A parameter-free, solid-angle based, nearest-neighbor algorithm

We propose a parameter-free algorithm for the identification of nearest neighbors. The algorithm is very easy to use and has a number of advantages over existing algorithms to identify nearest-neighbors. This solid-angle based nearest-neighbor algorithm (SANN) attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4π. The algorithm can be used to analyze 3D images, both from experiments as well as theory, and as the algorithm has a low computational cost, it can also be used "on the fly" in simulations. In this paper, we describe the SANN algorithm, discuss its properties, and compare it to both a fixed-distance cutoff algorithm and to a Voronoi construction by analyzing its behavior in bulk phases of systems of carbon atoms, Lennard-Jones particles and hard spheres as well as in Lennard-Jones systems with liquid-crystal and liquid-vapor interfaces.