Eigenvalue spectra of spatial-dependent networks.

Many real-life networks exhibit a spatial dependence; i.e., the probability to form an edge between two nodes in the network depends on the distance between them. We investigate the influence of spatial dependence on the spectral density of the network. When increasing spatial dependence in Erdös-Rényi, scale-free, and small-world networks, it is found that the spectrum changes. Due to the spatial dependence the degree of clustering and the number of triangles increase. This results in a higher asymmetry (skewness). Our results show that the spectrum can be used to detect and quantify clustering and spatial dependence in a network.

Percolation of immobile domains in supercooled thin polymeric films.

We present an analysis of heterogeneous dynamics in molecular dynamics simulations of a polymeric film supported by an absorbing surface. Using a bead-spring model for polymers, we show that slow, immobile beads occur throughout the film, with the probability of their occurrence decreasing with distance from the substrate. Still, enough immobile beads are located near the free surface to cause them to percolate in the direction perpendicular to the substrate, at a temperature near the glass transition one. This result is consistent with a recent theoretical model of glass transition.