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PubMed2001

Weighted evolving networks.

Many biological, ecological, and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most evolving network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total weight distribution converges to the scaling behavior of the connectivity distribution, but this convergence is hampered by strong logarithmic corrections.

Mathematical Computing↗

PubMed1999

Dynamical universality classes of vapor deposition models with evaporation.

Growth models for vapor depositions in which evaporation and deposition can occur, both at a randomly chosen column and at its nearest neighbor columns (NNCs), are studied by Monte Carlo simulations. The growth processes in these models are determined by comparing local chemical potentials of the chosen column and its NNCs to the chemical potential of vapor. The universality classes and the characteristics of the models are studied by the scaling ansatz of kinetic roughening and by measurements of tilt-dependent currents and height step widths. Through measurements of the ratio of number of growth processes at NNCs to those at the chosen column, the key processes which are relevant to the determination of the universality class are also studied.

Journal Article↗