The h Bar

10:10 AM

anyway, I need to go... see you all

@G.Bergeron adios

@Skyler sorry, work intervened ...

@JohnRennie np

I'm not sure what you're asking. The spinodal curve isn't generally symmetric ...

@JohnRennie i mean if were to let the spinodal decomposition occur and you took the bulk concentration along a cut of the material

10:13 AM

You mean what are the dynamics after the system tunnels through the barrier?

@JohnRennie basically at high temps hydrogen easily diffuses through Pd, but lets say you cool, you form hydrides in the Pd. So, if you have a concentration gradient at $t=0$ how would that time evolve as the spinodal decomposition occurs

as a function of position (1-dimensional)

obviously the microstructure will vary greatly from (about half of) its local neighboring structure but is there a correlated concentration flow I should be seeing at larger length scales

I don't know to be honest. I was normally working with systems at equilibrium.

@JohnRennie this is a pretty interesting problem tbh, hard to really wrap my head around it properly

btw, when determining composition of the microstructure for a spinodal decomp you use the spinodal lines in your construction right, not the phase transition lines

right?

user228700

@JohnRennie: I found this in my book: (Although I definitely wouldn't have understood this had you not explained it to me the other day)

I have read that article from head to toe, and my conclusion is that it seems to agree well with that nonorthogonal quantum state indistinguishability I heard in the seminar.
It is possible that the piece of info I heard in the seminar is one where they showed the state is real, and perhaps this article may have added to that is that the wavefunction is nonphysical.
I am not sure who is correct, but after running through the maths, I am kinda convinced by what the article say (especially when they define real as something on whether one can determinstically infer the event from an outcome, …

user228700

10:22 AM

Oh, nvm. It's taking too long. Internet very slow today :-/

@Skyler I don't think I calculated the microstructure. I was normally dealing with liquid systems where diffusion and mixing were fast. So you got macroscale phase separation.

@Kaumudi.H what was it?

@Kaumudi.H BTW do you have wireless Internet at home, or just through your phone?

Outside of science and more into social domains, a belief can be said to be something that is unphysical, yet its influence on whoever that tries to act based on it have a real impact to the world

@Skyler you're presumably working with solids ...

@JohnRennie yea

I am not saying that the belief itself somehow produce the outcome. Rather, it is those people who believe in that belief will perform actions in a way that actually carry impacts to the world. More concisely, people's action are guided by their beliefs

10:25 AM

the matter flow shouldnt really be THAT different here

since the H is pretty mobile

Ah, that's not an area I ever worked in. So I've mislead you about my vast knowledge of spinodal decomposition :-)

@JohnRennie hehe, all good, there are similarities for sure but the nuances can really be something

@Skyler Basically I was shaking liquids together and looking at the beaker to see if there were two phases.

Fascinating stuff actually. It was to do with depletion flocculation of dispersions by soluble non-absorbing polymers.

user228700

@JohnRennie About the elevation of boiling point...how it's related to entropy! :-)

@JohnRennie my new word for the day, flocculation

user228700

10:30 AM

@JohnRennie I do have WiFi, but ever since the cyclone happened, my "fast" connection has been down so we're using the slower one.

@Kaumudi.H OK. I asked only because you'll need WiFi to connect the laptop to the Internet. It is possible to connect a laptop through a phone, but it's very slow.

user228700

Yes, yes :-) Don't worry, we have WiFi- two different kinds, even!

Cool. Now you just need the laptop!

well, i had my new word of the day

i think that marks a good time to go to sleep

user228700

@JohnRennie :'-( WHAT IS TAKING SO LONG?!?!?!

user228700

10:34 AM

@Skyler Night :-)

All government agencies work on a time scale that has more to do with glaciers than everyday life. There's little to do except practice your deep breathing exercises :-)

user228700

>.< This is too much, hmph. How long are they gonna take to simply inspect it? Clearly, it's got almost literally nothing on it apart from movies.

user228700

I was s'posed to get it 2 days ago and the delay is not even because of the stupid cyclone.

user228700

@JohnRennie Bad move.

Actually that was in poor taste.

user228700

10:38 AM

:-P Sure, sure, by ur standards.

user228700

I've sort of lost hope that I'll get it, eventually, I'm not even kidding :-P

The customs guys probably have a stack of things they need to inspect. It will only take them a few minutes to check the laptop, and as you say there's nothing on it so it's easy to inspect. But the laptop will be sitting at the end of a queue.

@Kaumudi.H unnecessarily pessimistic :-)

user228700

No, I'll get it and all, but the excitement sort of wore away.

I know what you mean. At first I was checking the tracking page several times a day. Now I feel kind of ... meh

user228700

^ Exactly.

user228700

10:41 AM

@JohnRennie But they're reexamining it! They've done it once already. And they even called us and everything!

How they have written t effective

@Kaumudi.H Re-examining means examining it properly. At first they would have just opened the box to see what was in it. That's the point at which they would have phoned you.

user228700

Ah, depend on koolman to post random black-and-white pictures from time to time :-)

user228700

@JohnRennie Right. Oh, well.

@Kaumudi.H what do you mean by that :/

10:43 AM

It's just as well I left the battery fully charged or they wouldn't have been able to turn it on (the power supply currently has a UK plug) and that would have made they very suspicious.

This is not true. however I am still trying to formalise it

user228700

@koolman I meant that we can depend on u to keep the conversation going because u ask questions :-)

user228700

@JohnRennie Yeah, I actually did think of that. Thanks! :-)

Should I ask it later

user228700

What? No. Dude. I was appreciating ur enthusiasm!

10:48 AM

Ohk fine

@JohnRennie could you help me out

Ohk fine

Actually I'm not sure how to calculate the effective half life when you have two processes occurring. I'll have to think about it.

Ohk

user228700

Yeah, I'm thinking too...

user228700

I would've done it by multiplying the probability of occurrence of each with the half life but I don't get 1/6 when I do that. I guess there is some flaw in that line of reasoning...

Yeah i have also done it by some other way

But want to know how to write t effective

user228700

11:04 AM

What other way have u tried?

Got the answer

Effective half-life

In pharmacokinetics, effective half-life is the rate of accumulation or elimination of a biochemical or pharmacological substance in an organism, the biological half-life, when the kinetics are governed by multiple independent mechanisms. This is seen when there are multiple mechanisms of elimination, or when the drug occupies multiple pharmacological compartments. It reflects the cumulative effect of the individual half-lives, as observed by the changes in the actual serum concentration of a drug under a given dosing regimen. The complexity of biological systems means that most pharmacological...

But could not understand one thing

In textbook solution what is l$_A$ and l$_B$

11:19 AM

@koolman I have to confess that I don't understand what the book has done. If you calculate $t_{eff}$ using: $$t_{eff} = \frac{t_a t_b}{t_a + t_b} $$ then you get the same answer $t_{eff} = 1/6$. But I don't understand the calculation in your book.

No problem thanks for trying @JohnRennie

12:14 PM

hello everyone

yo everyone

@heather no I don't read private mesages on the site

@Mew, oh, okay

I can access them though if I go into the database directly but will only do so if I suspect auser is spamming/abusing the feature

ah, gotcha. no need, then.

Swapnil Das

Hi

12:29 PM

gday @SwapnilDas

@SwapnilDas, o/

what is o/

Swapnil Das

Hey @heather and @Mew

Yeah same question^^

What are guys up to nowadays?

hi, like if you take the o as a head and the / as an arm, it's like waving hello at someone

oh yeah i see it now

@SwapnilDas just stuff

@SwapnilDas did you know peak phosophorus may be approaching

12:34 PM

@Mew sounds like an end-of-world prediction =P

lol na

food production would dramatically reduce tho

we may run out of phosphorus even before we run out of oil and natural gas

Swapnil Das

Oh. Idk

yeah they don't want to panic the popuation

physics.qandaexchange.com/?qa=540/…

^having trouble with getting my mathjax to show up right...

any idea what's wrong @Mew?

i put the end dollar signs in in my edit; now they're not showing.

12:50 PM

Associativity mapping interpretation:

Def. 1. All elements in a Cayley table

Given a magma $(M,\circ)$, Let $S=\{s_1,s_2,\dots,s_n\}$ be the ordered set obtained by imposing an order $\mathcal{O}$ onto M. Then the cayley table $T$ is given by $T=\{\ x\lvert \forall (a,b) \in S \times S, a\circ b=x\}$. The tranpose is defined by $T^\textrm{T}=\{\ x\lvert \forall (b,a) \in S \times S, a\circ b=x\}$.

Def 2. Rows and columns and collections

A row $R_i \subset T$ is given by $R_i= \{\ x\lvert \exists i \in S,\forall (a,i) \in S \times S, a\circ i=x\}$. Similarly, a column $C_i=\{ x\lvert \exists i \in S,\forall (i,b) \in S \time…

(proof to be checked by maths guys. Hopefully I have not made too many errors to make it not understandable to them)

@heather latex fixed

How do you solve an equation like $x+y+z (\mod 3) \equiv 0$ for all $x$, $y$, and $z$ such that $x, y, z \leq 9$?

@Mew, thank you

it seems sometimes you need to put a "\" symbol bofore the underscore for the latex to render

ah, okay.

good to know

did you reopen the question?

yeah there is a bug wher you can't edit a question unless it is open

so i had to reopen it to test the latex

12:58 PM

okay, i thought that was just for non-mods. also good to know

@heather You could construct a table

@Mew, yeah, I should just write a program to do it, but I want to know if there's some less plug and chug way to do it.

must x,y and z be integers?

yes, and preferably, x, y, and z must not equal each other.

are x,y and z all >= 0?

do you allow negative integers?

1:06 PM

x,y,z are all > 0 , but none are equal to 0

ok

so 1-9 is the range, I suppose

right

the equation can be re-written as x + y + z = 3n where n is an integer

right

x + y + z = 3 has no solution

1:07 PM

right

x+y+z=6 has one solution

no

it has 3 solutions

oh...duh x=1, x=2, or x=3 and so on

sorry 6 solutiosn

i mean the solutiosn are:

for x y and z respectively:?

1, 2, 3

2, 1, 3

3, 1, 2

3, 2, 1

1, 3, 2

2, 3, 1

hmm, okay

so six solutions

1:09 PM

interestingly, the set 1,2,3 is the only thing that matters, not the different rearrangements of it, but that's still interesting

ah k

Slereah

So whatever happened to the physics talks

so for x+y+z=9

3 solutions i think

(excluding permutations)

6,2,1

5, 3, 1

4, 3, 2

hmm, thanks for your help @Mew, I'll keep thinking about this, I have to go

1:12 PM

I think going through all the options is the only way to solve this problem

(other than graphically since each value of n is a plane in 3d splace)

laterz

@Slereah watdya mean?

2:10 PM

What is the definition of temperature?

Q: What's the most fundamental definition of temperature?

7

What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general cases as Black Hole's Temperature, Accelerated Frame's Radiation,...

@JohnRennie thanks

2:33 PM

Yé! Done for now!

@JohnRennie wow

@JohnRennie Hey, by the way, is the guy I was talking too earlier always like that? He seemed a bit on the nerves...

@G.Bergeron AakashTomar you mean?

Yes

He's new around these parts. I haven't spoken to him before.

ok

2:57 PM

@Secret There seems to be a problem with your definition and your use of set constructor notation.

Hi @G.Bergeron and @JohnRennie

@JohnRennie how does the average KE of water depend on the temperature?

@DHMO It's not as nice as a gas

I know

At the mircoscopic level?

You would need to evaluate the degrees of freedom of water

2:59 PM

well is there any results on this?

There certainly is, but I was trying to think about what would be the best way to approach the question

@Danu Afternoon

John may have something to say as he worked with colloids

The new guy ignoring me doe :(

How are you doing, John?

@DHMO I'm not sure that the kinetic energy of a water molecule is a useful concept.

3:01 PM

@JohnRennie well i'm just curious

@JohnRennie I would guess under some energy level, they act like bound states and then can be considered free at higher energy

@Danu Life goes on. How are you getting on now you've washed your hands of us physcists? :-)

@JohnRennie Really great. I'm learning lots about beautiful geometry.

Although with an extremely short mean free path meaning highly interactive

I'm starting to get a really nice understanding of submanifolds of $\Bbb CP^n$ (complex projective spaces)

3:03 PM

So I guess highly interactive is indicative that the position/speed of water molecules are not the good coordinates to do statistical mechanics in

Because statistical mechanics assumes almost free particles in general

Today there was a tiny application of the ideas of the microcanonical example

@DHMO The motion of a water molecule is more like the vibrational motion of molecules in solids than it is like the motion of molecules in gases.

You could calculate the average energy per molecule

On how to count certain partitions (I learned in stat mech how to think about it, in the case of energy levels over which one needs to distribute "packets")

@JohnRennie but they slide past and collide with each other

3:05 PM

But they interact with each other constantly

@DHMO the translational motion is very slow compared to the vibrational motion because the mean free path is basically the same size as the molecule.

meaning statistical mechanics with those degrees of freedom is not the good approach

In gases the mean free path is many times the size of a molecule.

@JohnRennie that's new, thanks

@Danu What are you doing now?

3:06 PM

@G.Bergeron Studying geometry.

This was for the Veronese embedding $\Bbb CP^2\hookrightarrow \Bbb CP^{N(d)-1}$, where $N(d)$ is the number of partitions of $d$ into three summands ($d+1$ choose $2$, by the stat mech thing)

@DHMO To define a statistical ensemble you kind of assume that the particles don't interact, but still interact enough to bring the system to an equilibrium

In a very broad sense, too much interactions means that the particle view is not really pertinent.

@G.Bergeron i'm not really looking for the ideal case

@DHMO It's not a question of ideal case at all

If two particles are constantly interacting to the point of being stuck together, can there momentum be independent of the one of the other particle at least in principle?

How do you derive the quantum microcanonical distribution? I understand the classical distribution derivation using Liouville and additivity and phase space dimension 2s - 7 so that you need a delta function, but the quantum distribution?

There is a gap of logic there I just f***ing realised :(

2s - 7 ???

3:11 PM

Classical one sketched in 3 lines on page 7 arxiv.org/pdf/1103.4003.pdf

Or 6N - 7 if you prefer

s generalized coordinates, s generalized momenta, 7 additive integrals of motion, thus we live on a 2s - 7 manifold but integrate over a 2s phase space, so we have an infinite integral and need delta functions

@bolbteppa I don't even see the number 7 on that page besides in year and the page number...

Oh sorry, page 8!!!

Why should there be exactly 7 conserved quantities?

(I was half-way scrolled between page 7 and page 8 :p)

There are 7 additive conserved quantities

Energy, momentum, angular momentum

...charge, isospin, ...

whatever your model gives you

ok, maybe not isospin, not additive

These are just the ones coming from Poincaré/Galilé

Also this text has some not quite true passages

Slereah

3:21 PM

Hypercharge and color are conserved :p

and...

what's the third one

Thus avoiding any ergodic hypothesis, as there is no
ad-hoc introduction of any probability distribution. The
ρactual(p, q) is the actual probability distribution in the
system’s phase space from its tempora

Slereah

weak charge?

This not true

He's basically using the ergodic hypothesis to say that you don't need the ergodic hypothesis

Saying "It is obvious by the definition (6) of probability that the
statistical averaging (equation (7)) is exactly equivalent
to the infinite time averaging"

@G.Bergeron The book he's taking this from says: "It should be emphasised once more that this distribution is not the true statistical distribution for a closed system. Regarding it as the true distribution is equivalent to asserting that, in the course of a sufficiently long time, the phase trajectory of a closed system passes arbitrarily close to every point of the manifold defined by equations (4.3). But this assertion (called the ergodic hypothesis) is certainly not true in general."

But then the assertion is false

or I should say

He's hiding all the complexity behind that magical function

3:26 PM

What magical function?

$\rho_{actual}$

What I can say is, this is focusing on classical statistical mechanics, which is illogical as fundamental physics because of the entropy being defined only up to a constant

@JohnRennie what is a liquid and what is a gas? why is there a discrete transition? what is the transition in terms of molecules?

Sorry for asking three questions at once

The schematic derivation 1 - 6 of the classical microcanonical distribution is the interesting thing

@bolbteppa It's not that. He's basically assuming ergodicity on a coarsed grained phase space

Why not just use ergodicity?

3:30 PM

From the book he's discussing: "In the discussion of the foundations of classical statistical physics, we consider from the start the statistical distribution for small parts (subsystems) of systems, not for entire closed systems. This is in accordance with the fundamental problems and aims of physical statistics, and allows a complete avoidance of the problem of the ergodic and similar hypotheses, which in fact is not important as regards these aims."

Fair enough, but it's seems like suggesting that integrable systems don't exist (because you can coarse grain them into oblivion)... Just my view

You can just use the constraints given by the microstate and by Langrange multiplier you can find the microcanonical ensemble assuming some form of molecular chaos/statistical independence

@bolbteppa But to answer your question, with quantum mechanics, all hell breaks loose

So the derivation of $\ln (\rho_n) = \alpha + \beta E_n$ holds for classical and quantum distributions, but if you simply exponentiate to get $\rho_n = e^{\alpha + \beta E_n}$ you are, in the classical case, treating $\rho_n$ as a function of 2s variables $(p_i,q_i)$, but due to the integral of motion $E_n$ we should have $\rho_n$ as a function on a $2s-1$ hypersurface $H(p,q) = E_0$, not on all of the $2s$ phase space, so we correct for this by setting $\rho = A \delta (E - E_0)$.

Yes, that's introducing a lagrange multiplier, basically

The question is, the quantum case, why can't you exponentiate, why do you need the delta function?

Interesting

delta function?

that's in the classical case you just said.

3:38 PM

'To formulate mathematically this "quantum microcanonical distribution" we must use the following device. The energy spectra of macroscopic bodies being "almost continuous", we make use of the concept of the number of quantum states of a closed system which "belong" to a particular infinitesimal range of values of its energy. We denote this number by $d \Gamma$." ... $d w = A \delta (E - E_0) d \Gamma$

ok

That is the quantum microcanonical distribution, also as a delta function

But the logic of why you need a delta function is not clear at all

but that is just enforcing a constraint, I don't see the impact to the derivation

We are not on a $2s-1$ hypersurface in a 2s phase space, we are using a density matrix

That's what is the infinitesimal density of states

Yes I know

That doesn't mean there can't be constraints

You just replace the constraints by $Tr(\rho O)$

where $O$ is the relevant observable corresponding to the constraint

3:43 PM

So I have $\ln (\rho_n) = \alpha + \beta E_n$, and I say to myself, I know that energy is conserved. Thus, $\int \rho$, or rather $\mathrm{tr}(\rho)$, should somehow mess up, forcing me to write it as a delta function. But I don't see how exactly

Your looking for the extremum solution in the space of possible density matrix under some constraint

In the case of microcanonical it's constant energy

so that constraint is a delta function

Giskard42

Hey guys, sorry to barge in here...I've got a little electrostatics problem I'm trying to sanity check. Can I run it by you?

@bolbteppa I personnally think that the complexity theory approach to probability, and it's application to statistical mechanics is the very best in terms of intuition

Let me put it this way, does the density matrix live on a hypersurface due to energy being conserved?

I mean, the density matrix is a function of position in my mind

basically yes

3:55 PM

But of course we are in the occupation number formalism

So I'm not sure what the domain of the density matrix actually is :p

because you posit an isolated system

From what you've said, it seems as though Landau's approach is a complicated way of doing what all the books do :p

@bolbteppa All possible pure quantum states and statistical mixtures of such.

@bolbteppa The point is not how you calculate, its more on the foundations of stat. mech.

Your paper covers those issue

I just disagree with some phrasings

@Giskard42 yes

@DHMO The transition is not always discrete, it can even disappear beyond the critical point

Giskard42

Say I've got two plates of metal, and I charge them up, V across them, q on each plate.

Now, I vaporize one of the plates.

@bolbteppa It covers at the end the hell quantum stat. mech can bring in... It kind of shouldn't work

@Giskard42 ok

Giskard42

3:59 PM

(doesn't matter how, I just boil it away)

What happened to the charge on that plate?

So $\rho$ acts on a vector space, where the vectors represent the occupation numbers of stationary states of the entire closed system, and taking the trace of $\rho$ should give 1, but conservation of energy somehow makes this an infinite number, and so we should use delta functions?