We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.
This Chapter presents a generalized model of consensus formation, which is able to encompass all previous formulations of copy/invasion processes inspired by variations on the voter model and the Moran process. It considered the implementation of such generalized dynamics on a heterogeneous contact pattern, represented by a complex network, and derived the theoretical predictions for the relevant dynamical quantities, within the assumptions of the heterogeneous mean-field theory. The chapter provides a brief review of previous results that can be recovered by this generalized formalism, and considers a novel application to the case of opinion formation in a social network. In particular, it addressed the case in which the opinion strength of an individual is related to his/her degree centrality in the network.
Moretti, Paolo; Liu, S.Y.; Baronchelli, Andrea; Pastor Satorras, Romualdo European physical journal B Vol. 85, num. 3, p. 1-6 DOI: 10.1140/epjb/e2012-20501-1 Date of publication: 2012-03 Journal article
Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading
conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material resistance to irreversible deformation depends on sample morphology. Here we study the mechanisms of yield and plastic flow in inherently small crystals under uniaxial compression. Discrete structural rearrangements emerge as a series of abrupt
discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry
and elucidate the statistical properties of plastic deformation at such scales. Our results show that the absence of dislocation
storage leads to crucial effects on the statistics of plastic events, ultimately affecting the universal scaling behavior observed at larger scales.
Moretti, Paolo; Baronchelli, Andrea; Barrat, Alain; Pastor Satorras, Romualdo Journal of statistical mechanics: Theory and experiment Vol. 2010, num. P03032 DOI: 10.1088/1742-5468/2011/03/P03032 Date of publication: 2010-03 Journal article