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Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon Let's say the fluid is water.
Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon I am aware of this equipartition theorem. But I am worried that the mean deviation along a single dimension, $\langle x_j (t) ^ 2 \rangle$, changes with the number of dimensions, due to a change in effective viscosity, for example. This would make your argument invalid.
Feb
23
comment Dependance of diffusion coefficient on size?
Yes, now I get it, $u$ is $\sqrt(T/M)$ (which the typical velocity in Maxwell-Boltzmann distribution, up to some constant factors).
Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon So $\langle x(t)^2 \rangle$ is proportional to $n$? I know about the equipartition theorem, but maybe other things change when going from 3-dimensions to 2-dimensions, like the effective viscosity.
Feb
23
comment Dependance of diffusion coefficient on size?
Sorry I missed your edits for the last 5 days, but please @notify me in comments. Thanks :)
Feb
23
comment Dependance of diffusion coefficient on size?
Your $Re$ is a Reynold's number? So $u$ is not the instantaneous velocity of the sphere, it is just an estimate of the maximum magnitude of this velocity, which is a constant. If I am correct, you should maybe clarify this a bit in your answer
Feb
23
comment Dependance of diffusion coefficient on size?
So $u$ is the drift velocity? I don't understand why there is a drift velocity here. There isn't a drift velocity in 3-dimensions. Basically this is saying that the diffusion coefficient depends on the velocity of motion of the particles, i.e., it is not a constant, so Fick's law doesn't apply in 2-dimensions? I don't understand this
Feb
16
comment Dependance of diffusion coefficient on size?
What is $u$, in the last line?
Feb
16
comment Dependance of diffusion coefficient on size?
What is the paper by Oseen with the 2-dimensional drag coefficient?
Feb
14
comment Dependance of diffusion coefficient on size?
No, in your expressions $\eta_D$ increases with $a$ in 3D, but decreases with $a$ in 2D.
Feb
14
comment Dependance of diffusion coefficient on size?
hmmm, also, the diffusion coefficient decreases with $a$ in three dimensions, but increases with $a$ in three dimensions... that's weird. Are you sure?
Jan
25
comment Why are four-legged chairs so common?
What if you take into account the error in leg lenghts? In 4-legs, one of the legs can be shorter/longer than the others.
Jan
25
comment Why are four-legged chairs so common?
Moreover, 4-legs have the problem that when one leg is a bit shorter/larger, it will be unstable
Apr
2
comment Could any object have zero mass?
Can this invariant mass be negative?
Jun
3
comment Why is the application of probability in QM fundamentally different from application of probability in other areas?
In two words: Bell's inequality.
May
23
comment Minimum connectivity required for mean field to be a good approximation?
@Qmechanic Ok. You can edit it out if you like.
May
23
comment Minimum connectivity required for mean field to be a good approximation?
@YvanVelenik I am mainly interested in good approximate values of the free energy and the magnetization. I edited the question to add this. If you are willing to add some details, you should post your first comment as an answer.
May
9
comment The “replica trick” initial formula?
@AntonioRagagnin fixed.
Mar
18
comment Double double-slit experiment
As for the photon that you do measure, it loses the entanglement with the other photon after the measurement. And you lose the interference pattern after determining the slit through which it went.
Mar
18
comment Double double-slit experiment
I don't understand your argument. Why you say that the spatial superposition is built up during the evolution of the photons, and why this loses the entanglement? The fact that there's an uncertainty $\Delta x$ means that the second photon (the one you didn't measure) is in a superposition of states spreading through some spatial region on the order of $\Delta x$. If this spatial region is large enough as to include both slits, you have an interference pattern.