Recent content by vibe3

Possibly naive question. Wikipedia describes string theory as follows: The obvious next step (since string theory hasn't succeeded in describing our universe) would be to define elementary particles as 2D surfaces or 3D volumes or 4D space-time volumes, which may have vibrational modes similar...

So it would seem we do indeed need the strong field of a magnetar or something similar to drive a reasonably strong current. The Sun's magnetic field (about 10^{-4} T would then yield a current of only 8 \times 10^{-20} A/m^2 according to your numbers. This would be similar to the Earth's...

Interesting result, thanks for typing it out. I'm not sure offhand what order of magnitude h and \Phi would be for the recent GW detection events, but assuming we know that we could estimate how large B needs to be in order to have a chance of actually detecting something.

Your notes, or even an outline of the derivation would be most welcome! If indeed this result isn't in the literature, I think it would be worth publishing, have you thought about that?

Thanks for your response. Do you know of a paper which works out an equation for the predicted effect on a B field? For example if a GW with a given amplitude and frequency passes through a B field, what is the amplitude/frequency of the expected perturbation of the B field? The weak (B field)...

Suppose a gravitational wave propagating through space encounters a strong magnetic field (for example the wave might pass through a magnetar with a B field strength of 10^{11} Tesla). Would there be any observable perturbation in the magnetic field itself? In other words would the gravitational...

C is an n-by-n matrix of rank 1

Hello, if I have some given vector c \in R^n, then I want to find solutions X \in R^{n\times n} to the following equation: X C X^T = C where C = c c^T. Certainly X = I is a solution, but I'm looking for any nontrivial solutions. We can also assume X is invertible if that helps. This equation...

If I have some arbitrary conductor moving through a (nonuniform) magnetic field \mathbf{B}(\mathbf{r}), would the induced field in the frame of the conductor be something like: \mathbf{B}_{IND}(\mathbf{r}) = T \mathbf{B}(\mathbf{r}) where T is some diagonal matrix whose entries are related to...

I don't understand the analogy - we wouldn't need to generate a complex field, a simple dipole field, of sufficient strength would probably cause enough curvature of spacetime to cause observable gravitational effects no?

I'm aware of them and a better discussion is here: https://en.wikipedia.org/wiki/Maxwell's_equations_in_curved_spacetime I'm hoping an expert can let me know if a non-flat metric will cause a B field to satsify some other equation than Laplace. From staring at the equations for D^{\mu\nu} and...

According to the Einstein field equations, matter and energy both curve spacetime. I'm wondering how magnetic fields contribute to the curvature of spacetime. I have a few questions: 1. Does a magnetic field in a current-free region of a curved spacetime still satisfy Laplace's equation? Or is...

Yes, we can think of W as the image of V under the map A

I have two n-vectors e_1, e_2 which span a 2D subspace of R^n: V = span\{e_1,e_2\} The vectors e_1,e_2 are not necessarily orthogonal (but they are not parallel so we know its a 2D and not a 1D subspace). Now I also have a linear map: f: V \rightarrow W \\ f(v) = A v where A is a given n...

The problem is that my matrix A is very ill-conditioned, so computing eigenvalues from A^T A is unreliable (hence the reason I'm computing the QR decomposition instead). I'm looking for a numerically stable way to estimate the singular values from the QR decomposition for ill-conditioned...