Traffic flow behavior at un-signalized intersection with crossings pedestrians

Mixed traffic flux composed of crossing pedestrians and vehicles extensively exists in cities. To study the characteristics of the interference traffic flux, we develop a pedestrian-vehicle cellular automata model to present the interaction behaviors on a simple cross road. By realizing the fundamental parameters (i.e. injecting rates ${\alpha }_1$, ${\alpha }_2$, the extracting rate β and the pedestrian arrival rate ${\alpha }_P$), simulations are carried out. The vehicular traffic flux is calculated in terms of rates. The effect of the crosswalk can be regarded as a dynamic impurity. The system phase diagrams in the $({\alpha }_1,{\alpha }_P)$ plane are built. It is found that the phase diagrams consist essentially of four phases namely Free Flow, Congested, Maximal Current and Gridlock. The value of the Maximal current phase depends on the extracting rate β, while the Gridlock phase is achieved only when the pedestrians generating rate is higher than a critical value. Furthermore, the effect of vehicles changing lane ($P_{\mathrm{ch}1},P_{\mathrm{ch}2}$) and the location of the crosswalk $X_P$ on the dynamic characteristics of vehicles flow are investigated. It is found that traffic situation in the system is slightly enhanced if the location of the crosswalks $X_P$ is far from the intersection. However, when $P_{\mathrm{ch}1}$, $P_{\mathrm{ch}2}$ increase, the traffic becomes congested and the Gridlock phase enlarges.     

Percolation on infinitely ramified fractal networks

We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff ($D_H$), topological Hausdorff ($D_{tH}$), and spectral ($d_s$) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers ($D_H$, $D_{tH}$, $d_s$), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension $D_{tH}$, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension $D_H$. The effect of the network connectivity on the site percolation threshold is revealed.     

A physical pathway to understand individual's labeling behavior in signed social networks

In this paper we propose a reshuffling approach to empirical analyze individual's labeling behavior in signed social networks. In our approach, each individual is assumed to have the ability to re-label his/her neighbors randomly with the parameters $p_s$ and $p_{+}$. Many reshuffled networks, which have the same topological structure and different signs' configuration, are built through applying our approach to the given three signed social networks. The entropy $S_{out}$ and the giant component ${\rho }_G$ for each reshuffled networks are calculated and analyzed. We find that there exist two kinds of individual's labeling behavior according to the suppressed effect of $S_{out}$ and the exponent α in the relationship of ${\rho }_G$ and $q_{+}$. Additionally, the suppressed effect of $S_{out}$ shows the non-randomness factor in individual's labeling behavior. These results offer new insights to understand human's behavior in online social networks.     

Exact PsTd invariant and PsTd symmetric breaking solutions,symmetry reductions and Bäcklund transformations for an AB–KdV system

In natural and social science, many events happened at different space–times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, $B=\stackrel{?}{f}A$ for suitable $\stackrel{?}{f}$ operators. A nonlocal AB–KdV system with shifted-parity ($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal with a delay) symmetry where $B=\stackrel{?}{P_s}\stackrel{?}{T_d}A$ is constructed directly from the normal KdV equation to describe two-area physical event. The exact solutions of the AB–KdV system, including $P_s{T}_d$ invariant and $P_s{T}_d$ symmetric breaking solutions are shown by different methods. The $P_s{T}_d$ invariant solution show that the event happened at A will happen also at B. These solutions, such as single soliton solutions, infinitely many singular soliton solutions, soliton–cnoidal wave interaction solutions, and symmetry reduction solutions etc., show the AB–KdV system possesses rich structures. Also, a special Bäcklund transformation related to residual symmetry is presented via the localization of the residual symmetry to find interaction solutions between the solitons and other types of the AB–KdV system.     

On spacelike hypersurfaces of constant sectional curvature lorentz manifolds

Let $x:M^n\to {\overline{M}}^{n+1}$ be an n-dimensional spacelike hypersurface of a constant sectional curvature Lorentz manifold $\overline{M}$. Based on previous work of S. Montiel, L. Alías, A. Brasil and G. Colares studied what can be said about the geometry of M when $\overline{M}$ is a conformally stationary spacetime, with timelike conformal vector field K. For example, if $M^n$ has constant higher order mean curvatures $H_r$ and $H_{r+1}$, they concluded that $M^n$ is totally umbilical, provided $H_{r+1}\ne 0$ on it. If div($K$) does not vanish on $M^n$ they also proved that $M^n$ is totally umbilical, provided it has, a priori, just one constant higher order mean curvature.In this paper, we compute $L_r(S_r)$ for such an immersion, and use the resulting formula to study both r-maximal spacelike hypersurfaces of $\overline{M}$, as well as, in the presence of a constant higher order mean curvature, constraints on the sectional curvature of M that also suffice to guarantee the umbilicity of M. Here, by $L_r$ we mean the linearization of the second order differential operator associated to the r-th elementary symmetric function $S_r$ on the eigenvalues of the second fundamental form of x.     

Spin-gapped phases in the frustrated Hubbard chain with transverse spin anisotropy

At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy $J_1^{xy}$ and $J_2^{xy}$. At half filling, we obtain three different phases in the $J_1^{xy}$–${J_2}^{xy}$ plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange $J_2^{xy}$ accounts for the spin-gapped phases.