Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome
and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the groups opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about 10% of the population (with the findings being qualitatively similar for sparse networks as well). Here we study the more general case of opinion evolution when two groups committed to distinct, competing opinions $A$ and $B$, and constituting fractions $p_A$ and $p_B$ of the total population respectively, are present in the network. We show for stylized social networks (including ErdH{o}s-Renyi random graphs and Barabasi-Albert scale-free networks) that the phase diagram of this system in parameter space $(p_A,p_B)$ consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. These two regions are separated by two fold-bifurcation (spinodal) lines which meet tangentially and terminate at a cusp (critical point). We provide further insights to the phase diagram and to the nature of the underlying phase transitions by investigating the model on infinite (mean-field limit), finite complete graphs and finite sparse networks. For the latter case, we also derive the scaling exponent associated with the exponential growth of switching times as a function of the distance from the critical point.
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 th
at when the committed fraction grows beyond a critical value p_c approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c sim exp(alpha(p)N), while for p > p_c, T_c sim ln N. We conclude with simulation results for ErdH{o}s-Renyi random graphs and scale-free networks which show qualitatively similar behavior.
We theoretically design a graphene-based all-organic ferromagnetic semiconductor by terminating zigzag graphene nanoribbons (ZGNRs) with organic magnets. A large spin-split gap with 100% spin polarized density of states near the Fermi energy is obtai
ned, which is of potential application in spin transistors. The interplays among electron, spin and lattice degrees of freedom are studied using the first-principles calculations combined with fundamental model analysis. All of the calculations consistently demonstrate that although no d electrons existing, the antiferromagnetic pi-pi exchange together with the strong spin-lattice interactions between organic magnets and ZGNRs make the ground state ferromagnetic. The fundamental physics makes it possible to optimally select the organic magnets towards practical applications.
This paper presents one MEMS design tool with total six design flows, which makes it possible that the MEMS designers are able to choose the most suitable design flow for their specific devices. The design tool is divided into three levels and interc
onnected by six interfaces. The three levels are lumped-element model based system level, finite element analysis based device level and process level, which covers nearly all modeling and simulation functions for MEMS design. The six interfaces are proposed to automatically transmit the design data between every two levels, thus the maximal six design flows could be realized. The interfaces take the netlist, solid model and layout as the data inlet and outlet for the system, device and process level respectively. The realization of these interfaces are presented and verified by design examples, which also proves that the enough flexibility in the design flow can really increase the design efficiency.
