The h Bar

geocalc33

2:28 AM

@Slereah feel free to comment, answer, or edit :) math.stackexchange.com/questions/3562412/…

Novalium Company

5:52 AM

@geocalc33 I have no idea what that question means

I have learned a lot from everything. I discuss diverse topics with different people.

John Rennie

7:39 AM

We have another storm hitting the UK this weekend. That's three storms in three successive weekends. Storm Jorge.

My local store had no milk yesterday because the delivery truck got stuck in snow and couldn't reach them.

On the up side, if I drown in the floods I'm guaranteed not to get coronavirus.

Knight

@JohnRennie Flood can do nothing to you sir.

Which perfume do you use?

John Rennie

Perfume?

Knight

Yeah! Perfume spray.

Which one do you use?

Gucci? Benetton? US Polo ?

John Rennie

7:58 AM

Eau du physicist.

2

Actually mostly I do my best not to smell of anything.

Knight

Should I spray alcohol as a perfume on myslef?

@JohnRennie aha! I didn't know that you sometimes use French too

John Rennie

Alcohol evaporates very quickly so it doesn't make you smell of anything. Well, not unless you drink it, in which case it makes you smell of the ketones that are byproducts of alcohol breakdown.

But alcohol is very good at killing the bacteria on your skin, and it's those bacteria that are responsible for body odour. So alcohol is an effective deodorant.

Knight

@JohnRennie Thanks for telling me that I was searching for anti-perspirant

Can I make alcohol from home made stuffs? Or do I need to buy myself a drink?

John Rennie

8:21 AM

You can distill your own alcohol at home but that's a lot of bother and possibly illegal.

It would be simpler to just buy some Axe.

Loong

8:52 AM

@JohnRennie still selling Unilever products? ;-)

John Rennie

@Loong it was the only deodorant brand I could remember :-)

Axe is just ethanol + perfume. The active ingredient is the ethanol because it kills the bacteria. The perfume is just there to (briefly) smell nice.

At one time I experimented with using just ethanol as a deodorant, i.e. no perfume, and it worked just fine.

Loong

Axe Absolut

the best alcohol I could find at work

John Rennie

:-)

Alternatively drink the alcohol and don't worry about the smell.

(Legal disclaimer: do not drink absolute ethanol, or even 95% ethanol)

Novalium Company

9:16 AM

Coldplay - Paradise (Official Video)

►

Knight

11:07 AM

@JohnRennie That's great, what was your age at that time?

John Rennie

@Knight Mid 30s I suppose. I can't remember to be honest. It was while I was working at Unilever.

Knight

@JohnRennie Which mobile phone do you use these days?

John Rennie

@Knight OnePlus 3

Knight

@JohnRennie Don't you like Apple?

Physics Meta

0

Q: Why a bird sitting on a single wire has the same potential as the wire

I learnt that birds don't get electrocuted,because when they sit on a single wire without touching the other wire have the same potential as the wire it is sitting on .so ce there is no voltage difference ,current won't flow through the bird.but y does it have the same voltage .why won't the e...

Slereah

11:19 AM

Hello

Knight

Hi

Which perfume do you use Slereah?

@JohnRennie What Roger Waters is doing? I just read that he is supporting rebel groups of Indians? What has happened to him? Why so much interest in Politics?

thehindu.com/entertainment/…

It is said that The Hindu is a repuatble newspaper in India.

Yuvraj Singh...

@Knight leave them, everybody is behind India!

@JohnRennie hi.

Knight

@YuvrajSingh... That's the question, first he supported Assange the american con and then he supported Indian rebels, Why?

Yuvraj Singh...

11:36 AM

@Knight I do not know why he is doing it is his wish, he must have his own logic behind.

Knight

11:49 AM

@YuvrajSingh... I have a respect for him, but supporting someone like Assange or Indian rebels (I heard they did a good welcome to our President Trump by killing some Police officers on that very day) is something not right. He is acting like the way he described others in Pigs three different ones

MadSpaceMemer

2:01 PM

Can someone help me with the following task. On a path i have two trains. One start from Zero point with a high speed (given) and the other one have advantage of S meters (given) with a smaller speed. Both move with constant speed. It is to calculate the minimal required Acceleration for the first fast treen such that they do not crash . i have done this sofar

I calculated the time it is needed to crash without taking in consideration that the first train will deaccelerate. by making two equations.

How do i now find the acceleration? i tried couple of calculations but i get wrong answer from the one written in the book.

Aaron Stevens

I assume the acceleration is slowing the train down?

MadSpaceMemer

Yes it is a negative acceleration.

Aaron Stevens

Ok, so finding the time of crash when there is no acceleration isn't going to help I don't think

Although the method should be similar

@MadSpaceMemer Have you written out the equation of the position of each train as a function of time?

MadSpaceMemer

Yes.

Aaron Stevens

Ok, so then set those equal to each other

You should have an equation that is quadratic in t

MadSpaceMemer

2:09 PM

$1$ is the fast train from 0 and $2$ is the slower
So i say there is a point $x_s$ where they crash.
$x_s = v_1 .t + 0.5at^2$ = $x_s = v_2 .t + S $

Aaron Stevens

$S$ is the initial position of train 2?

MadSpaceMemer

Yes he has advantage of approx. 700 meters

Aaron Stevens

Ok good. So then now write out an expression for the collision time

MadSpaceMemer

But you have then a as varialbe

So it is equation with 2 variables t and a.

Aaron Stevens

@MadSpaceMemer Yeah, don't worry about that :) Solve for the collision time

MadSpaceMemer

2:11 PM

Ok, done that and then?

Aaron Stevens

Look at what you have. What must be true so that there is a valid solution?

MadSpaceMemer

not sure what you mean

Aaron Stevens

Does your collision time involve a square root?

MadSpaceMemer

I have $2S =264t+at^2$

Aaron Stevens

Oh, ok so now solve for $t$

Do you know how to solve for $t$?

MadSpaceMemer

2:23 PM

$t_1 ,t_2 = -264/2a \pm ((264.9 + 8a^2 s)/(a^3 .4) )^{0.5} $

Aaron Stevens

I think there is an error there

MadSpaceMemer

i think so too.

Aaron Stevens

You used some sort of calcuator?

MadSpaceMemer

What is the end point of doing this calculation?

No i just used my pen and paper

But where are you going with this?

Aaron Stevens

Well, once you have an expression for collision time you can determine what values of $a$ actually give you a valid solution

MadSpaceMemer

2:26 PM

But how do you determine them? since you have two unknown values anyways.

Aaron Stevens

Remember, for equations of the form $$At^2+Bt+C=0$$, the solution is just $$t=\frac{-B\pm\sqrt{B^2-4AC}}{2A}$$

MadSpaceMemer

Yes. I just devided throught a and used the other formel where a is 1

Well it its the same formel lol

Aaron Stevens

Ok so let's bypass this part, since it is not the main goal... what must be true in order for there to be a solution in the expression I gave

MadSpaceMemer

But I still do not get how you determine the values. I know T needs to be positive. But still does not that leave a lot of opportunities and possibilities for a

Aaron Stevens

@MadSpaceMemer I am trying to show you though

@MadSpaceMemer You are actually guaranteed to have a positive solution when a solution exists, so this isn't something we need to worry about

But what do we need to check to make sure that we actually get a real number here?

MadSpaceMemer

2:32 PM

that what under the root is positive

Aaron Stevens

@MadSpaceMemer Hey there you go :) Yes!

Technically not negative

$B^2-4AC\geq0$ is what we want

Do you see how this now puts a constraint on what your acceleration can be?

MadSpaceMemer

Yes. I am doing the equation again

ahaha

goddamn it

you are right

now i got the correct answer!

Basically the root gives a value which a needs to be smaller than in order to be real and thats the value we need to use.

Aaron Stevens

@MadSpaceMemer Yep, exactly. Good work

MadSpaceMemer

But just for the interpretation of this number. Why is it that this value exactly the one we need in order to avoid a crash?

Aaron Stevens

If the acceleration was any greater in magnitude, then the train would stop before a collision occurred

MadSpaceMemer

2:41 PM

But why would then the number be imaginary?

Aaron Stevens

Because there is no collision time anymore

If there is no collision then we can't get a valid collision time

MadSpaceMemer

Oh true. We set our equations such that t represents the time when they meet and collide at the specific point.

I understand!

Thanks!

Aaron Stevens

Good! :)

Of course, my pleasure

MadSpaceMemer

Ah one last thing, is it with this acceleration that they do not crash? so like they do not touch? or it needs to be bigger? Or is it like with this acceleration the first fast train reaches this point and halts before touching briefly? if it its like a graph, would they cut each other at point?

because with this value I got from a < value if I set this value in the root is zero but the left side is not

Aaron Stevens

@MadSpaceMemer In your case you should have gotten a > some negative value

In order to get a valid solution

MadSpaceMemer

2:54 PM

actually I have got a < Positiv value

Aaron Stevens

Hmm odd... because you originally had $x_1=v_1t+0.5at^2$

@MadSpaceMemer In your case $A=a$, $B=264$, and $C=-2S$

So $B^2-4AC=(264)^2+8aS\geq0$

MadSpaceMemer

Problably I made another mistake with the signs.

Aaron Stevens

Yes

@MadSpaceMemer Yeah, you should get $a\geq$ some negative value. And this makes sense. If $a$ is not negative enough, or even becomes positive, there will be a collision

Knight

Is it polite to ask the OP to have a look at my answer to which he has not responded for 24 hours and he has replied to someone in comments (this shows he comes online) ?

Aaron Stevens

Only when $a$ is even more negative will we not get a collision because then the first train stops before sollition

@Knight I do that sometimes. I usually just comment on the main post saying something like "Is there anything I can do to my answer to help address your question" or something like that

So it isn't a "hey pay attention to me" comment, but it shows that you want to help

geocalc33

3:11 PM

9

Q: Given a family of 2D curves, find a 3D manifold whose geodesics project to the plane curves

Below is an image of the family of 2D curves for reference. The image is arbitrary. Still trying to formulate a concise question. I know that the geodesics for flat Euclidean Space are straight lines. But I want to take these curved geodesics and tried to work backwards to determine the geometry...

general-topology differential-geometry manifolds general-relativity manifolds-with-boundary

Yuvraj Singh...

@AaronStevens hi.

Aaron Stevens

Hello

Yuvraj Singh...

@AaronStevens do you had a course in photonic during school days

?

Aaron Stevens

@YuvrajSingh... No, I did not

Yuvraj Singh...

Oh! It's OK.

Ok one more thing.

@AaronStevens

Aaron Stevens

3:23 PM

Yes?

Yuvraj Singh...

OK I am not sure at what level question is correct can light wave resonant?

I mean like standing waves.

Of sound and string.

@JohnRennie

Aaron Stevens

Yes, you can have standing EM waves. For example, they form in microwave ovens

John Rennie

@YuvrajSingh... hi :-)

Yuvraj Singh...

@JohnRennie hi sir.

@AaronStevens yes can you show up some visual or pictures.

John Rennie

Optical cavity

An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times producing standing waves for certain resonance frequencies. The standing wave patterns produced are called modes; longitudinal modes differ only in frequency while transverse modes differ for different...

Yuvraj Singh...

3:31 PM

@JohnRennie can I experiment this my room.

?

John Rennie

@YuvrajSingh... optical cavities are generally precision components, but they have to be made to a precision greater than the wavelength of light. So I doubt you could make one.

geocalc33

I need help understanding this picture from a physics perspective

is it basically diffraction of light?

Yuvraj Singh...

@JohnRennie can I use laser.

geocalc33

Can you convolute the differentiable structure of a real analytic manifold?

Slereah

3:46 PM

I guess?

Convolutions are diffeomorphisms, as far as I know

geocalc33

Why would anyone do that?

Slereah

Analysis reasons, perhaps

Aaron Stevens

@geocalc33 Looks more like just reflection off of a curved surface

geocalc33

@Slereah I wonder if you can you convolute the conformal structure of a smooth and bounded lorentzian submanifold @AaronStevens yeah I think you are right

and I wonder if there are physical implications of said convolution

Knight

@AaronStevens Should I post it on OP's question's comment section or should ping him in my answer's comment section?

@geocalc33 Hi, I saw you in Mathematics chat room.

geocalc33

3:58 PM

@Knight yeah I'm there a lot

how are you?

Knight

@geocalc33 Can you help me with understanding a the concept of stress and pressure in Fluid Mechanics?

geocalc33

@Knight probably not I'm checking my email but go ahead and ask anyway

Knight

@geocalc33 "In solids the reactions measured per unit of area are known as stresses; in the case of fluids we usually speak of pressures (negative stresses)"

What does the above statement means? Why reaction per unit area not the force per unit area? And what is negative stress?

Aaron Stevens

@Knight I usually do it on the question, unless the OP has already commented on your answer. I think you can notify people on posts that are not theirs only if they have also commented on it.

Slereah

Overall convolutional methods aren't super useful in GR because it's nonlinear

But they are fine for linearized gravity

Knight

4:08 PM

@AaronStevens I have pinged him in my answer ! should I take it back, have a look

Slereah when you said "linearized" did you mean the equations are linear or their pictorial representation is linear?

Aaron Stevens

@Knight There isn't anything wrong with it. They just probably won't get notified

Knight

@AaronStevens Why?

WHy they won't get notified?

Aaron Stevens

@Knight Because they haven't commented on your answer yet.

Knight

@AaronStevens Okay!

Aaron Stevens

I am sure the site is designed so you can't ping any user you want to on any post. They have to have commented first

If you comment on the actual question then the OP will be notified since it is the OP's post

To be honest, I VTC that question

Knight

4:11 PM

what is VTC ?

Aaron Stevens

Voted to close

or vote to close

geocalc33

@Slereah ah cool, I see. Suppose you take take the convolution of the conformal structure on a real analytic lorentzian sub-manifold and are able to linearize it with a change of the coordinate system. I think that would be cool to try

Knight

@AaronStevens Why?

Aaron Stevens

Because it is essentially just an off-topic homework and exercise problem

in my opnion

Knight

Okay

Aaron Stevens

4:13 PM

They have presented an exercise, and essentially just asked "How do I solve it"?

It is definitely more of an upper level question though, which probably explains the up votes and why it hasn't been closed

Knight

As far as my thoughts are concerned, OP actually wanted to know what's the use of those differential laws.

geocalc33

...because I don't know. Would the order of this process matter? Would one get different structures/geomtries in each case? Say in one case you first linearized the conformal structure and next you convoluted. And in another case you convoluted and then linearized...not really sure to be honest :)

Aaron Stevens

4:34 PM

@Knight Maybe? To me the way the post is worded it really just seems like they are concerned with this specific problem and how to solve it.

Knight

@AaronStevens I had the same question once therefore I understood it that way.

14

A: What is the evidence for 'billions of neutrinos pass through your body every second'?

As others have noted, the neutrinos come from the sun. Given that, there are two broad ways of estimating the flux of neutrinos: one is theoretical, and the other is experimental. The theoretical way is based on the Standard Solar Model. This is a well understood model with solid experimental ...

First time I have seen @Loong doing something on parent site.

Semiclassical

4:49 PM

@Knight the positive/negative aspect there is simply a matter of convention: stress which compresses the solid in a given direction is negative, while stress which tends to stretch the solid in a given direction (thereby placing it under tension) is taken as positive.

in fluids, by contrast, you mostly only talk about forces which would tend to compress the fluid. (e.g., atmospheric pressure acting on water in a beaker)

Knight

@Semiclassical What "reaction per unit area" signifies ?

Semiclassical

my guess is that it's the reaction force per unit area

reaction as in Newton's third law (action-reaction pairs)

not in the chemical sense

Knight

Why not the action per unit area? I mean if I compress an elastic solid, the stress would be the force that I will feel and divide it by the area

Have i got it right?

Semiclassical

in magnitude, yes, but perhaps not in direction. note that sommerfeld's previous paragraph does place this emphatically in the context of newton's third law

Knight

You're great, how do you know I asked it from Sommerfled's?

Semiclassical

4:55 PM

google :P

(I googled the phrase "In solids the reactions measured per unit of area are known as stresses")

Loong

@Knight Obligatory remark:

> A quantity defined as A/B is called ‘quotient of A by B’ or ‘A per B’, but not ‘A per unit B’.

Knight

I sometimes think of being one of 35 students in your class.

@Loong Wow! But your pasian wrote that.

Semiclassical

there's a remark that Peter Lax made, regarding how he got his fields medal: "I integrated by parts." for me, the answer to how I get my results is "I googled."

Knight

@Semiclassical But then he says the liquids are incompressible, so why to talk of compressive stresses when they cannot compress it.

@Loong Do you also have interest in movies? I saw you in the screening room.

Semiclassical

I think the point there is that those stresses would compress the fluid, were the fluid actually compressible

(also, no fluid is truly incompressible.)

Knight

5:00 PM

And why not to talk of positive stresses in fluids? Here is the paragraph

**Not so in the case of fluids. The cohesive forces in a fluid are weak, its “ultimate strength” under ordinary circumstances is exceedingly small if compared with that of solid. In other words, the resistance of fluids against tension is so small that positive stresses practically never occurs; we then prefer to deal in our equations with pressures p rather than stresses**

Why it's not becoming bold?

Semiclassical

hmm. test: bold

huh

Not so in the case of fluids. The cohesive forces in a fluid are weak, its “ultimate strength” under ordinary circumstances is exceedingly small if compared with that of solid. In other words, the resistance of fluids against tension is so small that positive stresses practically never occurs; we then prefer to deal in our equations with pressures p rather than stresses

wtf

How did you do that?

I have no idea

Do you curse? :)

I just copied and pasted what you did

JMac

5:01 PM

lol

Semiclassical

hmm. test again:

**Not so in the case of fluids. The cohesive forces in a fluid are weak, its “ultimate strength” under ordinary circumstances is exceedingly small if compared with that of solid. In other words, the resistance of fluids against tension is so small that positive stresses practically never occurs; we then prefer to deal in our equations with pressures p rather than stresses**

JMac

Not so in the case of fluids. The cohesive forces in a fluid are weak, its “ultimate strength” under ordinary circumstances is exceedingly small if compared with that of solid. In other words, the resistance of fluids against tension is so small that positive stresses practically never occurs; we then prefer to deal in our equations with pressures p rather than stresses

yeah weird

Novalium Company

helu

Knight

HAHAHAHHAH

What's happening?

Semiclassical

okay, it doesn't work if I include the extra lines

as in:

a

**a**

doesn't bold

but

Knight

5:02 PM

Okay

Not so in the case of fluids. The cohesive forces in a fluid are weak, its “ultimate strength” under ordinary circumstances is exceedingly small if compared with that of solid. In other words, the resistance of fluids against tension is so small that positive stresses practically never occurs; we then prefer to deal in our equations with pressures p rather than stresses

Semiclassical

a does

Knight

HA HA HA HA HA!

Semiclassical

huzzah

weird

Knight

Please explain me that para

Semiclassical

I think the analogy goes like this

JMac

5:03 PM

The way they define positive stress, it's tension. Fluids don't really resist tension, so talking about a positive stress on the fluid is kinda unusual and doesn't apply often. The negative stress (pressure) has much bigger effects so it's mostly what we talk about.

Semiclassical

Suppose I have a canister full of water. There's already atmospheric pressure, so if I push down on it harder or pull on one end all I'm doing is changing whether the net force is more or less positive

Novalium Company

what the hell is going on here

JMac

Well people are talking about physics I actually can understand, so that's always nice.

Knight

@Semiclassical Okay

Semiclassical

Why are compressive stresses in solids taken by convention to be negative, whereas pressures in fluids are taken to be positive ?

Knight

5:06 PM

@JMac The negative stress (pressure) has much bigger effects so it's mostly what we talk about. thats the problem. You see negative stress cannot compress it (liquids are not compressible) and positive stresses can make it flow.

Novalium Company

F = ma

Semiclassical

except, liquids are compressible. they resist compression quite strongly, but they do in fact compress

Knight

@Semiclassical Thats the dilemma here, pressure does nothing to it then also we talk about it

Novalium Company

F = ma is easily remembered as fck my as.

Semiclassical

...

moving right along

Novalium Company

5:07 PM

yeh, I is a physzuist.

JMac

@Knight Like Semiclassical mentions, real fluids actually are compressible. Just not as compressible as obvious examples like gasses and some solids. But also, the negative stress still changes how the fluid interacts with itself and other objects, even if you assume it's incompressible. Positive stress making fluids flow is a good example of how they can't really resist "positive" stresses. It barely resists at all.

Semiclassical

right

by contrast, a solid will resist both being compressed and being stretched

Knight

What does resist mean here?

Means it will not pull back on us?

Semiclassical

not push back with significant force

Knight

Just bear with me one more minute I'm making a diagram

Semiclassical

5:11 PM

also, note the bit about "ultimate strength". i take that as a reference to the fact that, if I pull on a spring hard enough, then ultimately it will deform and cease to act like a spring anymore

Novalium Company

fluid dynamics, yay

Semiclassical

so if I apply too much tension, then it stops being capable of resisting further applied force in the way it would at smaller tensions

Novalium Company

water

pipes

JMac

@Knight Have an internal reaction that oppose what is acting on it. You pull a piece of metal being held on the other end, and it will try to stop itself from being pulled. You do it with something that resists less and it stretches easier. You do it with water (somehow), and it falls apart basically right away, because it can barely resist positive stress (tension) at all.

Knight

The red thing is an elastic solid

Semiclassical

5:12 PM

for a fluid, the tension forces are so small that any virtually any applied tension will make it no longer 'stretch' but instead flow

Knight

OHO!

That's the great line Semiclassical

Semiclassical

as for why they talk about tension as giving positive stress, consider a rubber band

JMac

On more of a chemical level, the bonds basically have no problem breaking off each other, whereas a solid they want to stay in place.

Novalium Company

an actual physics discussion is taking place here. it's a miracle

Semiclassical

if you worked hard enough, you could probably talk about compressing a rubber band. but the more standard situation is that you pull on both ends

so for rubber bands, at least, it's more typical to talk in terms of tensile stress and thus take that to be positive.

Knight

5:16 PM

so when I stretch a rubber band the pull that I feel is due to restoration force or due to Newton's reaction law?

@JMac What does flow means at chemical level?

Semiclassical

main thing flow means at the chemical level is that there's no ordered structure in a fluid, whereas there is an ordered structure in a solid

JMac

@Knight Both. The band has an equal and opposite reaction because of the restoring force. If the band wasn't attached to anything, it would start moving as a whole instead of stretching.

Semiclassical

the bonding in a solid is strong enough that it'll try to retain its lattice structure if you apply an external force

Knight

please explain this

2 mins ago, by Knight

so when I stretch a rubber band the pull that I feel is due to restoration force or due to Newton's reaction law?

bolbteppa

On this topic, apparently the main (?) approach to non-equilibrium stat mech is in replacing n-particle density matrices (distribution functions) with 'partial density matrices' (partial distributions) which involve only single particle and two-particle interactions, setting up chains of eom between them, and trying to get 'statistical' concepts from these things

JMac

5:20 PM

I feel like they should have taught more mechanics of materials in high school. We barely learned anything about it at my school, and it seems so relevant to everyday physics.

Semiclassical

I'm hesitant to say that Newton's third law generates the force you feel. What I'd prefer to say is that 1) you apply the force, causing the rubber band to stretch. 2) as it stretches, it produces a restoring force to counteract that. 3) it'll continue to stretch further until said restoring force is so large that you don't pull further

Knight

@bolbteppa WHAT!

Semiclassical

at the end, though, you do end up with the forces being equal and opposite as a condition of the system being in equilbrium

non-equilibrium stat mech is hard af

Knight

you curse? ;)

Semiclassical

only with acronyms :P

(my phd adviser did a lot of work on field theory of non-equilibrium systems, specifically the Keldysh formalism. but i know virtually nothing of that myself)

Knight

5:23 PM

so in fluids there is no restoring force, ha? But I do apply a force and there is no reaction and stress is defined as "reaction per area" (following Loong) and hence the stress is zero, ha?

Semiclassical

there's not enough restoring force to keep the system from flowing

bolbteppa

"usually based on the two-point functions corresponding to excitations in the system" there you go!

Knight

@bolbteppa WHAT !

Semiclassical

yeah, though in the wiki article at least they're not using density matrices

Knight

@Semiclassical Why the positive stress is zero?

Semiclassical

5:26 PM

I wouldn't say it's zero, but it's such a small reaction force upon initially "pulling" on the fluid that it will cause the fluid to stop reacting like a spring would

at which point talking about a restoring force no longer makes sense

as an example: if I pull on a rubber band so hard that it snaps, then talking about the restoring force doesn't make much sense either :P

Knight

Okay!

Semiclassical

so the analogy would be that fluids 'snap' under tension very easily

Knight

VERY VERY THANK YOU

Semiclassical

I'm not sure how precise that analogy goes, but it seems decent enough

Knight

To me it's great

JMac

5:29 PM

@Knight This example might work? You have an open container with water and you can move one of the sides to change it's shape. As you expand an edge, the fluid won't try to pull back against you. It can only really apply a negative pressure, it can't apply a tension. The fluid will instead just flow to accommodate it instead of resisting a change in shape. I don't know if that's a great analogy.

Semiclassical

@jmac or, at least, the amount of tension it can provide is miniscule

a fluid does have surface tension, after all

JMac

The analogy kinda sucks because the water isn't really stuck to the walls anyways, but still.

Semiclassical

cohesive forces in fluids do exist, it's just that they're weak

Knight

@JMac Actually the problem was that it is too obvious that opening a container will cause the fluid to flow that I couldn't understand nothing about from it

JMac

@Semiclassical Yeah wont try to pull back against you hard.

Semiclassical

5:31 PM

I imagine one could design an experiment where fluid does indeed 'stretch' under very weak tension

Knight

I understood everything except whatever @bolbteppa has said.

@bolbteppa Can you explain me what is lie symmetry in simple words?

Semiclassical

bolbteppa's point re: what i said is just that he judges the Keldysh formalism as being in the vein of what he was saying about non-eq stat mech

Knight

@JMac @Semiclassical Thank you so much for explaining me.

Semiclassical

which is probably right, though again I can't judge

(amusingly, my adviser is listed twice in the references for the Keldysh formalism)

JMac

@Knight That's fair. In my opinion worrying about "stresses" on fluids really isn't a big deal until you really get into fluid mechanics or at least have a good foundation with mechanics of materials. If you're not already familiar with stresses, it seems to confuse things.

Semiclassical

5:35 PM

with all of the above said: it's still a bit strange that the default sign convention for solids is that compressive stress is negative. for instance, if I stack a bunch of stones on another, then surely it's compressive stress that's most significant

JMac

@Semiclassical Possibly a relic of hookes law with springs, or tensile tests or something.

I'm leaning more towards tensile tests since springs go both ways, but obviously it's all talking out my butt either way.

Semiclassical

yeah

i could also imagine it being the opposite in certain subfields

JMac

I'm just thinking of my own education and how tensile tests are like a classic introduction to stress-strain.

Semiclassical

also, if I compress a brick vertically, then it'll tend to stretch horizontally

JMac

The wrath of Poisson

Semiclassical

5:38 PM

and that does show up in rubber bands: if I stretch them laterally, then the cross-sectional area shrinks so as to keep the overall volume the same

so positive/negative stresses tend to arise hand-in-hand

i do find history questions like this fun

JMac

@Semiclassical Then there's always materials with a negative Poisson ratio...

Semiclassical

that's weird

my favorite right now is the joule-gough effect in rubber bands, though

Thermography of a Stretched and Relaxed Rubber Band

►

JMac

The Rubber Band Heat Engine

►

Pretty sure if he used that fan in the background on the other side he could even speed it up.

Semiclassical

(pull a rubber band apart rapidly, and it'll heat up to above room temp. now wait for it to come to thermal equillbrium with its environment, and release the tension. in doing so it'll cool to below room temp.)

bolbteppa

Rotations are lie symmetries

Knight

5:50 PM

@Semiclassical I know basics of Differential equations, I can solve the firs order equations. Can you tell me in simple words what is lie symmetry?

bolbteppa

It's just a continuous symmetry group

Semiclassical

not really, no.

Lie groups vs. Lie symmetry, to be clear

Knight

@bolbteppa “group”, is it the same “group” that my eyes saw during the turning of pages of abstract algebra books (I’m not kidding)

Semiclassical

yeah

but the typical groups in an abstract algebra group are finite

Knight

Group, ring and other things you know

Semiclassical

5:53 PM

i.e. there's only a finite number of elements in the group

bolbteppa

A lie group is basically a continuous symmetry group, such as the rotation group. In abstract algebra one usually studies finite (thus non-continuous) groups, like the permutation group, or say 'discrete rotations' like rotations of a triangle so that you end up with triangle in the same position all the time

Semiclassical

a Lie group has infinitely many such elements, with these elements being parametrized by some manifold

Knight

So how does it help to solve a differential equation which is totally a part of Calculus (or Analysis, I don’t Which one is correct)

Semiclassical

I think the logic is the other way around: If you consider the set of Lie symmetries of a given differential equation, then those symmetries form a Lie group.

but Lie groups can arise in other ways as well

Knight

But I read that differential equations deal with functions, don’t they?

And group is something like a space, I mean a collection like thing you know..

.....

Semiclassical

5:59 PM

I think an example goes like this. suppose you have a DE like y'=f(y). in that case, if y=g(x) is a solution, then so is y=g(x+a) for any a

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