International Journal of Modern Physics C

In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.

In order to investigate the effect of driver’s memory during a period of time upon traffic dynamics, an extended lattice hydrodynamic model for traffic flow is proposed and studied analytically and numerically in this paper. The linear stability analysis reveals that the time length of driver’s memory has an important effect on stability of traffic flow. The factor will lead to the occurrence of traffic congestion. Three typical nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equation are derived to describe the evolution of density wave for traffic flow in three different regions, which are stable, meta-stable and unstable region, respectively. The simulations are given to illustrate and clarify the analytical results. The results indicate that the time length of driver’s memory has a negative effect upon stability of traffic flow.

Traffic is one of the most fundamental dynamical processes in networked systems. With the traditional shortest path routing (SPR) protocol, traffic congestion is likely to occur on the hub nodes on scale-free networks. In this paper, we propose an improved optimal routing (IOR) strategy which is based on the betweenness centrality and the degree centrality of nodes in the scale-free networks. With the proposed strategy, the routing paths can accurately bypass hub nodes in the network to enhance the transport efficiency. Simulation results show that the traffic capacity as well as some other indexes reflecting transportation efficiency are further improved with the IOR strategy. Owing to the significantly improved traffic performance, this study is helpful to design more efficient routing strategies in communication or transportation systems.

The present paper maps the records of urban taxi trips into dynamic networks, where nodes are the communities and links represent the recorded taxi trips between them. The dynamic urban taxi trip networks, where nodes are the communities and links represent the recorded taxi trips between them, are formulated here as a special type of large-scale traffic system with an enormous impact on the city, in which the existence of uncertainties together with the spatial and temporal variation in the distribution of the taxi trips are considered. Three types of indicators are proposed to facilitate the measurement of the activities between and inside the communities (nodes of the network) from qualitative and quantitative perspectives. It could be found from the analysis of the records within the New York city that these indicators are inconsistent to each other, and nevertheless, none of them distributes uniformly within the city but generally follows the power law in spite of their time-dependent properties. Further, the unusually low values of the scaling parameters from the curve fitting with power law for all the proposed indicators illustrate the severe inhomogeneity of the networks (also the city).

In this paper, exponential synchronization in complex-variable network with distributed delays is investigated. By utilizing intermittent control scheme, some effective controllers are designed. Based on the Lyapunov function method and mathematical analysis technique, some synchronization criteria with respect to the system parameters, control gain and control rate are presented. From the criteria, for any given dynamical network, the needed values of control gains and rate can be easily estimated. Finally, two numerical simulations are performed to verify the derived theoretical results.

The dissolution and diffusion behaviors of H in the four low-Miller-index W surfaces ((110), (112), (100) and (111)) are systematically studied by the density functional theory approach to understand the orientation dependence of the H bubble distribution on surface. The results show that H accumulation on surface is influenced by H diffusion barrier as well as vacancy and H formation. The barriers of diffusion towards surfaces are larger than that in bulk. It indicates that H is prone to diffuse into the deep in bulk once H dissolves in surface. H is preferred to accumulate on the W(111) surface due to the lower formation energies of vacancy and H comparing to that in bulk. However, W(110) is the resistant surface for forming H bubble due to the higher formation energies of vacancy and H. The results are helpful for understanding the orientation dependence of surface damages on W surface and designing new plasma-facing materials.

In order to study the information communication ability (i.e. information conductivity) of CodePlex C# community, an Open-Source Online Community (OSOC), we first construct the models of weighted communication networks in 11 periods for the community based on large-scale data collections. Then by using two ways of quantum mapping of complex networks, we analyze the localization properties of information on the maximum connected graphs (named as communication networks) of these weighted networks according to the idea of analyzing the localization properties of an electron on a large cluster. We draw the following conclusions. (1) CodePlex C# OSOC usually has information isolativity. (2) The community has some degree of information communication ability and the ability increases as time goes on. (3) The localization of information on the communication networks in any period induced by its structure is weaker than that induced by its structure together with the connection intensities between its nodes. (4) Our idea and methods can be used to analyze the information communication ability of other online communities.

We present a fragmentation model that generates almost any inverse power-law size distribution, including dual-scaled versions, consistent with the underlying dynamics of systems with earthquake-like behavior. We apply the model to explain the dual-scaled power-law statistics observed in an Internet access dataset that covers more than 32 million requests. The non-Poissonian statistics of the requested data sizes $m$ and the amount of time $\tau$ needed for complete processing are consistent with the Gutenberg–Richter–law. Inter-event times $\delta t$ between subsequent requests are also shown to exhibit power-law distributions consistent with the generalized Omori law. Thus, the dataset is similar to the earthquake data except that two power-law regimes are observed. Using the proposed model, we are able to identify underlying dynamics responsible in generating the observed dual power-law distributions. The model is universal enough for its applicability to any physical and human dynamics that is limited by finite resources such as space, energy, time or opportunity.

In this paper, we propose a stochastic cellular automata (CA) model to study traffic dynamic at a single-lane traffic circle of $N$ entry/exit points. The boundaries are controlled by the injecting rates ${\alpha }_1$, ${\alpha }_2$ and the extracting rate $\beta$. Both the cases with and without the splitter islands of width $L_{sp}$ are considered. The phase diagrams in the space ${(\alpha }_1\beta )$ are constructed and the density profiles are also investigated. The variation of the phase diagram with the traffic circle size $(L)$, the number of entry point $(N)$, and the time needed for drivers to change their exit willingly $(T_{\mathrm{\text{exit}}})$ is studied. The results show that the phase diagram in both cases consists essentially of three phases namely free flow, congestion and gridlock. However, the large sized traffic circle shows better performance in the free flow phase, in contrary, the increase of $N$ enlarges the congestion and the gridlock phases. We have also found that the decrease of $T_{\mathrm{\text{exit}}}$ enhances the traffic flow situation in the traffic circle. Furthermore, as the $L_{sp}$ increases, the free flow phase enlarges while the congestion and gridlock ones shrink.

The time series of the states of several well-known hyperchaotic systems are analyzed numerically using the detrended fluctuation analysis based on the discrete wavelet transform. We report the finding of significant scaling behaviors (power-law like) in some of these time series, which can be used as an additional characteristic distinguishing the dynamical evolution of such systems.

Reservoir Computing (RC) refers to a Recurrent Neural Network (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here, we focus on the sequence learning problem, and we explore a different approach to RC. More specifically, we remove the nonlinear neural activation function, and we consider an orthogonal reservoir acting on normalized states on the unit hypersphere. Surprisingly, our numerical results show that the system’s memory capacity exceeds the dimensionality of the reservoir, which is the upper bound for the typical RC approach based on Echo State Networks (ESNs). We also show how the proposed system can be applied to symmetric cryptography problems, and we include a numerical implementation.

We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant velocities of circular motion, i.e. flat rotation curves. At smaller distances, the field switches to Newtonian regime, then to Schwarzschild regime. Deviations from Schwarzschild regime start below the gravitational radius. The dark matter prevents the creation of event horizon, instead, a spherical region possessing extremely large redshift is created. The structure of space-time for the obtained solutions is investigated and the implications for the models of the galaxies are discussed.

In this paper, one new coupled higher order two-scale finite element method (TSFEM) for thermoelastic problem in composites is proposed. Firstly, some new two-scale asymptotic expressions and homogenization formulations for the problem are briefly given. Next, some high–low coupled approximate errors corresponding to TSFEM are analyzed. Finally, some numerical results of the displacement and the increment of temperature are presented, which show that TSFEM is an effective method for predicting the mechanical and the thermal behavior of composites in quasi-periodic perforated structure.

The phonon, elastic and thermodynamic properties of L1₂ phase Rh₃Zr have been investigated by density functional theory approach combining with quasi-harmonic approximation model. The relaxed lattice parameters of L1₂ phase Rh₃Zr at zero pressure are in good agreement with the experiment. To judge the stability of L1₂ phase Rh₃Zr under high pressure, the phonon band structure has been studied. The results show that L1₂ phase Rh₃Zr possesses dynamical stability in the pressure range from 0GPa to 80GPa due to the absence of imaginary frequencies. The pressure dependences of elastic constants $C_{ij}$ have been analyzed. All the elastic constants of Rh₃Zr in a wide pressure range (0–80GPa) meet general mechanical conditions, suggesting that L1₂ phase Rh₃Zr is mechanically stable under pressure up to 80GPa. L1₂ phase Rh₃Zr exhibits ductility under high pressure and the pressure can improve the ductility from the results of the value of $B∕G$ and Poisson’s ratio $\nu$. Hence, it is obvious that the mechanical properties of Rh₃Zr can be improved under high pressure. Moreover, we have obtained the thermodynamic properties using the quasi-harmonic Debye model. We note that the effect of the temperature on the Debye temperature ${\mathrm{\Theta }}_D$ is smaller than that of the pressure. We believe that our result will be a good guidance to future works and applications.