We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value pc ≈ 10%, there is a dramatic decrease in the time, Tc, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < pc, Tc ∼ exp(α(p)N ), while for p > pc, Tc ∼ ln N . We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.

This study demonstrates high strain rate behavior of neat epoxy and epoxy resin reinforced with 2 wt% and 5 wt% alumina nanoparticles. The present study investigates effect of strain rate as well as effect of alumina nanoparticle dispersion on the compressive stress -compressive strain behavior of epoxy resin. Studies were carried out on compressive split Hopkinson pressure bar apparatus in the strain rate range of 700-3200 per sec. Significant enhancement of compressive strength of epoxy resin up to 147% was noted at high strain rate compared with that at quasi-static loading. The corresponding increase for alumina nanoparticle filled epoxy resin was up to 142%. It was also observed that the compressive strength of epoxy resin increases up to 8.6% with the addition of alumina nanoparticles at a strain rate of 3000 per sec. Synthesis of alumina nanoparticle filled epoxy resin, high strain rate and quasi-static testing and main findings of the study are presented in this article. POLYM. ENG. SCI., 54:2896-2901, FIG. 4. Stress versus strain plots: (a) for specimen A5, (b) for specimen A2, (c) for specimen A0. FIG. 5. Comparison of compressive stress versus compressive strain plots under quasi-static and high strain rate loading: (a) for specimen A5, (b) for specimen A2, (c) for specimen A0. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] FIG. 6. Strain rate versus compressive strength for A5, A2, and A0.

Abstract. We introduce the homogeneous pair approximation to the Naming Game (NG) model, establish a six dimensional ODE for the two-word NG. Our ODE reveals how the dynamical behavior of the NG changes with respect to the average degree < k > of an uncorrelated network and shows a good agreement with the numerical results. We also extend the model to the committed agent case and show the shift of the tipping point on sparse networks.

No abstract