Recent content by blalien

The pores in a foam are allowed to overlap with each other. This isn't a sphere packing problem though. This is a question of the expected value of the volume these pores will occupy.

Homework Statement This should be a pretty simple question but I can't find a straight answer in the literature. I want to simulate a 3D model of a metal foam by starting with an aluminum block and filling it with randomly placed spherical holes of constant volume. The foam should have a...

That's it, thanks. I don't know how we were ever supposed to solve this without knowing the beta function.

Homework Statement The problem is to find the moments E(X^k) of f_x(x) = (\theta+1)(1-x)^\theta, 0 < x < 1, \theta > -1 Homework Equations E(X^k)=\int_0^1 x^k (\theta+1)(1-x)^\theta dx According to Mathematica, the solution is \frac{\Gamma(1+k)\Gamma(2+\theta)}{\Gamma(2+k+ \theta )}. I...

I missed a detail that the solution is symmetric with y. That solves the problem. Thanks anyway.

The problem is that the two boundary conditions F(\omega)+G(-\omega)=0 and F'(\omega)+G'(-\omega)=0 imply that F(\omega) and G(\omega) are constant. This does create an inconsistency.

Homework Statement The problem is to solve \phi_{yy}-c^2 \phi_{xx} = 0 \phi_y (x,0) = f'(x), x>0 \phi_x (0,y) = \phi(0,y) = 0, y>0 or y<0 Homework Equations The solution, before applying boundary conditions is obviously \phi(x,y)=F(x+c y)+G(x-cy) The Attempt at a Solution I start...

Homework Statement You have a number system in base 10 with a precision of 5 digits. Which function is more accurate: x^2-y^2 or (x-y)(x+y)? Homework Equations None really. The Attempt at a Solution My intuition would tell me that (x-y)(x+y) is more accurate, since multiplication is...

Yeah, it might be. But your method works. Thank you so much for your help. You always overlook the simple solutions, right? It turns out the answer is: \frac{d\phi}{dr}=\frac{y-x y'}{(x+y' y)\sqrt{x^2+y^2}} I also need to find \frac{d^2\phi}{d r^2}, but I think you just need to apply...

This isn't a homework question out of a textbook. But here's what I'm looking for: Given variables phi, r, x, y such that x = r sin(phi), y = r cos(phi) and a function phi(r) I need to find dphi/dr in terms of x, y, and dy/dx.

So what should I do? I don't even have a guarantee that there is a general solution, so this could be a wild goose chase.

Sorry, I should clarify. We assume a function \phi (r) exists, but we're not given its definition.

Homework Statement Given Cartesian coordinates x, y, and polar coordinates r, phi, such that r=\sqrt{x^2+y^2}, \phi = atan(x/y) or x=r sin(\phi), y=r cos(\phi) (yes, phi is defined differently then you're used to) I need to find \frac{d\phi}{dr} in terms of \frac{dy}{dx} Homework...

Well, that's not exactly right. But you can work a little index magic and come up with \epsilon_{ijk}\epsilon_{pqr}=\left| \begin{matrix} \delta_{ip} & \delta_{iq} & \delta_{ir} \\ \delta_{jp} & \delta_{jq} & \delta_{jr} \\ \delta_{kp} & \delta_{kq} & \delta_{kr} \end{matrix} \right|

Never mind, I got it. You set A_{ij} = \delta_{ij} and get the epsilons in terms of the deltas.