Recent content by ozone

I just have a quick question, and I'm guessing the answer is no but I wanted to make sure that this was sensible. In general whenever we consider flux we think of some kind of closed surface or a scenario where charge closes back on itself. If I were to cut a hole in an infinite plate of...

Hello all, I was hoping to get some advice from people who have already completed their phd and have faced the real world situation of the post-doc pressures and job market. I am at a cross-roads now that I have been admitted to some graduate programs, and I am really struggling to decide...

I have recently been assigned a project in my undergraduate topology class. I would like to do something in physics which involves topology, but I am having trouble finding a basic topic. I understand that there are some very advanced topics in string theory and the like, but I would like to...

Fair enough, I agree with what you are saying. My main question then is what do we do with these constants of integration? May we just arbitrarily set them equal to one?

True but the equation above should only have one independent solution as best I can ascertain.. Suppose for simplicity we had a diagonal connection coefficient which is valued at 1 in some \bar{x} direction, I don't see how that is different from writing \dot{x}= x^2 (by substituting x =...

Sorry I should have been more clear, I believe that I have two independent solutions to the geodesic equation for a single direction, but perhaps I am misinterpreting the result. The equation is written as \ddot{x}(\tau)^a = A_{ab}(\tau) x(\tau)^b Here a,b are the two orthogonal...

Hello all, I have a geodesic equation from extremizing the action which is second order. I am curious as to what the significance is of having 2 independent geodesic equations is. Also I was wondering what the best way to deal with this is.

Hello, I am working on a research problem and I am not sure whether or not I will be able to figure this out in a suitable amount of time. I have never solved a single elliptic integral and they do seem non-trivial to gain an understanding of (most of the books I've glanced at assume a very...

I tried this substitution but I'm very certain it will not actually uncouple these ode's, unless I am missing a very interesting algebra trick

Hello all, I have boiled a very long physics problem down to the point that I need to solve the coupled equations \frac{\partial^2 x}{\partial u^2} + xf(u) + yg(u) = 0 \frac{\partial^2 y}{\partial u^2} + yf(u) - xg(u) = 0 We may assume that |f| ,|g| << 1. and that both f and g are...

Edit: I realized v is just a constant so what we really should have is something like N = \pm b(t) . Also I forgot to mention I had a factor of |\alpha(t)|^4 so that N = \pm |\alpha(t)|^4 b(t) but I assumed that the curve is parameterized by arc-length so that I could ignore this term...

Homework Statement Consider the tangent surface of some regular differentiable curve given as X(t,v) = \alpha(t) + v \alpha'(t) . Show that the tangent planes along X(t,constant) are equal. Homework Equations N = \frac{X_{t} \wedge X_{v}}{|X_{t} \wedge X_{v}|} The general tangent...

haha thanks for the help guys, I guess then I know which pair is redundant out of the 21 I came up with. Yes I am not looking forward to calculating this =/ I guess my Prof. must really want to punish his students.

Hello all, I have been given a problem where I am asked to calculate "all" the components of the Riemann tensor in a gross non-diagonalized metric. I know there exists at most 20 independent components of Riemann, but I want to actually compose a list of these combinations. It is easy...

Alright thank you guys. This does seem to closely parallel the stuff were about to be getting into with GR so I am pretty glad to have worked through the problem.. also thank you for linking to that more geometrical derivation.. it was a bit advanced for my taste but it was interesting to see...