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Due to the success achieved by graphene, several 2D carbon-based allotropes were theoretically predicted and experimentally synthesized. We used density functional theory and reactive molecular dynamics simulations to investigate the mechanical, structural, electronic, and optical properties of 8-16-4 Graphyne. The results showed that this material exhibits good dynamical and thermal stabilities. Its formation energy and elastic moduli are -8.57 eV/atom and 262.37 GPa, respectively. This graphyne analogue is a semi-metal and presents two Dirac cones in its band structure. Moreover, it is transparent, and its intense optical activity is limited to the infrared region. Remarkably, the band structure of 8-16-4 Graphyne remains practically unchanged at even moderate strain regimes. As far as we know, this is the first 2D carbon allotrope to exhibit this behavior., Comment: 09 pages, and 11 figures

Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social systems. We numerically analyze the growth of $d$-dimensional geographic networks (characterized by the index $\alpha_G\geq0$; $d = 1, 2, 3, 4$) whose links are weighted through a predefined random probability distribution, namely $P(w) \propto e^{-|w - w_c|/\tau}$, $w$ being the weight $ (w_c \geq 0; \; \tau > 0)$. In this model, each site has an evolving degree $k_i$ and a local energy $\varepsilon_i \equiv \sum_{j=1}^{k_i} w_{ij}/2$ ($i = 1, 2, ..., N$) that depend on the weights of the links connected to it. Each newly arriving site links to one of the pre-existing ones through preferential attachment given by the probability $\Pi_{ij}\propto \varepsilon_{i}/d^{\,\alpha_A}_{ij} \;\;(\alpha_A \ge 0)$, where $d_{ij}$ is the Euclidean distance between the sites. Short- and long-range interactions respectively correspond to $\alpha_A/d>1$ and $0\leq \alpha_A/d \leq 1$; $\alpha_A/d \to \infty$ corresponds to interactions between close neighbors, and $\alpha_A/d \to 0$ corresponds to infinitely-ranged interactions. The site energy distribution $p(\varepsilon)$ corresponds to the usual degree distribution $p(k)$ as the particular instance $(w_c,\tau)=(2,0)$. We numerically verify that the corresponding connectivity distribution $p(\varepsilon)$ converges, when $\alpha_A/d\to\infty$, to the weight distribution $P(w)$ for infinitely narrow distributions (i.e., $\tau \to \infty, \,\forall w_c$) as well as for $w_c\to0, \, \forall\tau$., Comment: 8 pages and 7 figures

The dynamics of opinion formation in a society is a complex phenomenon where many variables play an important role. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model an individual adopts an opinion contrary to the majority of its neighbors with probability $q$, defined as the noise parameter. Here, we introduce a visibility parameter $V$ in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For $V=0.5$ each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility $q_c(V)$ and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of $V$ favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution, and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.

The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located $d$-dimensional networks. In this paper, we study scaling properties of a wide class of $d$-dimensional geographically located networks which grow with preferential attachment involving Euclidean distances through $r_{ij}^ {-\alpha_A} \;(\alpha_A \geq 0)$. We have numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient, for $d=1,2,3,4$, and typical values of $\alpha_A$. Remarkably enough, virtually all the curves can be made to collapse as functions of the scaled variable $\alpha_A/d$. These observations confirm the existence of three regimes. The first one occurs in the interval $\alpha_A/d \in [0,1]$; it is non-Boltzmannian with very-long-range interactions in the sense that the degree distribution is a $q$-exponential with $q$ constant and above unity. The critical value $\alpha_A/d =1$ that emerges in many of these properties is replaced by $\alpha_A/d =1/2$ for the $\beta$-exponent which characterizes the time evolution of the connectivity of sites. The second regime is still non-Boltzmannian, now with moderately long-range interactions, and reflects in an index $q$ monotonically decreasing with $\alpha_A/d$ increasing from its critical value to a characteristic value $\alpha_A/d \simeq 5$. Finally, the third regime is Boltzmannian (with $q=1$), and corresponds to short-range interactions., Comment: 6 pages, 8 figures