1,144 reputation
514
bio website
location
age
visits member for 3 years, 4 months
seen Mar 23 at 13:04

Mar
20
comment Definition of non-degenerate metric tensor
I have never heard this definition of degenerate matrix. The identity matrix has only one eigenvalue (which is 1) and it corresponds to all the vectors (every vector is an eigenvector of the identity). Is the identity degenerate?
Mar
19
comment Definition of non-degenerate metric tensor
They are related in the same sense that the sentence "two times three is six" is related to the statement $2\times3=6$. It's the same statement, one in English, the other in algebraic notation.
Mar
19
comment Definition of non-degenerate metric tensor
The question is not clear. Is det$\ne0$ not the definition of non-degeneracy? Do you know a different definition and you search for a proof that the two are equivalent?
Mar
19
comment Electric field in a hollow object
Hint: when you write $$ ...=\oint_\Gamma E_i d\Gamma=E_i\oint_\Gamma d\Gamma=... $$ You assume that the electric field is constant over the surface of integration (and perpendicular to it). Is this true in the second example?
Mar
18
comment Insight into Torricelli's Equation ($v^2=u^2+2as$)
Suvat (also, Suvad) is a village in the Lachin Rayon of Azerbaijan.
Dec
10
comment Mass particle trajectory on a sphere
@KyleKanos, you've misunderstood the OP question. There's no gravitational field due to the sphere, he's talking about a motion in a constant gravitation constrained to a sphere.
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.