Recent content by pafcu

I don't understand how you get \mathbf{f} = \epsilon_0\left[ \boldsymbol{\nabla}\cdot( \mathbf{E}\mathbf{E}) + (\mathbf{E}\cdot\boldsymbol{\nabla}) \mathbf{E} \right] Looking at eq. 3 \mathbf{f} = \epsilon_0 \left(\boldsymbol{\nabla}\cdot \mathbf{E} \right)\mathbf{E} +...

I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia, 1. Start with Lorentz force: \mathbf{F} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B}) 2. Get force density \mathbf{f} =...

I'm trying to get some sort of value for the electronic contribution to the thermal conductivity of copper. Most sources seem to give the total thermal conductivity K=400 \mathrm{W/(m\cdot K)} at room temperature. The electronic contribution should be given by the Wiedemann–Franz law...

What exactly is the problem? How far have you gotten? I've been working on the same problem, and I solved it by using the Crank-Nicolson method. Look it up on e.g. Wikipedia. A worse, but far simpler method (especially since the source is non-linear) is to use the Forward Euler method...

No, number of unknowns is not a problem. Assuming u is defined at m m points (it has been discretized) we obviously end up with m unknowns: u_i^{n+i}, 1 \leq i \leq m. We get m-2 equations by plugging in i=2,3,4,...,m-1 into the equation in the original post. Plugging in i=1 doesn't work...

I was unclear. The point is that I wish to know the value of u at the next time step at every point, solving the mentioned equation for u_{i}^{n + 1} for each i (requires solving a set of linear equations) tells me just that.

Hi all, A diffusion equation is of the form \frac{\partial u}{\partial t}=k \frac{\partial^2u}{\partial x^2} Usually an equation like this seems to be solved numerically using the Crank-Nicolson method: \frac{u_{i}^{n + 1} - u_{i}^{n}}{\Delta t} = \frac{k}{2 (\Delta x)^2}\left((u_{i + 1}^{n +...