Recent content by Heimdall

Hi, I don't get which of the many matrix norms is invariant through a change of basis. I get that the Frobenius norm is, because it can be expressed as a function of the eigenvalues only. Are there others of such kind of invariant norms? Thanks

Hi, I see that nobody seems inspired by my post. I'll try to sum it up by a few concise questions. 1/ An observer, defining a reference frame R, sees a uniform magnetic field B and a uniform electric field E. Both B and E are constant over time. Can he conclude that the electric field is...

Hi, I'm stuck with a question concerning electric fields : Can an electrostatic potential drop exist in (what I would call) a 0 dimensional system ? Let's imagine we are in a region of space where there is nothing but a uniform magnetic field. So the problem is anisotropic but does not...

ok one more question : can you explain me a bit more this paragraph :

So if I understand well, Newtonnian et Galilean physics was ok for gravitation but not for electromagnetism... and special relativity is ok for electromagnetism but not anymore for gravitation... I see your point, but isn't electromagnetism built from the coulomb force ?

Hi, Could you explain me a few things I still don't get about special relativity ? I've been tought a few years ago that special relativity wasn't good for handling accelerations... well I've been reading books and a few topics here, and I'm now convinced it is not true... for exactly the...

Hi, I have an integral that I find quite difficult, I can't obtain anything from mathematica (but I'm far from being an expert). Would some of you have a hint ? is it analytical ? It seems to be a "simple" function, from the physicist I am it should be integrable... this integral is ...

All right, here is a solution to my problem. As I said, to me Erf(x) has the same behavior as tanh(x), and it is indeed easier to integrate. Tell me if you agree : I\left(A(x)\right) = \int_{-\infty}^{+\infty} e^{-\alpha v^2} Erf\left(v+A\left(x\right)\right)dv is now the integral I'm looking...

Hi, thanks for trying :) I think it would be helpful to rather consider this integral : \int_{-\infty}^{+\infty} e^{-\alpha x^2}Erf\left(x - \beta\right) Which is for the physicist that I am quite the same object..Edit : Well in fact the real object I would like to evaluate is ...

Hi, I'm trying to calculate this integral : \int_{-\infty}^{+\infty} e^{-\alpha x^2} tanh\left(x - \beta\right) dx \alpha,\beta being independent of x. Would somebody know how to do that ? Thanks :)

"Helmholtz equation" Neumann and divergence Hello, I'm trying to solve the following elliptic problem : S = B - \mu\nabla^2 B Where S(x,y) and B(x,y) are 3 component vectors. I have \nabla\cdot S = 0 and I want B such that \nabla\cdot B = 0 everywhere. I'm using finite differences on a...

Hi, I'm looking for an efficient algorithm to solve this kind of equation : S = (1-\nabla^2)B where both S(x,y) and B(x,y) can both be non-periodic functions. We know S and want to find out what is B. I was wondering if there was a 'well known' method to solve this kind or problem in the...

Hi, Let's consider a plasma of 3 distinct populations : 1 cold proton population of 0.2 density, 1 hot proton population of 0.8 density, and one electron population. I have T_i=T_e and I set the velocity of my cold population to 0. I expected that te energy of my hot proton population to...

Hi :) In the mean time I got another solution : I = \int\frac{f'dx}{\sqrt{1-\exp{\left(f/B\right)}}} let u^2 = 1-\exp{\left(f/B\right)} so we have : -2Budu\frac{1}{1-u^2} = f'dx and we get : I = -2B\int \frac{du}{1-u^2} = -2Bargth\left(u\right) I =...

I haven't seen it the first time but you can't even do this if x=0 (because f(0)=0)