International Journal of Modern Physics C

Nowadays, with the development of information communication technology and Internet, more and more people receive information and exchange their opinions with others via online environments (e.g. Twitter, Facebook, Weibo, and WeChat). According to eMarketer Report [Worldwide Internet and Mobile Users: eMarketer’s Updated Estimates and Forecast for 2015–2020 (eMarketer Report). Published October 11, 2016, https://www.emarketer.com/Report/Worldwide-Internet-Mobile-Users-eMarketers-Updated-Estimates-Forecast-20152020/2001897).], by the end of 2016, more than 3.2 billion individuals worldwide will use the Internet regularly, accounting for nearly 45% of the world population. By contrast, the other half of the global population still obtain information and regularly exchange their opinions in a more traditional way (e.g. face to face). Generally, the speed at which information spreads and opinions are exchanged and updated in an online environment is much faster than in an offline environment. This paper focuses on jointly investigating the challenge of consensus formation in opinion dynamics with online and offline interactions. Without loss of generality, we assume the speed at which information spreads and opinions are exchanged and updated in an online environment is $T(T\in \mathbb{N})$ times as fast as in an offline environment. We demonstrate that the update speed ratio in mixed online and offline environments (i.e. $T$) strongly impacts the consensus formation at complex networks: a large update speed ratio of online and offline environments (i.e. $T$) makes it difficult for all agents to reach consensus in opinion dynamics. Furthermore, these effects are often further intensified as the number of online participating agents increases.

A family of graphs optimized as the topologies for interconnection networks is proposed. The needs of such topologies with minimal diameters and minimal mean path lengths are met by special constructions of the weight vectors in a representation of the symplectic algebra. Such design of topologies can conveniently reconstruct the mesh and hypercube, widely used as network topologies, as well as many other classes of graphs potentially suitable for network topologies.

Application of Lagrangian meshless methods in modeling granular flow has been a major concern for researchers due to their particular nature. For modeling granular movement, it is assumed that the particles are continuous. The SPHysics code is developed for modeling the movement of Newtonian fluids in which the pressure is derived from the state equation. In this study, $\mu (I)$ and Herschel–Bulkley–Papanastasiou (HBP) viscoplastic models are implemented in the SPHysics code to analyze the movement of grains induced by the applied stresses. In the first model, the movement of granular particles is based on the characteristics such as inertia and friction coefficient, and in the second model, the movement is related to the non-Newtonian viscoplastic behavior of fluids. The accuracy of the models is evaluated by simulating the experimental benchmarks for granular dam break. The effect of length-to-height ratio on the failure mode of dam break phenomenon is also investigated. The performance of the models is increased by introducing the gate removal speed and also the harmonic mean of the viscosity instead of the viscosity proper to each particle. This study shows that the models could capture the behavior of grains in the static and the dynamic parts of the mass body.

Rhythmic patterns in the neuronal motifs are studied. For nonequal time-delays without noises, two situations are considered, where the conditions for synchronization, winnerless competition (WLC) and “two plus one” (TPO) are studied. In the first situation, if the coupling strengths are the same, then the time-delays are set the same. WLC and synchronization are easy to occur in this situation, while TPO is hard to occur. In the second situation, if the distances between two neurons are the same, then the time-delays are set the same. The complementary phenomenon is found and discussed in detail for TPO to occur in this situation. Next, when common noise with equal time-delay $\tau$ is added to the motifs, noise induced synchronization is compared for $\tau =0$ and $\tau =2.7$, where the motifs both exhibit WLC. When correlated noises with equal time-delay $\tau$ are added to the motifs, it is found that WLC is easier to be destroyed for $\tau =2.7$ than for $\tau =0$.

Recent generalization of the coevolving voter model [J. Toruniewska, K. Kułakowski, K. Suchecki and J. Hołyst, Phys. Rev. E 96, 042306 (2017).] is further generalized here, including spin-dependent probability of rewiring. Mean field results indicate that either the system splits into two separate networks with different spins, or one spin orientation goes extinct. In both cases, the density of active links is equal to zero. The results are discussed in terms of homophily in social contacts.

A representation formula for second-order nonhomogeneous nonlinear ordinary differential equations (ODEs) has been recently constructed by M. Frasca using its Green’s function, i.e. the solution of the corresponding nonlinear differential equation with a Dirac delta function instead of its nonhomogeneity. It has been shown that the first-order term–the convolution of the nonlinear Green’s function and the right-hand side, analogous to the Green’s representation formula for linear equations — provides a numerically efficient solution of the original equation, while the higher order terms add complementary corrections. The cases of square and sine nonlinearities have been studied by Frasca. Some new cases of explicit determination of nonlinear Green’s function have been studied previously by us. Here, we gather nonlinear equations and their explicitly determined Green’s functions from existing references, as well as investigate new nonlinearities leading to implicit determination of nonlinear Green’s function. Some transformations allowing to reduce second-order nonlinear partial differential equations (PDEs) to nonlinear ODEs are considered, meaning that Frasca’s method can be applied to second-order PDEs as well. We perform a numerical error analysis for a generalized Burgers’ equation and a nonlinear wave equation with a damping term in comparison with the method of lines.

A family of exponentially fitted two-step hybrid methods for the numerical integration of the Schrödinger equation is investigated. The asymptotic expressions of the local errors for large energies are presented. The stability of the new methods is analyzed. Numerical results are reported for the widely used Woods–Saxon potential to show the efficiency of the new methods. The error analysis is clearly tested by the resonance problem.

A modified cellular automata traffic model is proposed to simulate four-lane traffic flow, in which drivers are classified into aggressive drivers and cautious drivers and the anticipative velocity of the adjacent vehicles is considered. Analysis from the vehicles’ evolution pattern indicates that vehicles driven by the aggressive drivers are more powerful in behaviors of lane-changing and car-following. The model is refined by using the small cell of one meter long in order to simulate the traffic flow meticulously and realistically. The results indicate that the lane-changing maneuver exhibits different property as the density varies, and it does have a significant impact on the characteristics of the surrounding traffic flow due to their interfering effects on the following vehicles. Furthermore, the phenomenon of high-speed car-following is exhibited, and the results coincide with the empirical data very well. It is shown that the proposed model is reasonable and can partially reflect the real traffic.

In this work, we investigate computationally the dynamics of a nonlinear partial differential equation with anomalous diffusion that extends the well-known double sine–Gordon equation from relativistic quantum mechanics. The problem under consideration includes the presence of constant damping along with anomalous spatial derivatives. The model is defined on a close and bounded interval of the real line, and it is at rest at the initial time. One end of the interval is subject to sinusoidal driving, and the other considers the presence of an absorbing boundary in order to simulate a semi-infinite medium. The simulation of this system is carried out using a numerical method that resembles the energy properties of the continuous medium. The computational results shown in this work establish the presence of the nonlinear phenomenon of bistability in the system considered. We obtain hysteresis cycles for some particular scenarios, and employ the bistability of the system to simulate the transmission of binary signals from the driving boundary to the opposite end.

In this paper, an efficient scheme for image encryption based on the nested chaotic map and deoxyribonucleic acid (DNA) is introduced. In order to generate the initial condition values of the nested chaotic system, the Secure Hash Algorithm SHA-256 is used. The algorithm consists of two main layers: confusion and diffusion. In the first layer, the nested chaotic map is employed to create the scrambled image. The scrambled image is obtained through the ascending sorting of the first component of the nested chaotic index sequence. To ensure higher sensitivity, higher complexity and higher security, DNA sequence and DNA operator are employed additionally with the nested chaotic map and hash algorithm to modify the pixel values. The important advantages of our algorithm are the improvement of Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI) and entropy, which improve resistivity against several attacks. Experimental results and relevant security analysis demonstrated that our proposed encryption scheme has the highest security level because it is more complicated, and it has a sufficiently large key space. The proposed method is compared to other recent image encryption schemes using different security analysis factors, including NPCR, UACI, correlation coefficients (CCs), encryption quality (EQ) and entropy. It is also resistant to noise (Salt and Pepper, Gaussian and speckle) and data loss attacks. The illustrated results demonstrated that the proposed image encryption scheme is efficient, and can be adopted for image encryption and transmission.

We consider a phase field model for molecular beam epitaxial growth with slope selection with the goal of determining linear energy stable time integration methods for the dynamics. Stable methods for this model have been found via a concave-convex splitting of the dynamics, but this approach generally leads to a nonlinear update equation. We seek a linear energy stable method to allow for simple and efficient time marching with fast Fourier transforms. Our approach is to parametrize a class of semi-implicit methods and perform unconditional von Neumann stability analysis to identify the region of stability in parameter space. Since unconditional von Neumann stability does not ensure energy stability, we perform extensive numerical tests and find strong agreement between the predicted and observed stable regions of parameter space. This analysis elucidates a novel feature that the stability region in parameter space differs for a mono-domain system (single equilibrium slope) versus a many-domain system (coarsening facets from an initially flat surface). The utility of these steps is then demonstrated by a comparison of the coarsening dynamics for isotropic and anisotropic variants of the model.

Community detection is significative in the complex network. This paper focuses on community detection based on clustering algorithms. We tend to find out the central nodes of the communities by centrality algorithms. Firstly, we define the distance between nodes using similarity. Then, a new centrality measuring the local density of nodes is put forward. Combining the independence of the centrality, the nodes in the network can be divided into four classes. Leveraging the product of centrality and independence, the central nodes in the network are easily identified. We also find that we can distinguish bridge nodes from central nodes using centrality and independence. This research designs a community detection algorithm combining centrality and independence. Simulation results reveal that our centrality is more effective than existing centralities in measuring local density and identifying community centers. Compared with other community detection algorithms, results prove the effectiveness of our algorithm. This paper just shows one application of independence of the centrality. There may be more useful applications of it.

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ($T$), as well as the critical exponents $\gamma ∕\nu$, $\beta ∕\nu$, and $1∕\nu$ for several values of the rewiring probability $p$. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on $p$ ($0<p<1$), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.

Using the Nagel-Schreckenberg model, we investigate the flow characteristics in a traffic circle system, where the entry lanes are controlled by traffic lights operating in a fixed-time ($T)$. We considered four different strategies to control traffic coming from $N$ entry lanes. We found that depending on the strategy used, four distinct traffic phases can appear in the circulating lane of the traffic circle, namely free flow, congestion, maximum current, and gridlock. Also, we investigate the origin of the gridlock phase in both cases (i.e. with/without traffic lights). Furthermore, the lengths of queues of stopped vehicles in the entry lanes were studied. We found that the traffic flow behavior on the exit/entry lanes depends strongly on the flow characteristics at the circulating lane as well as traffic lights strategy. To improve the operation of the traffic circle system, we have studied the time delay between the traffic lights to switch where all entry lanes go red, which allowing vehicles to clear the circulating lane.