Wolfram Mathematica

@rcollyer Hi !!

What's up.

just drinking my last beer :)

That's too bad. I wish I had beer.

mmm

I may lend you some

1:07 AM

It would take a few days to get here.

Although, there's the uubp protocol.

I think there should be BTP (beer transport protocol) over IP somewhere in my machine

ha!

great minds ... etc

Do you know anything about Group Theory?

I used to. But not anymore

That's to bad. I have a question up on Mathematics that I'd like answered.

In fact I worked hard in solid state for a few years ... decades ago

1:12 AM

It has been pissing me off for several weeks now. Once I discovered how wrong my current method was. :P

@belisarius Ultimately, I'd be using it in Tight Binding model, so it applies.

I think it could take me a few days just to understand what you are asking

That's my problem. I've spent days on it.

Ask a fellow mathematician

The first part is easy. The second part is where the difficulty lies.

are you at uni?

1:14 AM

@belisarius That's why I posted it on Mathematics.

@belisarius In a sense. I'm working remotely.

oooo ... thats bad

But, I do hang out at my Alma Mater, so I could go ask someone from there ...

you should drink your morning coffee with mathematicians. All difficult questions are due to be answered by 10:30

I did that for yars

never fails

Ah, true. But, I only know 1 prof there any more. I should go bug him; he was my differential equations prof, and he may just know, or who to ask.

Thats the key point of being at uni. Know people. ask questions. get answers :)

a very underestimated gain

1:20 AM

For this problem, the idea is I'd like to block diagonalize the Hamiltonian according to the irreducible representations of it symmetry. Of course, this has the added benefit that doing that gives me all of the eigenvalues, too. But, the real benefit is you can create a model with that symmetry using the projections onto those subspaces, i.e. a modified spectral theorem.

What is a "block diagonal" matrix?

You turn a regular matrix into
$$\begin{pmatrix}\mathbf{A}&0 \\ 0&&\mathbf{B}\end{pmatrix}$$
where $\mathbf{A}$ and $\mathbf{B}$ are matrices themselves.

mmm my chat cant read TeX

Damned alignment is off. :P

What should I do with it?

1:27 AM

Better yet, read this link.

ok done

so you want something like a Jordan form?

where each eigenvalue subspace is closed under the linear transform?

It is like a Jordan form, yes. The idea is that the eigenspaces correspond to irreducible representations of the symmetry group, so using group theory you can, in principle, get part of the way to a full diagnolization by using that.

@belisarius bingo.

bingo ... what?

Now, different instances of the same representation still interact with each other, but different representations don't.

@belisarius just saying your comment was correct.

ahh ok

ok. now I understand the problem. Still miles away from having a useful idea about how to solve it

1:33 AM

If you look at the character table for the symmetry of a triangle, you'll note that the functions $(x^2 - y^2, x y)$ and $(x z, y z)$ each correspond to the $E$ representation and form their own little supspaces.

The issue at hand is how do I automatically generate both of those representations and not their sum?

And, that's my question on Mathematics.

I can generate their sum easily. Teasing them apart requires trial and error. I'd prefer there was less of either.

Sorry, my math is too rusty. It will take me a LOT of effort to remember all those once loved details

Don't worry about it. It is a lot more familiar to me, and I don't see it.

Unfortunately, the books I have seem to make it into a chicken and egg problem. :P

Hi @acl

Did you ask a GR physicist? They tend to work a lot with irr. representantations

No, but none are local.

damn

acl

1:40 AM

@rcollyer hi

hi acl!

@belisarius looking at mathoverflow, and it may have been a mistake. I don't understand 3/4's of what they're writing!

@rcollyer ask the rubber duck

@belisarius I've tried. it told me to quack off!

@rcollyer At MO they are real mathematicians. They are not people, you know.

1:45 AM

@belisarius I'm aware. I was hoping, though.

I wonder how you do science in remote. It usually takes a lot of interaction

like in this case

Computers are a wonderful thing.

yes and no

a shared coffee table makes wonders

a mail to an unknown person doesnt

That's the truth. But, my son was allergic to where we were living, so we moved. And, I'll finish up remotely.

a good reason indeed :)

1:50 AM

it ins't easy, but it is doable. and, with any luck, I'll have this wrapped up soon.

Is it your PhD?

yep.

nice

bout what?

with luck, I'll be employable, also.

@belisarius condensed matter. specifically, dft (density functional theory). more specifically, dft on the B20 structure, and whatever else I can think of throwing at it.

what uni?

Do you know him?

Leopoldo Máximo Falicov

Leopoldo Máximo Falicov (June 24, 1933 – January 24, 1995) was an Argentine theoretical physicist, specializing in the theory of condensed matter physics. Life Falicov was born in Buenos Aires with both parents of Eastern European Jewish origin. His father, Isaías Félix Falicov, was Argentinian and his mother, Dora Samoilovich, emigrated to Argentina as a child. Falicov attended the Colegio Nacional de Buenos Aires and then attended the School of Engineering and Natural Sciences at the University of Buenos Aires, where he got his undergraduate degree in chemistry in 1957. In 1958, he rec...

Not albert, of course

1:57 AM

@belisarius I know the name, but it has been a while.

CHM

@rcollyer @RM I've seen your comments. I don't think of SO anymore for MMA questions.

@CHM but, enough people do. We need to bring them over to the true "church."

@rcollyer I worked with him for a while

@belisarius cool!

@rcollyer many years ago

1:58 AM

@belisarius life moves on.

Ok. off to bed

nights all!

night.

I'm going to follow his lead: Good Night or Day (as the case may be) to you all.

CHM

@rcollyer so the question will be moved?

Oh, night.

And it has already been moved.

You guys are too fast.

2:14 AM

@CHM It was moved just a short time ago. Flagging can take a while, but my "helpful" flag count on SO is slowly getting to the point where it may come up in the queue a little faster.

@Verbeia the number of questions just exceeded our visits per day for the first time today!

@rcollyer I should patrol SO for migratable questions more, then. I already have a Marshal badge there.

Should help. Likely it will be most successful when we have a dupe here.

@rcollyer That's cool. Even more interesting to my mind: the entire time of the beta, visits has exceeded users.

We have 59 enthusiast badges now

anyway gotta go, was just dropping in. I promise to do the 90-day graphs tonight.

And 8 days away from a chunk of fanatic badges.

Night.

F'x

7:50 AM

9:43 AM

Updated site usage graphs on meta - now available

9:58 AM

11:56 AM

@Heike cool! I remember missing that by a little.

@Heike I did have 12345 :-)

Sjoerd C. de Vries

12:13 PM

@Fx That's 5 times The Number of the Beast

Well, almost

90 days in beta. What's next?

Hi Sjoerd!

@JM welcome :-)

@robjohn (I said hello to you already, so... :P)

@JM You said hello to some weirdo on Math :-p

He was a most peculiar fellow, yes...

...after all he underwent binary fission during April first...

12:26 PM

Hey @JM are you back now?

@JM Hi JM

ooh bedtime - see you all in the morning

Good night @Verbeia!

@Verbeia Wish me luck; if all goes well with this week I should be a regular visitor again...

@Szabolcs Hi also!

@JM in that case, almost welcome back

12:29 PM

@Verbeia it is the morning. :-)

no it's not, it's the afternoon

afternoon is certainly an odd time for the sun to be about to rise :-)

@Heike Hi.

my visit to the apple store went smoothly. No it's fingers crossed that I doesn't take too long to get my macbook back.

@Heike what was the problem?

12:32 PM

@robjohn broken dvd player

Ah, I have an old computer with a DVD player that doesn't even light its power light. I think it is too old to fix or find a replacement.

It makes it hard to reinstall software since most of the software was on CDs or DVDs.

@robjohn I have an external dvd player as well so I'm not too handicapped without it but it's covered by applecare (just) so I thought I might as well get it repaired for free.

Always a good idea to exploit warranties... :)

@Heike I have an external one as well, but the software to use it seems to be missing. Reinstalling it is problematic without the internal DVD player.

@robjohn apple distributes most of their software via their app store nowadays so I have hardly any software on dvds/cds

12:40 PM

@Heike This is a computer from the 2000-2001 era most software for it is on DVDs or CDs

@JM I have 3 days left on my applecare so it was now or never.

@robjohn I'm surprised it's still working.

@Heike I have several Apple computers from 1997 or before that are still running.

Then again, my brother in law was still using his Power Mac G4 until last year or so

I am planning on upgrading sometime soon, so that my server can run more current software.

@robjohn That was his main reason for upgrading as well.

I guess it's getting harder and harder to find software that still runs on a power pc.

12:46 PM

indeed

I remember when they switched from Motorola chips to PowerPC. I was wary then.

I was also working at Apple.

even my other macbook which is 6 years old is too old to run lion.

11 years makes it even harder :-)

@robjohn Can't have been a bad move. They became quite big with their PPCs.

@robjohn I think I still have a Pentium II with FreeBSD installed gathering dust somewhere.

@Heike It was the right thing to do. I was just disappointed that all of my investment into 68K programming was going for naught.

I wrote a 68K assembler and used it for quite a bit of programming.

@robjohn I never knew there were 68k processors.

12:55 PM

@Heike Those were the Motorola chips that were used before the PPC.

@Heike High-end TI calculators use processors like those. Motorola's, IIRC.

The oldest Macs used 68000, then 68020 and 68030. I think the final revision was the 68040.

1:40 PM

@JM Do you perhaps have any suggestions what's the right keyword to search for to learn about adaptive sampling You are quite familiat with numerical methods, I think. Yes, that question is not very well written ...

F'x

@SjoerdCdeVries even weirder, we have 25 questions with score 25, and 25 answers with score 25 (here)

3

@Szabolcs I would look to see what people do for finite element adaptive meshing

@Szabolcs Unfortunately, I'm far away from my personal library, so I can't give concrete references. The usual terms are "recursive subdivision", and yes, "adaptive sampling" (though it seems that search is "noisy", as you said).

since they also want to minimize number of mesh cells, and have large mesh in "boring" regions, finer mesh in "interesting" ones

interesting usually defined by some metric changing a lot with increasing mesh

@EliLansey I don't know much about FEM, but don't they determine the resolution based on the shape of the boundary?

1:44 PM

@Szabolcs somewhat. but imagine a plain rectangular space with changing material properties

if the function varies greatly in a particular region, adaptive meshing should give a finer mesh

if it varies slowly, then it's a finer mesh

yep

that's right

now, this might end up being more computationally intensive

but, if you can come up with some computable metric that you want to get below some threshold, or minimal variaiton etc

you can probably use FE adaptive meshing approaches to sample your space more effeciently

this is sort of useless, but look at slide 33

ansoft.com/workshops/hfssinfoday/…

this may be more helpful

cs.rpi.edu/~flaherje/pdf/fea8.pdf

Alright, I'll try to search about FE

Yes, the second one has some interesting things

2:03 PM

@Szabolcs this one actually deals with discontinuities

4:21 PM

@RM Congrats!

Shouldn't that be dancing?

5:01 PM

@RM Congrats!

That makes for some scary statistics on the site, though. 4 of 5 10k users are non-mods. The next highest rep user is a mod with 4300 points less! Below that, there seems to be an exponential tail, maybe a bit fatter than exponential, but definitely a quick fall-off.

6:12 PM

@RM Congrats, @RM

@rcollyer Is that a good or a bad sign?

Thanks, @Eli @rco @hei :)

6:29 PM

@RM Congratulations!

@Heike I don't know. It can be interpreted as a select group of individuals outpacing everyone else, and whether or not this is considered "unhealthy" is open for debate. At this point, it is just an observation. Of course, the 12k folks have slowed down their contributions considerably ... so, likely we won't be seeing much from @RM very soon now.

@robjohn Hey do you know anything about group representations? I've been beating my head for a while now about this, and would like to see if it can be answered.

Deven Ware

6:44 PM

Hey guys I have a quick question about a differential equation in mathematica that I was hoping someone could help me with here, as its not really substantive enough to pose as a question on the main site

Essentially I'm just trying to get mathematica to solve the differential equation for a forced harmonic oscillator,

It seemed to me, like "sol1 = DSolve[{x1''[t] + 2 b x1'[t] + w0^2 x1[t] == a Sin[w t],
x1[0] == 0, x1'[0] == 0}, x1[t], t];"

should solve it, but then when I just define a function to be the solution to this and evaluate its derivative at 0 it doesn't give me 0, which was my initial condition

@DevenWare f[t_] = x1[t] /. First@sol1;

f'[0]//FullSimplify gives you 0

Sjoerd C. de Vries

7:00 PM

@r.m Congratulations!

Deven Ware

See I knew it wouldn't be substantive enough for a question on the site ;)

@SjoerdCdeVries Thanks (and @robjohn) :)

8 more days and then I can take a break :)

@RM why in 8 days?

Sjoerd C. de Vries

@RM Same here. Just in time for my vacation. Getting Internet abroad just to get fanatic is a bit... fanatic. Well, I did it before.

@robjohn 100 days — fanatic badges :)

7:23 PM

@RM Aha :-) I just passed 200 days; unfortunately, that means nothing.

When I was at 62 days or so, I worked on a problem for a couple of days. I didn't realize that simply working on a problem, which seemed online, did not constitute as being connected. I was a bit upset that I had to start over.

I am at 202 days consecutive :-)

P. Fonseca

10:43 PM

For those interested in a Mathematica speed question: lwsffhs.wordpress.com/2012/04/17/…