LENS

The Local Environments and Neighbors Shuffling (LENS) descriptor is a single-particle descriptor which allows measuring local diffusivity by tracking the changes in particles’ neighbors identities along a trajectory.

LENS requires the particles in the system to be uniquely indexed. For a given particle with index \(i\), LENS is computed between frames \(t_1\) and \(t_2\) as

\[\text{LENS}_i(t_1, t_2) = \frac{\#(C_i^{t_1} \cup C_i^{t_2}) - \#(C_i^{t_1} \cap C_i^{t_2})}{\#(C_i^{t_1}) + \#(C_i^{t_2})}\]

where \(C_i^t\) is the set of neighbors of particle \(i\) at frame \(t\), and \(\#C\) is the cardinality of set \(C\).

In this way, LENS is defined as a number between 0 and 1, where 0 correspond to the case where no neighbors changed, and 1 to the case where all the neighbors changed. The set of neighbors of each particle at each frame is defined as the particles within a certain cutoff radius \(r_c\) from that particle.

Examples of how to compute LENS can be found at examples/lens.py.

Functions

• list_neighbours_along_trajectory
• compute_lens

Acknowledgements

If you use LENS in your work, please cite this paper. The LENS code was written by Martina Crippa.