The h Bar

2:16 AM

@EmilioPisanty I also (apparently) encountered an oscillation bug with some special function in Mma. I need to revise my code but if you find some alternate to Mma (maybe this python thing) please let me know. Will post my own update when I get to it.

vzn

Synthesis and observation of non-Abelian gauge fields in real space / science mag

Scientist Smith YT

6:01 AM

@rob I know I promised to deliver the paper by tonight. I've just been caught up elsewhere. But I'll for sure have it to you by tomorrow night. Sorry for the wait.

@rob I wish there was more time in a day on earth.

Slereah

6:59 AM

@RyanUnger Riddle me this, Batman

If a geodesic is initially outside of a hypersurface, and then crosses it

Must it immediatly come out the other side?

Also same question for a $C^1$ curve

I'm pretty sure that it must, bc the tangent vector would need to be towards the hypersurface, and that it could only stay in the hypersurface if it was tangent to it as well

Slereah

7:48 AM

Probably doable by considering the local coordinates I suppose

Although...

Bump function along the hypersurface

ACH

Bloody thing

Slereah

8:48 AM

Heyyy

I got money

I should get that diff geom book

Jeff or whatever

amazon.com/Manifolds-Differential-Geometry-Graduate-Mathematics/…

That's the one

Rumplestillskin

9:45 AM

Hello all! Is anyone here familiar with the concept of first order averaging which is sometimes used in celestial mechanics? If so, can you recommend a resource that I can use to learn?

Ajay Mishra

1:09 PM

How to solve this problem of finding the current along the resistor by superposition theorem? The problem in proceeding through the superposition position is that on taking sources individually I am getting $0A$ across the resistor which implies that net current would be zero, which does't seem to be the case.

rob

@AjayMishra What's the potential difference across the resistor?

Ajay Mishra

@rob 1 Voltage, are you asking the question or intentionally pointing out to use ohms law?

rob

I'm asking why you're trying to use superposition instead of Ohm's law.

Ajay Mishra

Because my prof asked me to do so, and he asked the reason if I am not able to do proceed through that method.

Ryan Unger

@Slereah if the hypersurface is one-sided, then no...

Slereah

1:16 PM

@RyanUnger It is separating

but yes obviously not, alas

Ryan Unger

then yes

the tangent vector is continuous

rob

@AjayMishra So how did you decide that each source was contributing current 0A to superpose?

Ajay Mishra

For using superposition, Say If I am considering only $V_3$, then I have to replace $V_2$ by short circuit, after doing that it is obvious that there wont be current across the resistor as it is shorted.

rob

@AjayMishra I think I don't understand this technique the same way you do. Do you have a problem handy where superposition works in a way that you understand? You could explain it to me.

Ajay Mishra

Yes. Can you please tell me the problem with my approach?

As we are told to replace voltage source by short circuit, and current sources by open circuit, while considering only one source.

And We have been given a seeming legit behind this.

rob

1:26 PM

@AjayMishra Well, that fails in this case. So there's an assumption that hasn't been articulated properly.

It clearly fails in this case.

Ajay Mishra

Can you provide that, or any reference?

rob

So if you have another problem where the technique does work, we can figure out what's different here.

@AjayMishra I mean, the problem with your approach is that Ohm's law gives a different answer.

Ajay Mishra

Here is an example.

I am pretty impatient about the assumptions.

rob

@AjayMishra Here's something that you can try to understand what's happening.

Ajay Mishra

I guess, the problem with my approach of using superposition principle is hidden in the assumption that superposition principle only works in the case when the circuit is reducible to parallel/series combination when considering the individual source.

rob

1:35 PM

In your problem that doesn't work, you have two ideal batteries in parallel. But a real battery has some internal reassurance in series with the voltage source.

So, add in some small internal resistances in series with your two batteries.

Ajay Mishra

but what about the ideal case?

rob

Approach the ideal case asymptomatically.

Ajay Mishra

What do you mean?

rob

Start with internal resistances of 1 ohm, then 0.1 ohm, etc

Also play with what happens if the two internal resistances are different.

Right now your problem has a hidden degeneracy: there's no way to decide how much current should come from each battery.

A real circuit wouldn't have this problem.

So, remove that idealization and see what happens.

Abhas Kumar Sinha

2:21 PM

@AjayMishra Is that Linux? GNOME Environment looks cool na? I too use it :)

Semiclassical

A modified version of the non-ideal case is one I liked having students do as a lab: Replace the voltage sources with an adjustable power supply and a resistor in series, and reverse the polarity of one of the power supplies

the two power supplies would produce opposite currents in the middle branch if taken individually

so in particular you can look for what voltages on your power supply produce zero current/voltage in the middle

the condition you end up with is just V1/V2 = R1/R2, with the middle resistor R3 serving to determine how close to zero voltage/current you get when that ratio is not exactly right

Ajay Mishra

3:07 PM

@AbhasKumarSinha Yes.

@rob Thanks. :)

The East Wind

3:20 PM

Can someone help me with this?

5

Q: Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well described by \begin{align} V(x) &= 0, & 0 \leq x \leq L \\ V(x) &= \infty, & \text{otherwise} \end{alig...

user193319

3:42 PM

0

Q: von Neumann on the Hamiltonian

I'm reading von Neumann's book on QM and I'm slightly confused by a simple point. He writes, "The energy is a given function of the coordinates and their time derivatives: $E = L(q_1,..,q_k;\dot{q}_1,...,\dot{q}_k) = H(q_1,...,q_k;p_1,...,p_k)$. (This $H$ is the Hamiltonian function.) This...

classical-mechanics energy lagrangian-formalism hamiltonian-formalism textbook-erratum

Slereah

4:03 PM

The Lagrangian and Hamiltonian are rarely equal

Though they are for free particles

Slereah

4:14 PM

Not quite true but rule of thumb is $L \approx T - U$, $H \approx T + U$

bolbteppa

4:31 PM

@user193319 what von Neumann has to mean is that the Lagrangian 'represents' the energy, because the Hamiltonian is just a Legendre transformation of the Lagrangian, i.e. the Hamiltonian is just the Lagrangian just in new variables found by doing a Legendre transform, but simply equating it that was is not good, but the comment is just an aside in brackets in the book and he refers you to other books for more details there

ACuriousMind

5:56 PM

@Slereah They are not

They are functions on entirely different spaces and cannot be equal :P

Slereah

@ACuriousMind You know what I mean

mister picky

ACuriousMind

You're the guy asking about the formalization of mechanics as theories on fiber bundles for the last few days and you're calling me picky? :P

Slereah

Also i think the numerical quantities at the same times are identical

is my point

ACuriousMind

Not if you modify the Lagrangian by a total derivative ;)

bolbteppa

You're both pickier than me, if that helps :p

Slereah

6:11 PM

@ACuriousMind Dang it :V

ACuriousMind

I win!

Slereah

I give thee the physics crown

bolbteppa

6:38 PM

So the bosonic Nambu-Goto is $S = - T \int d^2 \sigma \sqrt{-\deg g_{ij}}$ for $g_{ij} = \partial_i X \cdot \partial_j X$, well in Green-Schwarz the superstring is (partially) described by $S = - T \int d^2 \sigma \sqrt{-\deg g_{ij}}$ for $g_{ij} = \partial_i \Pi \cdot \partial_j \Pi$, where $\Pi_i^{\mu} = \partial_i X^{\mu} - i \overline{\theta} \Gamma^{\mu} \partial_i \theta$, but putting conditions on the $\theta$ spinors gives the 5 different string theories...

There is a way to write the five superstring theories depending on different choices for $\Pi$, any idea how to write the five $\Pi$'s

3 given here in confusing notation

Superstring theory

Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory. == Background == The deepest problem in...

Or how do you interpret those 3 as giving the 5 properly

I guess you could ask how do you see the HE/HO in the heterotic one to distinguish that one into two

ACuriousMind

6:57 PM

@bolbteppa type I is simply type II with different boundary conditions, so it has no term of its own.

bolbteppa

Hmm, how does "the Type I string is derived from the Type IIB theory by taking it's world sheet parity even sector (and adding open strings and Chan-Paton to cancel anomalies)" affect the form of the IIB given in the wiki (or does it?)

bolbteppa

7:20 PM

This really is astounding that you can see the difference in terms of the basic action in the GS formalism

adamaero

8:20 PM

If I found the vector E-field intensity at a point, is the scalar voltage at that same point just the magnitude of E-field intensity?

enumaris

nope

the voltage is the path integral of electric field over some path

The E-field would be the gradient of the voltage (in electro statics at least)

adamaero

maybe I'm saying it wrong then

scalar electric potential instead of scalar voltage?

ACuriousMind

@adamaero The zero point of any potential is arbitrary, so it doesn't make sense to talk about its absolute value unless you've defined the zero point

adamaero

E.g., -180a_z V/m = E(0,0,0)...

ACuriousMind

But also, the electric field is the gradient of the potential and there is no relation between the magnitude of the gradient and the value of the potential at a point - the derivative of a function at a point is not related to the value of the function at that point.

adamaero

8:26 PM

The point is at (0,0,0)

enumaris

where's (0,0,0)?

ACuriousMind

@enumaris next to (1,1,1)

enumaris

seems legit

Maybe we can define (0,0,0) to be at the center of the universe

adamaero

enumaris

Right so if you found E, and then just took the magnitude, you don't get V

adamaero

8:29 PM

Ok

I see now I only did half of the problem

Thanks.

enumaris

np

adamaero

8:56 PM

oh, it's zero?

enumaris

9:16 PM

at some point V will be 0, but that's just an arbitrary definition. You are asked to calculate V(x,y,z)

it's not 0 over all (x,y,z)

Generally you choose V to be 0 "at infinity"

adamaero

but isn't it zero at (0,0,0)?

(otherwise my equation for the first part is wrong)

enumaris

uhm...it might be 0 at (0,0,0), but that requires doing the problem.

for part 1 thought you are asked to find V(x,y,z)

adamaero

yes, I mean for the second part

enumaris

Right, it might be 0...I'm a bit rusty tbh lol

I think since it's equidistant from a positive and a negative charge it'll be 0 for the "usual definition"

don't take my word for it though lol

adamaero

I'll type it up in latex since I don't have a phone to take a pic

Where 1.11e-10 equals 4*pi*(epsilon naught)

Aaron Stevens

9:42 PM

If I have a question that is asking about the various ways people non-dimensionalize differential equations, would that be better to ask here or on mathematics SE? The question is mathematical in nature, yet I would also prefer an answer that discusses how the choice of non-dimensionalization relates to the physical parameters of interest of the system.

I am particularly interested in reaction-diffusion equations at the moment

Novalium Company

@PM2Ring How much liquid soap? About a drop for a small plate (about 5 cm diameter) of water, naoh and tio2 evaporating?

enumaris

11:10 PM

oh man...my medium sized t-shirt that I have to wear for our grand opening today ripped...there are no more mediums so I have to wear a small...uncomfortable -.-

ACuriousMind

If the medium ripped it sounds like you should rather wear a large :P

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