International Journal of Modern Physics C

Based on multi-phase car-following model proposed by Nagatani, the control theory method is used to analyze the stability of the model. The optimal velocity function is improved to have more turning points. The original optimal velocity with one turning point shows two-phase traffic, while the improved model with $n$ turning points exhibits $n+1$ phase traffic. Control signal is added into the model. Numerical simulation is conducted to show the results for the stability of the model with and without control signal.

The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma =10^{-5}-10^{-1}$. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of $\gamma$ for different sizes of the data sample. In particular, it has been found that even in case of pure fractals ($\gamma =0$) as well as for tiny noise ($\gamma \approx 10^{-5}$) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 and more, with natural saturation limited by the embedding dimension. This prohibits the power-like scaling of the error. Moreover, the noise effect cannot be cured by taking larger data samples.

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen–Ledoit–Sornette (JLS) model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power $s^a$ (with $a>1$) of the cluster sizes $s^{}$, similarly to a generalized percolation susceptibility. The power $s^a$ of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold $p_c$. Realistic dynamics are generated by modeling the density of traders on the percolation network by an Ornstein–Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.

Monte Carlo simulations of lattice spin models are employed to investigate the effects of an external field on the creation and evolution of inversion walls in nematic films with conical boundary conditions. The simulations, based on the well known Lebwohl-Lasher potential, allow to produce simulated polarized microscopy images which are followed during their evolution when the field is applied.

Research in network controllability has mostly been focused on the effects of the network structure on its controllability, and some methods have been proposed to optimize the network controllability. However, they are all based on global structure information of networks. We propose two different types of methods to optimize controllability of a directed network by local structure information. Extensive numerical simulation on many modeled networks demonstrates that this method is effective. Since the whole topologies of many real networks are not visible and we only get some local structure information, this strategy is potentially more practical.

This paper has studied the minimum traffic delay at a two-phase intersection, taking into account the dynamical evolution process of queues. The feature of delay function has been studied, which indicates that the minimum traffic delay must be achieved when at least one of the two constraint inequalities take the equal sign. We have derived the minimum delay as well as the corresponding traffic signal period, which shows that two situations are classified. Under certain circumstance, extra green time is needed for one phase while otherwise extra green time should be assigned to neither phase. Our work indicates that although the clearing policies were shown in many experiments to be optimal at isolated intersections, it is sometimes not the case.

In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms $L_2$ and $L_{\infty }$. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.

The quantification of the complexity of network is a fundamental problem in the research of complex networks. There are many methods that have been proposed to solve this problem. Most of the existing methods are based on the Shannon entropy. In this paper, a new method which is based on the nonextensive statistical mechanics is proposed to quantify the complexity of complex network. On the other hand, most of the existing methods are based on a single structure factor, such as the degree of each node or the betweenness of each node. In the proposed method, both of the influence of the degree and betweenness are quantified. In the new method, the degree of each node is used as the constitution of the discrete probability distribution. The betweenness centrality is used as the entropic index q. The nodes which have big value of degree and betweenness will be have big influence on the quantification of network’s structure complexity. In order to describe the relationship between the nodes and the whole network more reasonable, a entropy index set is defined in this new method. Therefore, every node’s influence on the network structure will be quantified. When the value of all the elements in the entropic index set is equal to 1, the new structure entropy is degenerated to the degree entropy. It means that the betweenness of each node in the network is equal to each other. And the structure complexity of the network is determined by the node’s degree distribution. In other words, the new structure entropy is a generalization of the existing degree structure entropy of complex networks. The new structure entropy can be used to quantify the complexity of complex networks, especially for the networks which have a special structure.

In this paper, we show the reaction of a hydroxyl, phenyl and phenoxy radicals with DNA base pairs by the density functional theory (DFT) calculations. The influence of solvation on the mechanism is also presented by the same DFT calculations under the continuum solvation model. The results showed that hydroxyl, phenyl and phenoxy radicals increase the length of the nearest hydrogen bond of adjacent DNA base pair which is accompanied by decrease in the length of furthest hydrogen bond of DNA base pair. Also, hydroxyl, phenyl and phenoxy radicals influenced the dihedral angle between DNA base pairs. According to the results, hydrogen bond lengths between AT and GC base pairs in water solvent are longer than vacuum. All of presented radicals influenced the structure and geometry of AT and GC base pairs, but phenoxy radical showed more influence on geometry and electronic properties of DNA base pairs compared with the phenyl and hydroxyl radicals.

Predicting missing links in complex networks is of great significance from both theoretical and practical point of view, which not only helps us understand the evolution of real systems but also relates to many applications in social, biological and online systems. In this paper, we study the features of different simple link prediction methods, revealing that they may lead to the distortion of networks’ structural and dynamical properties. Moreover, we find that high prediction accuracy is not definitely corresponding to a high performance in preserving the network properties when using link prediction methods to reconstruct networks. Our work highlights the importance of considering the feedback effect of the link prediction methods on network properties when designing the algorithms.

We analyze the impact of the network structure, the default probability and the loss given default (LGD) on the loss distribution of systemic defaults in the interbank market, where network structures analyzed include random networks, small-world networks and scale-free networks. We find that the network structure has little effect on the shape of the loss distribution, whereas the opposite is true to the default probability; the LGD changes the shape of the loss distribution significantly when default probabilities are high; the maximum of the possible loss is sensitive to the network structure and the LGD.

In this paper, we investigate the random walks on metro systems in 28 cities from worldwide via the Laplacian spectrum to realize the trapping process on real systems. The average trapping time is a primary description to response the trapping process. Firstly, we calculate the mean trapping time to each target station and to each entire system, respectively. Moreover, we also compare the average trapping time with the strength (the weighted degree) and average shortest path length for each station, separately. It is noted that the average trapping time has a close inverse relation with the station’s strength but rough positive correlation with the average shortest path length. And we also catch the information that the mean trapping time to each metro system approximately positively correlates with the system’s size. Finally, the trapping process on weighted and unweighted metro systems is compared to each other for better understanding the influence of weights on trapping process on metro networks. Numerical results show that the weights have no significant impact on the trapping performance on metro networks.

The rise of empires can be elucidated by treating them as living organisms, and the celebrated Verhulst or Lotka–Volterra dynamics can be used to understand the growth mechanisms of empires. The fast growth can be expressed by an exponential function as in the case of Macedonian empire of the Alexander the Great whereas a sigmoidal growth can be expressed by power-law equation as in the case of Roman and Ottoman empires. The superpowers Russia and the USA follow somehow different mechanisms, Russia displays two different exponential growth behaviors whereas the USA follows two different power-law behaviors. They did not disturb and mobilize their social capacity much during the course of their rise. The decline and the collapse of an empire occur through a kind of fragmentation process, and the consequently formed small states become rather free in their behavior. The lands of the new states formed exhibit a hierarchical pattern, and the number of the states having an area smaller than the largest one can be given either by an exponential or power-law function. The exponential distribution pattern occurs when the states are quite free in their pursuits, but the power-law behavior occurs when they are under the pressure of an empire or a strong state in the region. The geological and geographical conditions also affect whether there occurs exponential or power-law behavior. The new unions formed such as the European Union and the Shanghai Cooperation increase the power-law exponent implying that they increase the stress in the international affairs. The viscoelastic behavior of the empires can be found from the scattering diagrams, and the storage $(G^{\prime })$and loss modulus $(G^{\prime \prime })$, and the associated work-like and heat-like terms can be determined in the sense of thermodynamics. The $G^{\prime }$ of Ottomans was larger than that of Romans implying that they confronted severe resistance during their expansion. The $G^{\prime }$ of Russia is also larger than that of the USA; in fact the USA did not face severe resistance as they had an overwhelming superiority over native Americans. The $G^{\prime }>G^{\prime \prime }$ indicates solidity in the social structure and Romans, Ottomans, and Russians all have $G^{\prime }$ larger than $G^{\prime \prime }$. The $G^{\prime }$ is slightly larger than $G^{\prime \prime }$ for the USA indicating that they have had a very flexible social structure. By the same token the ratio of the work-like term to the internal energy is larger for Ottomans than that of Romans, and larger for the USA than that of Russia. That means the fraction of the total energy allocated to improve the social capacity is larger for Romans than that of Ottomans, and is larger for Russians than that of the USA.

Using molecular dynamics (MD) simulation, we study the temperature-induced $\alpha \leftrightarrow \gamma$ phase transformation of an Fe${}_{0.9}$Cr${}_{0.1}$ alloy. We find that the austenitic transition temperature is increased with respect to that of an Fe${}_{0.9}$Ni${}_{0.1}$ alloy containing the same concentration of impurity atoms. During the austenitic transformation, heterogeneous nucleation of close-packed (cp) nuclei leads to a polycrystalline structure. The microstructure formed closely resembles that found in pure Fe and in FeNi alloys.