Maybe, I just had an idea:
Am I right, that the -\sum_{l=1}^N (\vec{v}_i\cdot\vec{r}_l)(\vec{r}_l\cdot\vec{v}_j) are nothing else than the off-diagonal components of the inertia tensor when being expressed in the coordinate system defined by the eigenvectors of the inertia tensor? (for the...
Hi Haborix,
thanks a lot for your idea. Unfortunately, I also don't see how to use this relation...
Still hoping, someone might see why the sum is vanishing.
Cheers,
derivator
Hi,
the \vec{\omega}_i are just the hypervectors build from the cross products of the eigenvectors of the inertia tensor and the particle positions (length 3*N). Frankly, I don't know, if they have any physical significance. They just happen to be an intermediate step in my calculation and I...
Hi,
I've written a little fortran code that computes the three Eigenvectors \vec{v}_1, \vec{v}_2, \vec{v}_3 of the inertia tensor of a N-Particle system.
Now I observed something that I cannot explain analytically:
Assume the position vector \vec{r}_i of each particle to be given with respect...
Dear all,
periodic DFT codes (e.g. VASP) effectively simulate an infinite crystal due to the periodic boundary conditions. However, the energy value that one obtaines at the end of a simulation if finite. Frankly, I'm quite confused right now.
Is the energy to be understood 'per unit cell'...
Hi,
in this article:
http://dx.doi.org/10.1016/S0021-9991(03)00308-5
damped molecular dynamics is used as a minimization scheme.
In formula No. 9 the author gives an estimator for the optimal damping frequency:
Can someone explain how to find this estimate?
best,
derivator
As I showed in my first post, I only can see that
$$\begin{matrix} A \, dx = \frac{\partial f}{\partial x} \, dx + const_1 \\ B \, dy = \frac{\partial f}{\partial y} \, dy + const_2 \end{matrix}$$
Why do the both constant have to vanish?
Derivator
Hi all,
In thermodynamics one often has equations like
A dx + B dy = ∂f/∂x dx + ∂f/∂y dy
From which follows
A = ∂f/∂x
B = ∂f/∂y
Can anyone explain to me why this conclusion is necessary from a mathematical point of view, please?
Here is my try:
A dx + B dy = ∂f/∂x dx + ∂f/∂y...
Thanks for your answer.
Well, I should have mentioned that the physical argumentation is clear to me. I'm really interested in the pure mathematical justification.
(By the way: the (unnormalized) probability density, when expressed as a function of the energy, is given by g(E)...
Dear all,
I'm wondering, how one could justify mathematically the equality
\int O(E(\vec{x}_1,...\vec{x}_N)) exp(-\beta E(\vec{x}_1,...,\vec{x}_N)) d\vec{x}_1...d\vec{x}_N = \int g(E) O(E) exp(-\beta E) dE
where O(E(x)) is an observable and g(E) the density of states.
Is there a...