Network analysis of 3D complex plasma clusters

Kurzfassung

Network analysis was used to study the structure and time evolution of driven three-dimensional complex plasma clusters. The clusters were created by suspending micron-size particles in a glass box placed on top of the rf electrode in a capacitively coupled discharge. The particles were highly charged and manipulated by an external electric �eld that had a constant magnitude and rotated uniformly in the horizontal plane. Depending on the frequency of the applied electric �eld, the clusters rotated in the direction of the electric �eld or remained stationary. The three-dimensional positions of all particles were measured using stereoscopic digital in-line holography. The network approach was used to elucidate the structural changes in the cluster consisting only of a very limited number of particles (64). The Analysis revealed an interplay between two competing symmetries in the cluster. Spherical and cylindrical ordering of the particles was examined by comparing network measures of the experimental data with null models. The null models were arti�cial data with a certain number of points in perfectly spherical order, and the rest in cylindrical order. The well established network measures local connectivity, clustering coe�cient and average path length were considered. Network analysis of the clusters showed that the rotating cluster was more cylindrical than the nonrotating cluster. These �ndings were in agreement with the estimate of the radial con�nement with the aid of a dynamical force balance. Neglecting friction and inertial forces due to the low particle velocities in the cluster, the pro�le of the electrical con�nement could be estimated by calculating the repulsing Yukawa-type interaction between the particles. The radial con�nement was shown to be stronger in the case of cluster rotation, increasing the cylindricity of the cluster. The emergence of vertical strings of particles was also con�rmed by using a network analysis. While the traditional method of a �xed threshold has limitations such as erroneously including passing by particles and a somewhat arbitrary threshold, community �nding algorithms yield a more elegant approach of �nding structures in complex systems. With the aid of multislice networks, it is possible to examine the whole time series at once and thus resolve the time evolution of the strings. As we demonstrated, network analysis is a powerful tool to analyze the structure of complex plasma clusters and may have numerous applications in other complex systems where the characertization of the spatial structure plays a vital role. 1