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location Belgium
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visits member for 1 year, 10 months
seen Sep 2 at 18:01

Aug
3
comment How to numerically solve a complex equation?
Would Mathematics be a better home for this question?
Jul
21
comment Hodge star operator
@ACuriousMind Pure math questions that arise in a physical context have recently become on-topic. Arguably, no such context has been explicitly given in this question, but I think it's clear what the physical motivation for it is.
May
23
comment Algebra: What allows us to do the same thing to both sides of an equation?
You currently have written $f(s)=1/x$ as an example in your fifth paragraph (if you don't count the first sentence as a separate paragraph). This should be $f(s)=s/x$. A very good answer otherwise.
Mar
23
comment Explicit proof of the derivative of a matrix logarithm
Hmm, in that case I'll probably have to ask another question because I'm trying to prove $\delta \det{X} = (\det{X}) \mathrm{Tr}\,(\delta M M^{-1})$. A friend asked me about this and I told him I had proved it in the context of a course on general relativity. But when I went back and looked at that proof, I noticed some of these subtleties that I seem to have brushed over when I originally wrote down the proof.
Mar
23
comment Explicit proof of the derivative of a matrix logarithm
Interesting, would $\text{d}\log{X} = \text{d}X X^{-1}$ hold if $X$ were a diagonal matrix? If not, is there any other particular property that $X$ must have for this to hold? And would I be right to say that the definition in terms of a Taylor series is the fundamental one for the matrix exponential and the matrix logarithm?
Mar
23
comment Explicit proof of the derivative of a matrix logarithm
@JasonZimba Thanks for the references! In my particular case $X(x)$ is a general (square) diagonalizable matrix.
Aug
14
comment Find value of a line integral using Stokes' theorem
For future reference: mathematical physics doesn't mean "any mathematics in the context of a physics problem". And I would also suggest migrating this to Math.SE since there is no physics to be explained here and that is what Physics.SE is all about. On Math.SE, they will still ask you to show your own work but the question would be on topic there.
Jan
29
comment Cylindrical waves
That's right. On a sidenote: in this case there's no problem applying the boundary conditions because they are zero. However in general, if the BC's are e.g. $u(R,t) = f(t)$, you'd have to fourier transform those as well before applying them. (or inverse-fourier transform your solution and apply the original BC's)
Jan
29
comment Cylindrical waves
To see that this is a Bessel DE, try rescaling your $r$. (i.e. substitute $r' = kr$ where $k = \omega/c$)
Jan
19
comment Radius of convergence for the exponential function
Ahh, beautiful :) Thank you for this clear explanation, @Tunococ was right that I was looking for one sequence of $a_k$ for all $R$.
Dec
8
comment Solving the vector Laplace equation in cylindrical coordinates
@Fabian: I'll take a look at Jackson's book, thanks for the reference. But perhaps I should have said the external magnetic field is along the z-axis and the cylinder lies along the z-axis as well, so it's not really a waveguide problem. The physical context is that of a superconducting nanowire along z in an external magnetic field along z, which I am describing using the Ginzburg-Landau equations. This Laplace equation is derived from the second GL equation with the assumption that the order parameter is zero outside and constant inside the nanowire (and the regime is stationary).
Dec
8
comment Solving the vector Laplace equation in cylindrical coordinates
@Fabian: let me be more clear about what I did. Originally the equation was rotrot(A) = 0. So I used the gauge condition to get to this Laplace equation. I don't see how it is coupling the equations?
Dec
8
comment Solving the vector Laplace equation in cylindrical coordinates
@Matt: are you sure about that? Again referring to the same wolfram page (mathworld.wolfram.com/VectorLaplacian.html), the equations for the radial and the angular component of the vector are coupled. So separation of variables is not possible, right?
Dec
8
comment Solving the vector Laplace equation in cylindrical coordinates
@Fabian: the gauge condition is necessary to obtain this Laplace equation and I didn't plan on using it anywhere else, I just thought I'd mention it to be complete. Unfortunately, according to this wolfram page (mathworld.wolfram.com/VectorLaplacian.html) the equations for the radial and the angular component of the vector are not independent. They are coupled, which is what's making things difficult for me.