- #1
Irid
- 207
- 1
Hello, I'm studying The Theory of Polymer Dynamics by Doi and Edwards and on page 98 there is a tensor, defined as a composition of two identical unit vectors pointing from the monomer n to the monomer m:
[itex]
\hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm}
[/itex]
As far as I understood, the unit vectors have a uniform distribution in space. The authors then calculate the average of the tensor and it turns out to be 1/3 of the identity tensor:
[itex]
\text{average}(\hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm}) = \textbf{I}/3
[/itex]
No actual steps are given and I am confused by this result. I think the average should be zero. Any ideas?
[itex]
\hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm}
[/itex]
As far as I understood, the unit vectors have a uniform distribution in space. The authors then calculate the average of the tensor and it turns out to be 1/3 of the identity tensor:
[itex]
\text{average}(\hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm}) = \textbf{I}/3
[/itex]
No actual steps are given and I am confused by this result. I think the average should be zero. Any ideas?