Bert Van Schaeybroeck

Biased percolation on scale-free networks

Biased (degree-dependent) percolation was recently shown to provide strategies for turning robust networks fragile and vice versa. Here, we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes i and j to be retained is proportional to (k(i)k(j)(-alpha) with k(i) and k(j) the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating-functions method. The theory is found to agree quite well with simulations. By presenting an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well-described by the q-->1 limit of the q -state Potts model with inhomogeneous couplings.

Interface tension of Bose-Einstein condensates

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reproduce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.

Static interfacial properties of Bose-Einstein-condensate mixtures

Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths

Criterion for explosive percolation transitions on complex networks

xi_1

Normal-superfluid interface for polarized fermion gases

and

Collective excitations of trapped imbalanced fermion gases

xi_2

Trapped phase-segregated Bose-Fermi mixtures and their collective excitations

and by the inter-species repulsive interaction

Weakly interacting Bose mixtures at finite temperature

K

Assessment of calibration assumptions under strong climate changes

. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case

Degree-dependent network growth: from preferential attachment to explosive percolation.

xi_2/xi_1 = 1/2