Anisotropy Factor [1]

The anisotropy factor \(\kappa^2\) is an invariant of the radius of gyration tensor G. It is a measure of symmetry and dimensionality of a polymer.

Definition

It is defined as

\[\kappa^2 = 1 - 3 \frac{\lambda_1\lambda_2 + \lambda_2\lambda_3 + \lambda_3\lambda_1} {(\lambda_1 + \lambda_2 + \lambda_3)^2}\]

where \(\lambda_1 \ge \lambda_2 \ge \lambda_3\) are the eigenvalues of the radius of gyration tensor.

Command Line Input

-af
--anisotropyFactor
Calculate \(\kappa^2\). Optionally provide an output filename.
Default: anisotropyFactor.csv

Example

MakroLyzer -xyz polymer.xyz -af myAnisotropyOutput.csv

Output

The output file contains one row per frame:

Column

Description

Frame

Frame index in the trajectory

Anisotropy Factor (\(\kappa^2\))

Anisotropy factor for the full graph