Narrow Results

Around us, the society structure and external field, such as government policy, the newspaper, the internet and other mass media, play a special role in shaping the attitudes, beliefs and public opinion. For studying the role of the society structure and the external field, we propose a new opinion model based on the former models. With computer simulations of opinion dynamics, we find that the smaller the clustering coefficient and the society size, the easier the consensus phase is reached and other interesting results.

We investigate the external field effect on opinion formation based on the majority rule and $q$-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability $p$ agents following the mass media opinion. Based on our Monte Carlo simulation, the mass media effect is not strong enough to make the system reach a homogeneous state (complete consensus) with the magnetization $m=1$ for all values of $p$, indicating the existence of a usual phase transition for all values of $p$. In the $q$-voter model, the mass media eliminates the usual phase transition at $p\approx 0.21$. We obtain the model’s critical point and scaling parameters using the finite-size scaling analysis and obtain that both models have the same scaling parameters. The external field effect decreases both models’ relaxation time and the relaxation time following the power-law relation such as $\tau \sim N^{\beta }$, where $N$ is the population size and $\beta$ depends on the probability $p$. In the majority rule model, $\beta$ follows a linear relation, and in the q-voter model, $\beta$ follows a power-law relation.

We present an alternative finite-size scaling (FSS) of the contact process on scale-free networks compatible with mean-field scaling and test it with extensive Monte Carlo simulations. In our FSS theory, the dependence on the system size enters the external field, which represents spontaneous contamination in the context of an epidemic model. In addition, dependence on the finite size in the scale-free networks also enters the network cutoff. We show that our theory reproduces the results of other mean-field theories on finite lattices already reported in the literature. To simulate the dynamics, we impose quasi-stationary states by reactivation. We insert spontaneously infected individuals, equivalent to a droplet perturbation to the system scaling as $N^{-1}$. The system presents an absorbing phase transition where the critical behavior obeys the mean-field exponents, as we show theoretically and by simulations. However, the quasi-stationary state gives finite-size logarithmic corrections, predicted by our FSS theory, and reproduces equivalent results in the literature in the thermodynamic limit. We also report the critical threshold estimates of basic reproduction number $R_0={\lambda }_c$ of the model as a linear function of the network connectivity inverse $1∕z$, and the extrapolation of the critical threshold function for $z\to \infty$ yields the basic reproduction number $R_0=1$ of the complete graph, as expected. Decreasing the network connectivity increases the critical $R_0$ for this model.

The effect of the exponential pair creation from vacuum by the external field periodic in time is discussed. Two prospective applications of this physical effect in quantum field theory and in inflationary cosmology are considered. Being a nontrivial example of a parametric resonance, the effect of exponential pair creation may serve as an illustration of the effectiveness of mathematics in physical theory.

We suggested a geometric approach to address the external field influence on the DNA molecules, described by the WLC model via geometric coupling. It consists in the introduction of the effective metrics depending on the potential of the external field, with further re-definition of the arc-length parameter and of the extrinsic curvatures of the DNA molecules. It yields the nontrivial impact of the external field in the internal energy of macromolecules. We give the Hamiltonian formulation of this model and perform its preliminary analysis in the redefinition of the initial energy density.

In this paper, we investigate the influence of a gate electric field on the tunneling current for the contact of impurity graphene nanoribbon with a metal or quantum dots. Based on the Hamiltonian for graphene in the tight-binding approximation, the density of states is calculated, which allows us to obtain a tunneling current. We analyze the effect of the field magnitude on the detecting possibility of an impurity in the graphene nanoribbon. A sufficient change of current–voltage characteristic (CVC) of the contact is observed, with an increase in the constant electric field applied parallel to the nanoribbon plane.