Physics Forums

Can the crystal particle expand?

mazwan — Thu, 20 Jun 2013 08:52:58 GMT

1. The problem statement, all variables and given/known data

With increasing the temperature, can the crystal particle expand? Actually, what really happen to the structure when increase the temperature? Why its look bigger size compare to actual size. Does it mean the crystal of particle expand? or something happen to the particle? Can you explain for me what actually happen?

2. Relevant equations

3. The attempt at a solution

The Movie: Gravity

AnTiFreeze3 — Thu, 20 Jun 2013 08:40:42 GMT

I felt I had to be a little explicit with the title, because just "Gravity" is a little too vague for a forum like this :smile:

Thoughts? I think it certainly has a nice 2-person cast with Clooney and Bullock, but I'm wondering if the plot might be too limited; this whole movie appears to cover what happens in about 2 minutes in 2001: A Space Odyssey.

Double-slit experiment, thought experiment

tomwilliam2 — Thu, 20 Jun 2013 08:09:49 GMT

I'm trying to understand the implications of the double-slit experiment, and I have been considering what QM theory would predict as the outcome of the following experiment:

Consider an electron gun firing electrons towards a detection screen two metres away (gun perpendicular to screen), and there is a blocking partition halfway between the gun and the detection screen. We shall consider the screen and the partition to be infinite planes, for simplicity.

Now, we open up a slit in the partition, directly in front of the gun, whereupon we start to see electrons being detected on the screen. Now I know that if a second slit is opened up, the familiar diffraction pattern is seen, consistent with wave-like behaviour, and we can't really state which slit the electrons have travelled through. But what if the second slit is opened up, let's say, 500m along the screen from the first? I understand that any diffraction pattern would probably be almost unnoticeable, but let's say the instruments are extremely precise. My thinking is this: if the electrons "passing through" the second slit were having to travel sqrt(500^2 + 1) metres before getting to the screen, then at an average speed of, say 10^6 m s^-1, wouldn't we already notice some difference in arrival time? If the individual blips detected on the screen differed greatly in travel time, wouldn't this give us a clear indication of which slit the electron had travelled through?

Thanks in advance, this subject is a little freaky to me!

Modified diffusion equation PDE

Clouis523 — Thu, 20 Jun 2013 08:07:50 GMT

Hi I'd appreciate any help on identifying the type of PDE the following equation is...

*This is NOT homework, it is part of research and thus the lack my explanation of what this represents and boundary conditions. I have a numerical simulation of the solution but I'm looking to have a math win on my thesis.*

dC/dt = D(del^2(C)+[itex]y_{1}[/itex]del(σ))

I've used seperation of variables into a space function and a temporal function (which I've already solved since it's the exact same as the standard Diffusion equation). Long story short this is very similar to a Sturm-Louisville Problem but instead of getting a characteristic equation with lambda squared times the space function I end up with after subbing in the conditions for sigma.

d^2U/dr^2+(1/r)dU/dr+(ψ*δ(r-[itex]r_{0}[/itex])+λ^2)*U=0

I have two issues with getting a solution here first is the dirac delta before the eigenvalues (lambda) and second is that I have no idea what type of PDE this falls under other than it is very similar to S-L problems. I'm positive that the solution will include bessel functions (as you can probably tell this is in cylindrical.

If someone could point me to the type of PDE or even better a text that I could reference for this type's solution method you would make my day.

Cheers.

Proof about sum of integers

cragar — Thu, 20 Jun 2013 07:44:54 GMT

1. The problem statement, all variables and given/known data
Prove that every integer bigger than 6 can be written as a sum of 2 integers
bigger than 1 which are relatively prime.
3. The attempt at a solution
Ill first look at the case where our number is odd.
Let x be an odd integer. I will just add (x-2)+2=x since x is odd so is x-2 and 2 is even
so x-2 and 2 are relatively prime.

Now Lets look at the case where our number 2y is even.
and y is even. 2y=y+y=(y+1)+(y-1) now since y is even y+1 and y-1 are odd. and y-1 and y+1 are odd numbers separated by a factor of 2.
Lemma 1: Let n be an odd number. Lets assume for contradiction that n and[itex] n+2^x [/itex] have a common factor so it should divide their difference but [itex]n+2^x-n=2^x[/itex] but n and [itex]n+2^x [/itex] do not have a factor of 2 because they are odd.
so y+1 and y-1 are relatively prime by lemma 1.

Now lets look at the case where 2z=z+z where z is odd.
we will just look at 2z=z+z=(z+2)+(z-2) since z is odd z-2 and z+2 are odd and they are odd numbers separated by a power of 2 so they are relatively prime.

Rolling without slipping

andyrk — Thu, 20 Jun 2013 07:22:53 GMT

Why don't we consider radial acceleration on the lowermost point in rolling without slipping?

Expanding/ Stretching Universe

Alonzo.nieves — Thu, 20 Jun 2013 06:19:48 GMT

Hello all. I'm quite new to this forum. I was wondering about the expanding or stretching universe. Can someone please tell me if my thoughts are correct and if not please correct me.

The expanding universe. A common definition of the universe is everything. But if the universe is expanding it has to be expanding into something. Expanding into a larger universe maybe? But I believe that a more accurate description of the universe is stretching. You can see the universe as a collection of galaxies a certain amount away from each other. A theory I have developed is that maybe the universe is just stationery. But as time passes the space between each galaxy and celestial bodies slowly move away, this shows the stretching of the galaxy. According to Einstein's theory of general relativity we have to think of space as a much more complex entity not just a vast amount of nothingness. Incorporating his theories of general relativity space should be capable of "bending" and "stretching".

If the space between celestial bodies are moving then what about the atoms, the building blocks of all matter. Maybe the spaces between them too are moving apart from each other. Or maybe its just the larger objects. Is the universe really powerful enough to rip the very fabric of everything we know into nothing? Does anyone know any recent research on this?

Thermodynamics perfect gas law

tigertan — Thu, 20 Jun 2013 05:56:19 GMT

1. The problem statement, all variables and given/known data

Air inside a sealed tin can is initially at a pressure of 200 kPa and temperature of 20 ◦C. The tin can is
known to burst at a pressure of 500 kPa. If the pressure is raised through heating, at what temperature will
it burst?
If you used an air compressor to pump up the can to high pressure, would the temperature before bursting
be the same? If not, why not?

2. Relevant equations
Pv=RT
P1/T1=P2/T2

3. The attempt at a solution

I'm confused. Why can't I just use the perfect gas law with constant volume to solve for the second temperature?

I get a result of 459.5degrees but solutions state that the answer should be 483 degrees.

Motion of Reference Frames wrt each other

srjoglekar246 — Thu, 20 Jun 2013 05:36:27 GMT

I am currently working on a Python script to simulate motion of reference frames wrt each other, and I need some help with the math.

Here is the problem statement-

Suppose I have a frame A
A frame B
frame B's origin has pos-vector P_B,A (function of time) wrt A in frame A
frame B is oriented at angle τ (function of time) wrt Some axis of A (Call it ψ )-I have the dcm for this transformation

Now, I have these two things-
1) Basis vectors of B
2) a pos vector (x, y, z) in B

How do I map the above 2 to frame A? As in, the math of the complete transformation

Deriving terminal velocity

spacetimedude — Thu, 20 Jun 2013 05:24:04 GMT

Hello PF,
I have once simple (well, not so simple for me) question.

I'm trying to derive an equation for the velocity of a falling body with accordance to terminal velocity.

The equation incorporates drag proportional to the speed.

m*dv/dt=mg-bv

and

mg/b=terminal velocity v_t

So the steps I took were:

m*dv/dt+bv=mg

(m/b)*(dv/dt)+v=v_t

dv/dt=(b/m)(v_t-v)

dv/(v_t-v)=(b/m)dt

Integrating both sides would give
ln[(v_t-v)/(v_t)]=(b/m)t

But the textbook says that I'm supposed to get negative (b/m)t on the left side.

Have I made a mistake on the integration part?

Any help will be deeply appreciated.

Continuity equation and air flow

Bill Nye Tho — Thu, 20 Jun 2013 05:16:06 GMT

Although continuity equation is often part of fluid mechanics, does it have an application in air flow? For example, lets assume we have a frictionless air duct where air is introduced at a constant velocity and temperature. If the air duct varies in dimensions will the flow rate at the end point be equal at all points along the duct?

Diffusion of a species through a sphere

chatoma — Thu, 20 Jun 2013 05:12:51 GMT

Hi guys,

This is my first post here, this place looks like a great resource. Well, jumping straight in, I have a couple of questions on diffusion.

At work, I did a couple of experiments with Ion Exchange Resins. Not getting the results we wanted, my boss asked me to do an analysis of diffusion in two scenarios: through a simple "plate" (in 1 dimension), and through a sphere (in 3 dimensions).

Now, I am a Chem Eng, so this should be easy, but I have found myself struggling way more than I should with this topic; its a bit embarrassing at this point. For the first scenario, I used Ficks First Law, and I think that process was rather straightforward.

However, for the second scenario, I am completely stuck. So basically, I'm looking at diffusion in 3 dimensions; from the center of the sphere and to the outside. I don't think I need to complicate myself too much with technical details, so I'm assuming steady-state and I want to use Fick's First Law again. As I understand it, for 3 dimensions, Fick's Law is: J = -D∇C (where J=Diffusive flux, D=Diffusion Constant, C=Concentrations).

Now if I'm correct, this would work out as: J = -D(∂C/∂x + ∂C/∂y + ∂C/∂z). Would you guys agree, thus far, I am on the right track? If so, now the embarrassing part is that I'm not sure what to do next. That means, I'm not sure how to solve for J. Also, I was going through some reading material, and I saw that using spherical coordinates might make my life easier; is that correct?

Although its been two years, I can't believe I've forgotten so much about mass transfer...I'm actually kind of glad I'm getting these assignments so that I can brush up on this essential stuff. But anyways, any help is appreciated, and any clarifications/questions, I'll try to answer them in a timely fashion. Thanks!

chatoma

PhD astronomy in Australia

subny — Thu, 20 Jun 2013 05:07:55 GMT

Hi

I am a Physics masters student from India in a college in Texas.

I want to pursue a PhD in Astronomy (observational/radio) Australia.

I have heard Australia is very good at obs astronomy - however google searches are revealing a lot about the telescopes and other facilities there but not much about the names of the Universities that offer a doctorate in Radio astronomy.

To that end I want to approach the forum members for some help - does anyone of you know which are the universities in Australia to which we can apply for a doctorate in Astronomy.

Thanks

Photons being affected by pseudo forces

deep838 — Thu, 20 Jun 2013 05:02:23 GMT

I was reading a book called "Hyperspace", by Michio Kaku, and there he gave a sort of introduction to general relativity. Well its not at all technical, just for reading and knowing...

There he claimed that space is curved because light rays will take a bent path inside an accelerating spaceship.

But he didn't explain why light rays would bend in the first place!

Differential Equations Question

Miike012 — Thu, 20 Jun 2013 04:58:00 GMT

Can anyone tell me how the book arrived at the portion that I underlined in the paint document?

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