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visits member for 2 years, 10 months
seen Oct 6 at 23:55

Sep
21
comment Density of States vs Dispersion
en.wikipedia.org/wiki/…
Aug
26
comment Looking for a simple proof of symmetry of linear susceptibility tensor
I think it is. millersville.edu/~jdooley/macro/derive/elpol/alphasym/…
Aug
21
comment Looking for a simple proof of symmetry of linear susceptibility tensor
@ValterMoretti I agree with the math, but disagree with the interpretation. This whole $P\propto E$ relation is a linear response theory. It is derived the other way around: The energy, to leading order in $\vec E$, is given by $U\approx U_0 +\chi_{ij}E_iE_j$. The lack of a linear term is because $U$ is minimal when $\vec E=0$. Therefore, WLOG $\chi$ can be chosen to be symmetric. $P_i$ is defined as $\partial U/\partial E_i$.
Jul
14
comment Why plane stress condition is taken for thin plates
As I wrote in my answer, this is not a proof, nor a consistent derivation. Plane-stress equations are an APPROXIMATION, which is not exactly valid. Specifically for the profile you suggested, it is not enough in order to determine whether it is a possible solution. You need the other stress components, and if they satisfy the force-balance equation $$\sum_j \frac{\partial \sigma_{ij}}{\partial j}=0$$ then you're good.
May
17
comment How can I determine whether the mass of an object is evenly distributed?
This is true, but the OP only wants to know if it's evenly distributed or not, which is an easier prblem than "find the distribution". For example, you could measure the moment of inertia around an axis, and compare that to what you'd get if it were homgenously distributed. If there's a discrepancy - you can catch it. I wonder whether one can find a counterexample of a body that has the full tensorial moment of inertia of a homogeneously distributed one, but is actually not.
May
2
comment Will a hole cut into a metal disk expand or shrink when the disc is heated?
@jamesdlin I agree that it's heuristic and as such one could argue differently. The real solution is sketched by David Z. If you want more justification, you can say that the thermo-elastic equations with $T=const$ and stress-free BC will result in a stress free configuration (easily verified). Therefore, having the disc in place or cut out has no effect on the surrounding - the "interaction" is the stress, and therefore stress free boundary conditions are equivalent to not having a disc at all. Again, I stress that this can be solved analytically and then there's no ambiguity.
Feb
7
comment When driving uphill why can't I reach a velocity that I would have been able to maintain if I started with it?
@Gugg In my experience, the phenomena is pretty common. Also, there are surely many other factors involved (the computer regulating fuel injection, exauhst, wind/friction dissipation...) so this simplified model does not capture the difference between "hard" and "impossible".
Feb
7
comment When driving uphill why can't I reach a velocity that I would have been able to maintain if I started with it?
@dmckee I agree, but I think the car is not yet at this regime.
Feb
7
comment When driving uphill why can't I reach a velocity that I would have been able to maintain if I started with it?
I'd say that the newtonian-gravity is not relevant.
Feb
6
comment How does the correlation length of weather emerge?
I agree, but that's a totally different effect. It would be awefully wrong to say that the typical length-scale of the waves in lakes stems from the lake size, scaling-wise.
Feb
6
comment How does the correlation length of weather emerge?
The wave length in lakes is determined by the lake size? This sounds weird to me. The wavelength is typically a few orders of magnitude smaller.
Jan
27
comment Scattering from a box potential of width $L$ doesn't reproduce a step potential in the limit $L \rightarrow \infty$
@Joe Well, unless your function grows exponentially for large $x$, you have no freedom in choosing the sign of $k$.
May
24
comment Crushing a magnetic field
I would suggest to add a "mumbo-jumbo" tag.
May
1
comment A conceptual problem with Euler-Bernoulli beam theory and Euler buckling
@Raskolnikov No, it has 2 derivatives less.
Apr
2
comment Power laws and deterministic systems
This is a totally different question. The answer, in short, is that a deterministic system can be described deterministically. Very often, however, you can't do that because the system has too many degrees of freedom (e.g. sand-piles) so that a full deterministic solution is both infeasible and useless. In such cases, a probabilistic description usually casts more light on what is going on.
Apr
1
comment Deriving the Lagrangian for a free particle
I think the best advice one can give you is don't read Landau & Lifshitz. They are great books for reference, but practically impossible to learn from. If you're into analytical mechanics then Goldstein is a good place to start, or Arnold, if you're more interested in the mathematical aspects.
Mar
29
comment Is there analysis library for stress-strain data?
In that case, send my your credit card number and I'll do it for 500$!
Mar
29
comment Is there analysis library for stress-strain data?
I don't know of any software, but at least for the Young's modulus, yield stress and work it will be very easy. I doubt that you can get the fracture toughness from these data.
Mar
21
comment Calculating Ground State Energy in 1D Potential
This is exactly the point. As the particle is large, it is localized. The localization will be around the minimum of the potential. Could you write up a solution and post it, answering your own question?
Mar
19
comment How many photons does it take to measure a linear polarization?
What do you know about the measuring device? If it is perfect then you can get an exact result (as many bits as you like) with two measurements.