physical copy though because the book is fundamental for my field

@0ßelö7 Then why not print it yourself?

@0ßelö7 ah ok

@lılostafa You're the one who brought up libgen.

@EmilioPisanty I think of it like this. If someone has no background in Riemannian geometry, why on Earth would they buy a book about optimal Sobolev inequalities on manifolds? It's silly.

And, the introduction references textbooks on Riemannian geometry many times because it's not possible to prove everything he needs in that space. So it's not self-contained at all.

@0ßelö7 it's the editor that said it's self-contained, not the author

From what you've said

@EmilioPisanty I guess. It's not like anyone signed their name on the back cover

@0ßelö7 I know it's not ideal but I guess you could go used from Amazon :p

@CooperCape what?

I have the book, people

oh right lel

oopsie

scrap that

Sigh, when you spend over an hour on a math problem only to realize that you misread the plus sign as a minus sign

@SirCumference Excellent!

Must have been a fabulous experience, right? :P

@Sid Unfortunately a very common experience for me :P

Finding out that the problem is actually much easier to solve than you thought

@Sid I have an interesting problem.

Speak it out, young man. :P

Does any energy get stored due to tension?

You could probably think of Elastic Energy and stuff like that

@Sid What is the formula for that?

imgur.com/a/k52Ql

@Sid I have solved the entire question.

However, conservation of energy doesn't work when I consider the block of mass m.

Well... you don't need Elastic Energy for that problem

@Sid The results are: $\dfrac{\sqrt{50gl}}{3}$ towards left

Heavy ball $\dfrac{\sqrt{2gl}}{3}$

@Sid Wait I am coming to it.

Then using, conservation of mechanical energy for larger ball $l/9$ is the height it reaches.

@Sid All these answers are correct but when I apply conservation of mechanical energy to the lighter block, I get a height greater than $2l$(the diameter) and I wonder what's wrong?

So @Sid, I think that I am unable to notice some other mechanical energy.

Huh... weird. If one of them works, the second should also work..

If anyone else has any contribution to make, please do so :).

@Sid Yes, exactly!

Well then, I looked up the solution and it used the fact that minimum velocity for vertical circle completion is $\sqrt{5gl}$ and the velocity we have is (only very slight slightly) greater than that, so the ball executes verticle circular motion and hence maximum height it reaches is $2l$ but why does my method not work? The solution doesn't answer that.

slightly*

@Abcd What I have understood is that, you converted the whole Kinetic Energy to Potential Energy, right?

@Sid yes.

@Sid Which velocity?

The Velocity of the lighter block?

@Sid I am at rest xD

@Sid $\dfrac{5\sqrt{2gl}}{3}$

Wait, what? You wrote that the velocity of heavier ball is that.

@Sid Edited.

@Sid yes.'

Okay.

Obviously, the string can't be greater than 2l, right?

@Abcd you there?

One of my professors just said doubt

I'm so done with life

@0ßelö7 Indian Professor?

No

@EmilioPisanty more applied math

amazon.com/…

@0ßelö7 Reminds me of another text we did not mention, Pedersen's Analysis Now, lol.

@Jasper I don't think one needs to know all of the analysis books