Propensity and stickiness in the naming game: tipping fractions of minorities.

Agent-based models of the binary naming game are generalized here to represent a family of models parameterized by the introduction of two continuous parameters. These parameters define varying listener-speaker interactions on the individual level with one parameter controlling the speaker and the other controlling the listener of each interaction. The major finding presented here is that the generalized naming game preserves the existence of critical thresholds for the size of committed minorities. Above such threshold, a committed minority causes a fast (in time logarithmic in size of the network) convergence to consensus, even when there are other parameters influencing the system. Below such threshold, reaching consensus requires time exponential in the size of the network. Moreover, the two introduced parameters cause bifurcations in the stabilities of the system's fixed points and may lead to changes in the system's consensus.

Opinion dynamics and influencing on random geometric graphs.

We investigate the two-word Naming Game on two-dimensional random geometric graphs. Studying this model advances our understanding of the spatial distribution and propagation of opinions in social dynamics. A main feature of this model is the spontaneous emergence of spatial structures called opinion domains which are geographic regions with clear boundaries within which all individuals share the same opinion. We provide the mean-field equation for the underlying dynamics and discuss several properties of the equation such as the stationary solutions and two-time-scale separation. For the evolution of the opinion domains we find that the opinion domain boundary propagates at a speed proportional to its curvature. Finally we investigate the impact of committed agents on opinion domains and find the scaling of consensus time.

Phase transition to super-rotating atmospheres in a simple planetary model for a nonrotating massive planet: exact solution.

An energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow on a massive nonrotating sphere is introduced and solved exactly for phase transitions to rotating solid-body atmospheres when the kinetic energy level is high. Unlike the Kraichnan theory which is a Gaussian model, we substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based on sound physical principles. This yields a spherical model with zero total circulation, microcanonical enstrophy constraint, and canonical constraint on energy, leaving angular momentum free as is required for any model whose objective is to predict super-rotation in planetary atmospheres. A closed-form solution of this spherical model, obtained by the Kac-Berlin method of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking rotating solid-body flows. The critical values depend linearly on the relative enstrophy, with proportionality constant derived from the spectrum of the Laplace-Beltrami operator on the sphere, as expected within an energy-enstrophy theory for macroscopic turbulent flows. This model and its results differ from previous solvable models for related phenomena in the sense that the model is not based on a mean-field assumption.