Diffusion Processes on Power-Law Small-World Networks

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.Comment: 4 pages, 3 figures, added references, modified Fig. 2 with added data (PRL, in press

Effects of the Bologna process on the motivation of secondary school-leavers behind their choice of higher education institutes – Hungarian case study

Peer Reviewe

An ϵ\epsilon-expansion for Small-World Networks

I construct a well-defined expansion in $\epsilon=2-d$ for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green's function, and is used to calculate the average Green's function and fluctuations to first non-leading order in $\epsilon$, giving results which agree with numerics. This technique is also applicable to other problems of diffusion in random media.Comment: 7 pages Europhysics style, 3 figure

SN 1998bw at late phases

We present observations of the peculiar supernova SN 1998bw, which was probably associated with GRB 980425. The photometric and spectroscopic evolution is monitored up to 500 days past explosion. We also present modeling based on spherically symmetric, massive progenitor models and very energetic explosions. The models allow line identification and clearly show the importance of mixing. From the late light curves we estimate that about 0.3-0.9 solar masses of ejected Nickel-56 is required to power the supernova.Comment: With 3 figures Accepted for ApJ Letter

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure