The h Bar

bolbteppa

16:00

okay thanks man

ACuriousMind

@Danu What's the $*$. Dual?

Danu

Yeah

I have no intuition whatsoever for the dual of $\mathbb{Z}_p$ :P

ACuriousMind

Which dual

Danu

And it's not been introduced before, so it should be purely from cyclicity

Algebraic dual

ACuriousMind

Groups can have more than one

Danu

16:01

Ohhhh wait a second!!

ACuriousMind

Algebraic dual doesn't tell me uniquely what it's supposed to be, either

Danu

I think what may be causing the confusion is that $*$ may represent "invertible elements of" instead of "dual" here

Urgh, damn you mathematicians and your notation

ACuriousMind

The unit group of a field is usually ${}^\times$, not ${}^*$.

Danu

Well, Vinberg used that notation before

a lot

I should've rememebered

ACuriousMind

Sigh...but he denotes the dual of modules/vector spaces by ${}^*$ as well?

Danu

16:03

Plus I think Leeb also used $\mathbb{R}^*$ for $\mathbb{R}\setminus\{0\}$

@ACuriousMind Not @ modules yet so I hope not

Yeah so it means "the multiplicative group of" here

I'm sure now

ACuriousMind

It has to, because a "dual group" is not defined in general

Danu

Still not quite sure why it has index 2

I'm trying to think about cosets

user54412

@Danu Um, count elements?

Danu

@ChrisWhite But the author presents it as if it should follow immediately from cyclicity

user54412

@Danu Imagine a circle 0 -> 1 -> ... -> (p-1) -> 0

user54412

16:09

we eliminate 0 to get your "dual" :P

user54412

then we take every other element

Danu

And then the second half doubles over the first

user54412

hmm, I think my words aren't conveying the image in my head

Danu

Right? I think I see it but it's not a very nice argument IMO

and it doesn't really involve cyclicity only

ACuriousMind

@Danu Cyclicity means all elements are the power of one generator. They're squares if the power is even, they differ from a square by the generator if the power is odd

Danu

16:10

@ACuriousMind Now that's good

ACuriousMind

Hence there are two cosets - the even powers, and the odd powers.

Danu

Yes, very nice. Addition of integers

of course

ManishEarth

@Waffle'sCrazyPeanut Actually I suck at Hindi. Remember, only came hear a couple of years ago

Marathi I know well

my hindi is probably only slightly better than yours

Danu

Addition of integers is my favorite group structure thingy

Before I'd ever heard about groups, I already felt something was going on there

and that it was the same as e.g. multiplying even/odd functions (hence the name, of course)

ACuriousMind

@Danu "something is going on here" is very often the beginning of finding algebraic structures where you don't expect them ;)

Danu

16:16

I don't have many of those moments haha

user54412

@ACuriousMind that phrase also describes the feeling you get reading the wiki articles for all the things in the xkcd that @tpg2114 distracted me with

John Rennie

16:34

@user929304 I've been keeping an eye on the question since I saw you'd put a bounty on it (thanks by the way :-). The answers are basically saying that the singularity isn't part of the spacetime, which is what I should have anticipated.

I read yess' answer, decided I didn't understand it so I read it again and decided I still didn't understand it. I'll have to put some more effort in.

@ManishEarth Are you from Maharashtra?

The only place in India I have visited is Pune.

user54412

@JohnRennie I think there are a number of good points in that answer, though it is a bit stream-of-consciousness-y; section headers wouldn't go amiss.

user54412

If you want to think about weird spacetimes, that answer alludes to one in passing: one in which all geodesics are complete, but some timelike paths aren't, so you can reach a singularity with a finite rocket.

tpg2114

@ChrisWhite Kentucky meat showers sounds like some really disturbing sexual fetish... The actual answer is still pretty gross though.

user54412

@tpg2114 I didn't read that one yet -- maybe later when it's not lunchtime

Danu

@tpg2114 Nom nom nom

John Rennie

16:42

@tpg2114 What have I been missing?

user54412

I also want to add a third axis -- money spent investigating

tpg2114

At the bottom left: The mystery of why, when I know I needed to be asleep an hour ago, I decide it's a good time to read through every Wikipedia article in the categories 'Out-of-place artifacts', 'Earth mysteries', 'Anomalous weather', and 'List of people who disappeared mysteriously'.

@ChrisWhite Better do that in log scale. Otherwise Oak Island will be really far away from the rest

I found the "Why I keep putting ice cream back in the fridge instead of the freezer" wikipedia page lacking though...

user54412

apparently Randall Munroe and I were both recently distracted by the same out-of-place artifacts article

John Rennie

Ah yes. XKCD is one of my Sunday morning treats.

user54412

I got there by linking from quantum interpretations, I think

tpg2114

16:46

@JohnRennie Oh, I'm sorry for pre-empting your Sunday routine!

John Rennie

@tpg2114 Now I'll have to resist Googling all the items for two days! :-)

tpg2114

@JohnRennie I spent like 2 hours reading wikipedia articles this morning! I stopped to do some real work

Stan Shunpike

@JohnRennie hey John!

John Rennie

I did Google the Kentucky Meat Shower though. I wonder if the chap who tasted the meat and pronounced it mutton knew it was buzzard vomit.

tpg2114

But my real work right now is typing in 228 chemical reactions for a detailed mechanism... so I'm still taking breaks

Jimnosperm

16:48

It's obvious Carly Simon was singing about me

John Rennie

@StanShunpike Hi Stan

tpg2114

@JohnRennie And/or had really bad nightmares in between the buzzard vomit and infant human lung tissue ideas...

John Rennie

I've eaten lung tissue, and very nice it was too.

2

tpg2114

As have I, but I can't say it was from baby humans... at least I hope not anyway.

John Rennie

@tpg2114 :-) No. I'm fairly certain it was sheep's lung.

Stan Shunpike

16:50

@JohnRennie So I never really paid much attention to orbital mechanics until you mentioned they were difficult. For some silly reason, I thought they might be simple because it just involves two objects right? For insfance, the earth and the moon or the earth and a satellite. I didn't quite get a sense from you why physically orbital mechanics presents such a tricky issue.

John Rennie

For all you non-Scots, I am of course referring to haggis.

tpg2114

Yeah, that's the form I had it in as well.

Well, and scrapple but there it's all mixed in with everything else so you can't identify it

And it's pork

ACuriousMind

@ChrisWhite You ended up at out-of-place articfacts from quantum interpretations?

Also, the Dyatlov Pass incident seems not all that clear in explanation to me as it looks on the chart

Jimnosperm

@StanShunpike Orbital mechanics and dynamics was one of my favourite subjects. But yeah, it can be tough at times. That's why we take pride in being able to hit a 2km area on Mars.

tpg2114

@ACuriousMind Yeah, I agree on that one

John Rennie

16:52

@StanShunpike I wouldn't take my comments about orbital mechanics too seriously,

but it always seemed weird to me that circular motion in a central field is so simple, but when move to an ellipse it starts getting hard very quickly.

Add a few extra bodies and it rapidly turns into a nightmare!

tpg2114

@ACuriousMind Pretty sure it was Sock Cthulhu again:

ACuriousMind

@tpg2114 Awwwwww. No one would flee in fear from that one!

Stan Shunpike

@Jimnosperm Do you study orbital mechanics?

Jimnosperm

@StanShunpike I have a degree in space engineering, so yes, I had to study orbital dynamics closely

Stan Shunpike

@Jimnosperm do you know a good book where I could read more about them?

tpg2114

16:56

@JohnRennie Orbital (and flight) dynamics was always too much for me. The whole gimbal lock thing was virtually impossible to wrap my head around

user929304

@JohnRennie Alright. will kinda need your input on their answers to decide to whom the bounty should go, difficult for me to judge. So let me know whenever.

Jimnosperm

@JohnRennie It's not complicated to calculate the orbit something is in. It's changing that orbit to something else that is tough because of changes in mass, third body effects, fuel efficiencies, etc

Danu

@tpg2114 Welllllp, there go my next several hours

The Lindbergh kidnapping alone is fascinating

tpg2114

I really need an undergrad assistant right now...

Danu

...although it's not super super super mysterious to me---it appears they found the guy

Jimnosperm

16:59

@StanShunpike We used "Orbital Mechanics for Engineering Students" 3rd ed

tpg2114

@Jimnosperm Oh hey, that's what our orbital mech class uses too

Jimnosperm

But I'm sure there's plenty of books out there about it. The equations are really easy and all out there, it's the experience in how to work with them that the classes should be teaching

Danu

If you want a challenge on orbital mechanics, try Arnold ;D

Stan Shunpike

@Danu like Arnold....the classical mechanics guy?

@Jimnosperm where did you go to school? My school doesn't have space engineering. :/ but its a cool field

Danu

@StanShunpike Yeah

Jimnosperm

17:08

@StanShunpike York University. It's the only school in Canada with an undergrad in space engineering. All the other ones are aerospace engineering. And they act like that's the same

Stan Shunpike

@Jimnosperm totally different. Wow that's surprising. I guess for marketing purpose people would treat them the same.

Jimnosperm

@StanShunpike There didn't used to be space eng. Rocket Scientists were all aerospace engineers. That's why people still think it's the same. Even though they learn about planes and we learn about spaceships and rockets.

Jiminion

17:23

@tpg2114 That looks like more of a "Mountains of Madness" dude.

Stan Shunpike

@ACuriousMind what is the advantage of using exterior analysis to describe the laws of electromagnetism?

John Rennie

On a mildly related topic, someone of Facebook has just mentioned this:

arxiv.org/abs/1503.05845

which looks an entertaining read ...

Jiminion

Dellschau prints.

ACuriousMind

@StanShunpike $\mathrm{d}F = 0$ and $\mathrm{d}\star F = j$ look much nicer than Maxwell's laws usually do

Stan Shunpike

Is this what is known as the "covariant formulation"? If so, why?

@Jimnosperm just to clarify, did you like the text book you used?

user54412

17:31

@StanShunpike Yes, because the only objects that appear are right and proper tensors

ACuriousMind

@StanShunpike No, covariant formulation is simply formulating EM in terms of $F$, not $E$ and $B$, since $F$ has proper Lorentz indices, while $E$ and $B$ don't.

user54412

@ACuriousMind Isn't formulating EM in terms of F exactly what you just did?

ACuriousMind

@ChrisWhite You can write $\partial_\mu F^{\mu\nu} = J^\nu$ without ever mentioning the exterior derivative or forms

Stan Shunpike

@bolbteppa Landau vol 3 arrived!

ACuriousMind

I think one shouldn't, but it is sometimes done.

Stan Shunpike

17:34

Right, so what does exterior analysis provide that the covariant formulation doesn't?

ACuriousMind

Beauty

Jimnosperm

@StanShunpike Yeah it was alright

ACuriousMind

Really, if all you want is being able to calculate stuff, you can stay with Newtonian mechanics and non-covariant EM

user54412

@StanShunpike barrier to entry for the less abstractly inclined ;)

Stan Shunpike

@ACuriousMind but then you miss fun stuff :D

@ChrisWhite lolol

Well done

@ACuriousMind it seems my profile has stopped mutating

ACuriousMind

17:38

@StanShunpike So this is your final form?

Stan Shunpike

I guess. I wouldn't have chosen gray I must say, so perhaps I will substitute it with something else. But it hasn't changed in +24hrs so I think it may have stopped

It was very amusing

@bolbteppa wow landau has some neat exercises :D

Stan Shunpike

17:53

@ACuriousMind Do you like Shakespeare? Just curious. I'm a fan. I like his word play

NikolajK

I was going to make a 50 Shades of Gray pun

Stan Shunpike

@NikolajK about Shakespeare?

bolbteppa

@StanShunpike Cool, here themindofatheorist-theblog.blogspot.ie/2010/10/… is an overview of the book and here amazon.com/Quantum-Mechanics-Third-Non-Relativistic-Theory/dp/… are reviews

Stan Shunpike

Sweet. Its an intense book. I probably will need to read the prior two volumes

@ACuriousMind Ryder says the "paths" in path integration are paths in the normal sense, but really Markov chains. Do you agree?

NikolajK

@StanShunpike: I don't see how. What are the points along the chain supposed to be? I'd say any full path is assigned a number and it's the integral over those values. No stepwise feature as far as I can see. Also, not a pun about Shakeespeare but about you saying you chose gray.

Stan Shunpike

18:13

Have you heard of 50 shades of Wayne? A batman parody apparently.....

@0celo7 do you concur with @NikolajK on this point about Markov chains?

alarge

@NikolajK Well, take the simplest path integral, the brownian particle. The Wiener measure used there can be through of as the result of an infinite limit of a Markov chain (e.g. Feynman-Kac to see the relation between path integrals and Ito calculus, the latter of which is kind of a continuous Markov). Now in QM you have mathematical issues, and as such this idea does not rigorously speaking work, I think.

Stan Shunpike

What is a moment? Like for instance a magnetic moment? I never understood this. Why is it called that? I always associate moment with like moment in time...

alarge

@StanShunpike I think moment is torque in some languages (German, maybe?)

Stan Shunpike

Really? Wow you are right! That puts my mind at ease lol

ACuriousMind

18:30

@alarge Yes, rotational torque is Drehmoment

0celo7

@StanShunpike Markov what?

ACuriousMind

@StanShunpike As alarge says, the Feynman-Kac formula indeed relates the path integral to statistical processes

Stan Shunpike

@0celo7 I think it has been cleared up. Go back its no very far and you will see my comment from Ryder

Not*

ACuriousMind

There even is an interesting question here that does Levy quantum mechanics by basing it on a Levy random walk rather than the Brownian motion that lies under the usual non-relativistic QM:

7

Q: Quantum mechanics on Cantor set?

Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a Cantor set? I can only guess that: i) There will be no momentum operator. ii) Hilbert space w...

The alluded link between relativistic fermions and Levy process at the end of Ron's answer is very interesting

NikolajK

@alarge: You point out that there is a relation between the path integral and markov chains. Why does that say that the (quotes) paths (unquotes) should not be thought of as paths but as markov chains?

alarge

18:52

@NikolajK Well my point was really just that the measure (which you need to define the integral) comes from the probabilistic Markov process. This given, you can think of them as "regular" paths.

NikolajK

I guess I should think of women as dresses, because women like to wear clothes.

2

alarge

To sum over the paths, you need to know how they are generated/sampled, otherwise you're missing half the information (if I ask you to give me the expectation value of a dice roll, you first need to know the probability of each number; knowing just the numbers is not enough. Similarly I can't just take paths and sum them without knowing the probability of each). But I think this is really an uninteresting matter of terminology, and I can't be sure what the original author meant with "paths".

tpg2114

Wow, I'm blowing my own mind with python and regular expressions right now...

alarge

@tpg2114 Effective Python was just released a couple of weeks ago. If this is half as good as the Meyers books on C++, I should really buy this.

tpg2114

@alarge I haven't actually purchased any books on python

I just learn by trial and a ton of error

And StackOverflow

alarge

19:09

Well that's what I've done with Python (I have no books yet use it as my main prototyping/scripting language). Trial and error was also what I did with C++ in the beginning (before the age of SO), but the books I bought proved enormously helpful.

tpg2114

I'm using Cantera to do some chemistry right now, and it has a bunch of python functionality

And one of the things you can do is define reactions with it. For example:

reaction("H + O2 <=> O + OH", [0.352e17, -0.70, 17070.0],
         id = '5G')

Which is cool and all, but you also need to define the mixtures of things:

ideal_gas(name = "gri30",
      elements = " O  H  C  N  Ar ",
      species = """ H2  H  O  O2  OH  H2O  HO2  H2O2  C  CH
                   CH2  CH2(S)  CH3  CH4  CO  CO2  HCO  CH2O  CH2OH  CH3O
                   CH3OH  C2H  C2H2  C2H3  C2H4  C2H5  C2H6  HCCO  CH2CO  HCCOH
                   N  NH  NH2  NH3  NNH  NO  NO2  N2O  HNO  CN
                   HCN  H2CN  HCNN  HCNO  HOCN  HNCO  NCO  N2  AR  C3H7
                   C3H8  CH2CHO  CH3CHO """,
      reactions = "all",
      kinetics = "GRI30",

But it's kind of a pain to update/track that species and elements list when you write a mechanism. The one I'm writing right now is 228 reactions, 40 species

NikolajK

GRI3.0 is a 20 year old meme

we'll never get rid of it

tpg2114

Annoying. So, I made the elements and species arguments call a class that executes itself with redefined functions so it doesn't call the Cantera ones

And these redefined functions populate a list of reactions

Which I can then parse apart into elements and species using regular expressions

And so the script (which Cantera executes) in turn executes itself to generate the info

@NikolajK It's good for detailed hydrocarbon combustion. We'll replace it when something better comes along

The JetSurf mechanism is good

NikolajK

"We'll replace it", I doubt it, not as long you haven't killed all old poeple

tpg2114

@NikolajK If it ain't broke, don't fix it. Until somebody comes along and shows why it sucks and proposes a better alternative, why would it be replaced? By people old or young? Like I said, JetSurf works better in some instances -- and in those cases, people use it.

I'm putting in a nitramine mechanism right now and not using parts of GRI30 because the parameters are slightly different for the reactions

alarge

19:19

@tpg2114 Has nobody written the parser before? It sounds like something you'd basically always want to use. Maybe if you have a nice solution you should make a pull request.

tpg2114

I am unaware of anything like this

Stan Shunpike

@ACuriousMind I'm confused about the solution to the SE for the free particle case. When I took the time derivative and rearranged I got $i\hbar\frac{\partial \psi}{\partial t} = E \psi$ but when I did the RHS I got $\frac{\hat{p}^2}{2m}\psi =\frac{p^2}{2m}\psi$ with no $E$ term? How are these equivalent? Obviously if I assume this follows the TISE, then I have $\frac{p^2}{2m}\psi=E\psi$, but I don't get why I would be using the TISE given that I am considering a moving system....

tpg2114

The Cantera people certainly don't have it in their code or anywhere I've found online

NikolajK

nitramine?

tpg2114

Explosives -- RDX, HMX, CL20, etc

ACuriousMind

19:21

@StanShunpike $E = \frac{1}{2}mv^2 = \frac{p^2}{2m}$

tpg2114

I have to do it for perchlorates and nitrate-esters also but one mind-numbing chore at a time

NikolajK

Why do you look at those?

tpg2114

My thesis is on developing computational tools to understand/predict the performance, sensitivity and safety of existing and novel explosives

Stan Shunpike

@ACuriousMind Like, I began wanting to show the free particle solution satisfies the TDSE. But it seems like to show that, I have to use the assumption it satisfies the TISE. Why?

tpg2114

For use as propellants or explosives

Stan Shunpike

19:23

@ACuriousMind the thing you just said...what justifies that assumption?

NikolajK

ah, kewl

K2(O2NNCO2) + 2H2SO4 → O2NNH2 + CO2 + 2KHSO4

2big4me

ACuriousMind

@StanShunpike Because you assumed that $\hat p \psi = p \psi$, i.e. that $\psi$ is an eigenstate of the momentum operator, which would also be an eigenstate of the Hamiltonian, and hence a stationary state.

NikolajK

Did you guys know there is Sonic hedgehog and Pikachurin?

ACuriousMind

@StanShunpike: Also, there is nothing to show. Everything in the Schrödinger picture of QM obeys the time-dependent Schrödinger equations, I don't know what you are trying to do.

@NikolajK Sonic is a gene, right? Making flies look like him, I think

Stan Shunpike

@ACuriousMind every valid solution you mean, right? Not just anything is a solution to the SE, right?

alarge

19:27

@tpg2114 Oh that sounds cool. What kind of computational tools do you use (and what does develop in your case mean: parameters or novel algorithms)? How heavy are the calculations?

ACuriousMind

@StanShunpike We might have differences in what we regard as "anything". I meant that every quantum state obeys it, so I don't know what you want to do when you want to show that "the free particle obeys the Schrödinger equation".

NikolajK

@alarge: he said he uses Cantera, which is one of the free chemical reaction simulation tools

code.google.com/p/cantera

Stan Shunpike

@ACuriousMind i just want to verify that $\psi(x,t} = Ae^{i(px-Et)/\hbar}$ is a solution to the SE. All I want to do is the trivial calculus and rearrangement of plugging it in and seeing that it fits. But I didn't have $\hat{p} \psi = p \psi$ as one of my assumptions. And I don't get why I can make that assumption.

ACuriousMind

@StanShunpike You have written there the solution to the time-independent SE, a "plane wave". The general solution is a superposition $\int c(E)\mathrm{e}^{\mathrm{i}(px-Et)}\mathrm{d}E$ of the plane waves.

36

Q: Can I thank websites that host illegal book downloads in the acknowledgements section of my thesis?

My stance is that these websites are a great boon to the research community and they were certainly extremely helpful for my research. I think they should be applauded rather than persecuted, and while they may be illegal now, I think a way to make them legal should be found (in the same way I ca...

thesis acknowledgement

NikolajK

why does the chat not display $ formulas to me

:/

ACuriousMind

19:36

Academia certainly produces very different questions

@NikolajK You need to activate ChatJaX, see this

NikolajK

I was gonna point out before that the Landau book is just three clicks away

ciao

Stan Shunpike

@ACuriousMind why does plugging my equation into the TDSE give me $i\hbar \frac{\partial \psi}{\partial t} = E \psi$? If its not a solution, why do I get this?

ACuriousMind

@StanShunpike I said "You have written there the solution to the time-independent SE"

Have you not realized that every solution to the TISE is trivially one to the TDSE?

tpg2114

@alarge So we have our in-house massively-parallel, multiphysics code that can handle gas and solid phase, plus dense and dilute sprays of liquids or solid particles

Stan Shunpike

Yes, but I'm still trying to work out the why's for everything and I'm getting confused.

tpg2114

19:49

My project is on multi-scale modeling -- so we take some information from molecular dynamics folks and run it through a peridynamic structural solver (which is what I wrote myself) on the micro-scale

ACuriousMind

@StanShunpike I see that you are confused, but I don't see what confuses you.

tpg2114

Homogenize the results from that to go into our Eulerian multi-physics code and from there do rocket motors or detonations

Pretty intense computational load -- I have access to a dozen machines all the the top 500. About half are in the top 25

Routinely use thousands of processors for hundreds of millions of cells when we are at the full-scale runs

I also need to work on coupling the structural solver directly to the Eulerian solver so I can have embedded zones of micro-scale resolution

To do things like fracture, penetration burning, erosion, ablation, etc

alarge

@tpg2114 What's your definition of multi-scale? The codes communicate back and forth, or you just take their end data and parametrize it? Anyway, is the code accurate? I'd be very surprised if something from MD gave better results than a well calibrated continuum model.

Stan Shunpike

@ACuriousMind I have two equations. TDSE and TISE. I have this equation $\psi(x,t} = Ae^{i(px-Et)/\hbar}$. This is only a solution for the TISE, right? When I plug it in I get $\frac{1}{2}\frac{p^2}{m}\psi = E \psi$. Do you disagree with anything I have said so far?

ACuriousMind

20:05

@StanShunpike I don't really agree with calling the TISE an equation on its own because it is just searching for the eigenvectors of $H$, but I don't disagree with anything technical you've said.

Also, I would prefer to solve the TISE time-independent, i.e. only write $\psi(x) = \mathrm{e}^{\mathrm{i}px}$ as the solution

tpg2114

@alarge Are you familiar with large eddy simulation for turbulence?

Stan Shunpike

(1) What would you call the TISE then if not an equation on its own? (2) why do books and articles I have seen write $\psi(x,t} = Ae^{i(px-Et)/\hbar}$? I agree, if it isn't time dependent why write it that way....

@ACuriousMind

tpg2114

From the MD folks, they just run their stuff and give me continuum data -- elastic moduli, EOS properties, etc.. My peridynamic code is continuum but it resolves all of the fine-scaled structures of the randomly packed explosives, and can do things like viscoplastic heating due to void collapse and resolve all the other physics related to localized heating that can trigger detonations

ACuriousMind

@StanShunpike Well, your $\psi(x,t)$ is a solution to the Schrödinger equation, and a very important one - it is a state that does not evolve in time, a stationary state.

tpg2114

From there, we are taking two approaches. One of them is to filter the continuum, Eulerian governing equations in space (similar to large eddy simulation filtering) to generate governing equations in terms of homogenized variables and use the peridynamic solver to generate model information for the unresolved micro-scale terms

ACuriousMind

20:12

And, yes, the TISE is an equation, but calling it "TISE" implies that it is somehow special - an equation of motion like the TDSE or something, but it is not, you are just searching for the eigenvalues of the Hamiltonian.

tpg2114

The other approach, which we will use for deflagration cases, is to have the peridynamic code running tightly coupled with the Eulerian code. The peridynamic code would be resolving the micro-scale structure of the materials only at the fluid-structure interface

And both of them are my thesis

ACuriousMind

Also, note that you do not have a probability interpretation for the free particle, since the $\psi(x,t)$ is not normalizable, since it is not square-integrable.

Stan Shunpike

Is the generalized solution you mentioned earlier square-integrable ?

ACuriousMind

@StanShunpike If you choose the $c(E)$-coefficient reasonably, yes. If you choose it as a Gaussian, you get what's called a Gaussian wavepacket

alarge

@tpg2114 Sounds cool. I mostly worked (in my PhD) with MD, and I wouldn't trust any of the numbers to be quantitatively sound (for example, almost none of the models can, or could, get the properties of water right; surface tension is typically off like 30% or whatever if you're interested in interfaces). Maybe gases and solids are easier, though.

tpg2114

20:21

@alarge No, I have zero (maybe negative) faith that they are anywhere close to right

ACuriousMind

More precisely, if $c(p)$ expressed as a function of the momentum is a Gaussian, then you get a Gaussian wave packet. $c(E)$ as a function of energy is a bit unusal, but in the 1D case, energy and momentum are interchangable, after all

tpg2114

But our project funding requires us to integrate with them. So it is what it is

They're using ReaxFF

alarge

@tpg2114 Yeah, well that doesn't really help with the confidence issues. That said, I've never done reactions myself, though.

tpg2114

The... questionable nature... of the data is why I have to spend a lot of time doing uncertainty and sensitivity analysis through the whole chain of scales

So if I get data that's 20% off from MD, how bad is it by the time I run a full rocket motor after it passes through all of the models to get there

Stan Shunpike

@ACuriousMind do you integrate over momentum then or E still? (It was E right?)

ACuriousMind

20:27

@StanShunpike Okay, the more reasonable way to gain a wavepacket would be to write $\int c(p)\mathrm{e}^{\mathrm{i}(px-Et)}\mathrm{d}p$. But you should see that, since $E= \frac{p^2}{2m}$ and so $\mathrm{d}E = \frac{p}{m}\mathrm{d}p$, that doesn't really matter.

alarge

@tpg2114 Can the data not be measured from experiments (so you'd know how much off you might be)? Also, is your work more of the qualitative proof-of-concept kind, or are you actually trying to make real predictions (with the sensitivity analysis and all, sounds like the latter)?

tpg2114

@alarge The end goal is to integrate experiments, MD and simulations to be predictive when it comes to the design of novel explosives

alarge

@tpg2114 Yeah that's cool. So when you write papers, do they go to engineering journals or something like theory&computation or what?

tpg2114

So we are partnered with Cal Tech for MD and TUM in Munich for experiments. TUM comes up with these insane new explosives and how to manufacture them, some of their theoretical properties, and some small-scale experiments. Cal Tech figures out their properties for us (EOS, elastic moduli, etc). We then take all of that information and simulate a full-sized explosive with it

@alarge All of the above. So we're working on some papers for Physical Review, we had a paper published in Combustion and Flame, I submitted one to Journal of Energetic Materials, Computational Physics Communications and Computers & Structures

The last two were more about algorithm development. JEM was about results

bolbteppa

@StanShunpike the Schrodinger equation is time-dependent, $\dfrac{\partial \psi}{\partial t} = H \psi$, where $H = T + V(x,t)$ or $H = \dfrac{p^2}{2m} + V(x,t)$ or $H = \dfrac{-\hbar}{2m}\nabla^2 + V(x,t)$. If the potential does not depend on $t$ then you can use the PDE's method of separation of variables to reduce the time-dependent-SE to the time-independent-SE. Furthermore, if $V = 0$ you have not only a time-independent SE you have a solution of the form in your post

28 mins ago, by Stan Shunpike

@ACuriousMind I have two equations. TDSE and TISE. I have this equation $\psi(x,t} = Ae^{i(px-Et)/\hbar}$. This is only a solution for the TISE, right? When I plug it in I get $\frac{1}{2}\frac{p^2}{m}\psi = E \psi$. Do you disagree with anything I have said so far?

tpg2114

20:32

Combustion and Flame was more engineering -- come up with a model and calibrate it

We need something like MD though because you can't (and definitely shouldn't) do things like tensile/fracture tests with pure energetic crystals

alarge

@tpg2114 So after your degree (I'm assuming you're going to graduate rather soon), are you still going to work on something similar? i.e. do you think it's interesting, long term?

tpg2114

So finding out the continuum material properties for the crystals requires numerics

@alarge Hopefully done in a year. And I don't really care much to work in explosives per se. I want to work in computational fluids though. I would like to go either into atmospheric dynamics (physics of hurricane formation, cyclogenesis, supercell formation etc) which is still very much multi-scale modeling

Or go into the sports engineering side and do aerodynamic analysis and performance prediction of cyclists. Try to replace the time spent in the wind tunnel perfecting design and positioning with high fidelity simulations

Stan Shunpike

@ACuriousMind So the only thing the TISE does it spit out the eigenvalues of the Hamiltonian? Its not an equation of motion.

tpg2114

Which would also require some pretty creative modeling techniques to make it cost effective

ACuriousMind

@StanShunpike Well, it's $H\psi = E\psi$. What do you expect it to do?

You should observe that the eigenvalues of $H$ are exactly the states that do not evolve in time except for a phase, though.

Stan Shunpike

20:40

@ACuriousMind why is the spectrum of the free particle operator continuous?

ACuriousMind

@StanShunpike Uh...because there's a plane wave to every momentum $p$?

Stan Shunpike

@bolbteppa why does it matter if the potential is time dependent?

@ACuriousMind thanks for your help! Ive learned a bunch. Now I can go back and read the sections in Griffith's I wasn't understanding :D

bolbteppa

@StanShunpike this is basic pde's dude, you can't solve it if $V$ is complicated, further the eigenvalues will be time-dependent, you've already seen the eigenvalues are continuous if there's no potential, if there's a certain potential then the eigenvalues are discrete but time-independent, and with a general potential are time-dependent.

Phonon

hey folks

ACuriousMind

@Phonon Heyhey

Phonon

20:54

just got home from campus... hectic weeks lately

Stan Shunpike

@bolbteppa right right right, I remember now

ACuriousMind

@Phonon What is occupying your time?

Phonon

@ACuriousMind on fridays it's the lab works, changes between exp to theoretical ones, last week and this week it was free energy estimation... they give you some package written in some messed up lang like tcl or fortran and you have to build a harness script that uses it and calculate sth... last week I spent 12 hours on it!

very frustrating experience if you're not that into coding

ACuriousMind

@Phonon You are handed a package in a language you don't necessarily know and have to make it work? That sounds horrible

tpg2114

@Phonon Hey now... I happen to like both tcl and Fortran

Although I will say tcl is a bizarre little language

Phonon

21:01

@ACuriousMind exactly... it's never sth nice like python... don't ask me why

@tpg2114 yeah, maybe it's just my own personal experience then, never had to learn either of em, it was always either cpp or python...

tpg2114

@Phonon I like python a bajillion times more than tcl

But it's a cool language.

Phonon

@tpg2114 we're very much alike in that sense ;)

tpg2114

Tcl was the 2nd language I learned. QBasic, then Tcl cause I could do fun stuff and make GUI's appear with Tk

Then I learned C and Win32API

ACuriousMind

I've never had to really code in a university-related course at all. The worst was fighting pre-made IDL programs (and that was already horrible)

Phonon

@ACuriousMind long story short, you just enjoy the *** out of that free time right now ;D

yeah

well in a sense I understand why they push for this, I mean you can't not be good in computational physics if you wanna do any research in condensed matter physics these days

ACuriousMind

21:05

@Phonon Hehe...I'm doing my best

Phonon

it just annoys me when they limit your programing language option like this...

tpg2114

@Phonon And you also can't survive long if you can't figure out how to use some ancient dialect of a long forgotten language written by a dinosaur of a scientist

Phonon

@tpg2114 I guess... what do you study yourself?

tpg2114

@Phonon Aerospace engineering. Computational multi-physics -- our lab is mostly turbulent combustion but I'm doing condensed phase energetic materials, solid-fluid interaction and multi-scale modeling

But the vast majority of my time every day at work is programming or software engineering

Phonon

@tpg2114 aha! that sounds freaking exciting, computational multi physics? what does "multi" exactly entail here :D?

tpg2114

21:10

@Phonon Haha, I literally just had this discussion with @alarge like 20 minutes ago! Multi-physics meaning gas phase, liquid and solid sprays (both dense and dilute), and solid phase all together

Phonon

@tpg2114 ahhh right, could have guessed. So nothing soft matter related? it'd be a pity ^^

alarge

I think multiphysics in general can mean that you take the equations of two or more different phenomena and put them together. Like say coupling electrodynamics with elasticity. But I don't think it's a well-defined term.

tpg2114

Our lab does engineering type applications like liquid fueled swirl combustors for power generation through to more fundamental studies of supersonic combustion and mixing processes for (sc)ramjets through to very fundamental studies of turbulence, flow instabilities, detonations, etc.. And we have some MHD capabilities also

We have a lot of rocket problems, in the past mostly it's been liquid fueled rockets but now my work is bringing in solid fueled rockets

alarge

@Phonon I used to work on soft matter related stuff (mostly MD). Not that anyone asked me.

Phonon

oh boy :D

tpg2114

21:13

Soft matter?

Phonon

@alarge nice nice, not anymore? why?

yeah polymers, colloids, liquid crystals etc (all the good jazz really) :D

tpg2114

@Phonon So the binder materials that they use to shape solid rocket propellants and explosives -- HTPB, Estane, etc

alarge

@Phonon I'm no longer in academia. Lost interest (I still like physics-y stuff, though, just don't want to be doing it as my job).

Phonon

@tpg2114 hahahaha that's one nasty way of putting it :D

tpg2114

That's my only exposure to polymers and colloids... I have to simulate the combustion and detonation of the heterogeneous mixtures

So @alarge, what did you work on with MD?

Phonon

21:16

@alarge I hear you, probably for the best! not easy to make any stable living in academia these days...

@tpg2114 sounds neat, why the interest in solid fuel at all? let's say what's the first biggest benefit that comes to mind?

alarge

@tpg2114 My main interest was in biological systems (for example how the cell membrane interacts with... stuff, e.g. proteins). Personally I was more interested in writing out like continuum style models and then running some simulations to see if they worked. But I had to do my share of tinkering with the ugly details, too.

Phonon

@tpg2114 storage?

tpg2114

@Phonon I'm funded by the Office of Naval Research and they are looking at replacing ammonium perchlorate, RDX and HMX with the next-generation of energetic materials. So my project is a collaboration with two other universities to develop a framework to integration theory, MD, experiments, and simulations to evaluate and predict the stability, performance, and safety of these new energetics as they are developed

Including things like environmental impact and toxicity

So my single biggest benefit in working with condensed phase energetics is that it's paying for me to get a PhD :) Otherwise I wouldn't be in this specific area

Phonon

@tpg2114 oh I see, haha, well thanks for the explanation!

tpg2114

My passion is in the methods far more than the applications

Phonon

21:23

then you're really in the wrong place :D

tpg2114

@alarge Continuum models of biological systems?

Phonon

hopefully you get more prospects into what you like more after your phd

tpg2114

That's what's cool about the computational work and model development I'm doing -- the same equations and techniques are used for weather, astrophysics, biological systems... Heck, years ago a PhD from our lab went to work at a movie studio to work in CGI to make more realistic looking flames and explosions for movies

alarge

@tpg2114 There's plenty. For example polymer theory (say, self consistent field theory, the stuff of de Gennes, Edwards etc.) is quite beautiful (and has immediate applications to biological systems). Then obviously there's DFT for a bit more microscopic view. And then there are elasticity-based approaches, and phase separation models etc.

tpg2114

The knowledge base is transferable to an almost-limitless number of applications

Phonon

21:25

@tpg2114 indeed it really does branch out to very diverse possibilties

@alarge uff DFT don't remind me.... struggling with DFT of complex liquids at the moment, what a nightmare!

alarge

@tpg2114 I follow SIGGRAPH stuff more or less regularly, so I should note that a lot of the CFD they do in movies is about finding new shortcuts: The aim is to be visually impressive rather than physically correct, after all.

@Phonon Hansen? (that's mostly simple liquids, though)

Phonon

@alarge yep!

@alarge it's complex to me... :D it's only simple to Hansen and no one else.

tpg2114

@alarge Agreed -- but if you can get creative, you can make more physically accurate simulations that are cost effective as well

My peridynamic structural code is just a mass-spring lattice model, so I've been reading a lot of SIGGRAPH stuff

alarge

@tpg2114 Sure. Oh, and games too use CFD. Increasingly so. I think even the new SimCity-like builder had some kinda CFD in it.

tpg2114

Taking their information and methods and making a rigorous assessment of their application to physically-accurate systems.

alarge

21:30

@Phonon Hansen is a bit dense, but like everything in thermodynamics, it gets easier with time. Hansen more recently wrote another book, right? I think it's more introductory. Have you tried that?

On that note, there's even a quote attributed to Sommerfeld about "this": "Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more."

Phonon

@alarge you're right. which recent book? the one with Barrat?

alarge

@Phonon Maybe. I think it had DFT in the title.

Phonon

@alarge ahaha I just read the quote, loved it :D

alarge

So I Googled, and I think I indeed meant the book with Barrat (and it doesn't have DFT in the title).

Phonon

ah okay, yeah figured

tpg2114

21:34

Man, it probably would have been faster for me to write an OCR program in python that converted these reactions into Cantera format automatically

Even if not faster, far less painful

Phonon

undoubtedly...

tpg2114

122 reactions down, 106 left to go

Phonon

:)

tpg2114

For this one anyway. I still have to do the same for PETN, TATB, AP...

alarge

@tpg2114 How do you test that? I mean, how can you be sure you got it right?

tpg2114

21:36

@alarge Well my initial plan is just to run it and pray like I've never prayed that it works

I don't have a plan after that

Except to go through reaction by reaction and check that I entered everything right

Phonon

alright guys, nice talking, afraid gotta head off to eat sth before I pass out! :D Cya

tpg2114

Preferably with a coworker who doesn't mind being bored for 20 minutes

alarge

@tpg2114 Is your lab big? Can you get some younger students to do stuff for you?

tpg2114

@alarge It is big but I don't have that kind of pull... hah

Since my project is still very heavily in the code/theory development stage, I don't have underlings yet. Soon, once things are production-ready in terms of the code

So they can just change the inputs and process results

alarge

@tpg2114 Out of curiosity, how is your lab organized? What grade are the most junior members, and how are they funded etc.? Are they under the direction of a post-doc, say, or tenured staff?

tpg2114

21:43

@alarge It's organized very, very poorly... There is a single tenured professor in charge but it's basically just a free-for-all after that

We have 3 post docs currently, but senior students (like myself) are actually way ahead of them in terms of knowledge in the field and programming/computer skills. Junior members are just kinda thrown in and expected to fend for themselves

Funding wise, our advisor takes care of all of that for us. Which means we tend to get bounced around projects a lot. I've worked under 5 different funding sources at this point, all of them radically different projects

alarge

Have the lab interests changed, or why are the senior students ahead of the post-docs in terms of knowledge?

tpg2114

Our main code is something like 700,000 lines for Fortran with 250,000 lines of python utility/analysis tools. And about 50,000 lines of C/C++ code that all works together. All written by 4 of us, and now it's really only managed by me since the rest have graduated.

alarge

Also, do you also have undergrads?

tpg2114

Undergrads don't last long... I started as an undergrad, but most only stick around for a semester before finding jobs elsewhere.

Our lab is lately unfocused and so our post-docs who come in are very good in whatever they did but it doesn't apply to what we do. So it's kind of poor hiring choices too

And then poor management -- we have a post doc who did a PhD using ReaxFF. But he's not the one working with me on this project, instead I'm working with a post-doc who has never done reacting flows or any large-scale simulations. Only ran stuff in Matlab

alarge

@tpg2114 But I suppose part of that might be due to changing interests of the post-docs as well (if the other guy got bored of ReaxFF, say)?

tpg2114

21:50

Lately we've had a lot of turnover in grad students too. There's the 3-4 senior people that are left who have been around for ~5-6 years, and like 15-20 people who have been here under 2 years. And nobody in between

@alarge That could be as well

alarge

Thanks for all the info. Was interesting. I'm gonna let you get back to writing your equations without interruptions.

tpg2114

@alarge Heh, any time. It's nice to take a break from mindless data entry

bolbteppa

22:05

@ACuriousMind what do you think of this: The Virasoro algebra is the lie algebra of the central extension of the Lie group $Diff(S^1,S^1)$. That is the standard view, and I think what you were focusing on. But what I said is the intuitive motivation for that construction, however my intuition should have been formulated more mathematically as you noticed. Luckily, in CFT there is the notion of a Sugawara construction, have you heard of this?

Basically it allows one to obtain the Virasoro algebra from a Kac moody algebra by noticing that the group $Diff(S^1,S^1)$ acts projectively on the loop group $Map(S^1,G)$ (for some group G, no idea what this is about!) so one builds the Virasoro generators out of Kac Moody generators which are Lie algebra elements in the current algebra which is just the Lie algebra to the loop group.

ACuriousMind

@bolbteppa Very interesting, I hadn't heard of it

7

Q: How to interpret the Sugawara construction from a physical or mathematical viewpoint?

In theoretical physics, the Sugawara theory is a set of formulae and theorems that allow one to construct a stress-energy tensor of a specific type of conformal field theory from a bilinear expression involving currents. How to interpret the Sugawara construction from a physical or mathematical ...

lie-algebras

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