International Journal of Modern Physics C

Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al. in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy.

In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds of confidence. Second, it will give the bifurcation diagrams of cluster configuration in the homogeneous model with uniformly distributed initial opinions. Third, it will review the several extensions and the evolving phenomena which have been studied so far, and fourth it will state some open questions.

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of Robinson–Trautman spacetimes.

In this paper, the effects of passing lanes on traffic flow on a single-lane highway are investigated based on a cellular-automaton (CA) model proposed by Lee et al. (2004) with periodic boundary conditions. A new driving strategy for the diverging and interacting processes are proposed by considering dual-time-headways (an interaction headway and a safe headway) as the criteria for a vehicle to select a lane or change lane. The proposed dual-headway rule has a clear physical sense and can be calibrated in the real world. We can see that (i) At low- (or high-) densities, there are no obvious increases of flux due to very weak (or very strong) interactions between vehicles. However, flux has an obvious increase at intermediate-density regions with the increase of the length of a passing lane; (ii) the space-time patterns before a passing lane are different from that after a passing lane, which is caused from vehicular reconfigurations on a passing zone; (iii) passing lanes can merge several narrow jams into one or few wide jams when increasing the length of passing lanes; (iv) if vehicles are allowed to travel with even higher speed, traffic can be further improved.

A multiparty quantum secret sharing scheme based on Bell-state entanglement swapping [Z. J. Zhang and Z. X. Man (2005)] is generalized to the qutrit case, that is, with qutrit-pair entangled states we propose a multiparty quantum secret sharing (QSS) scheme of classical messages by swapping qutrit-state entanglement. The security of our scheme is analyzed and confirmed with respect to some attacks. Compared to the scheme being generalized, this scheme possesses the distinct advantages of higher code capacity and higher security. Moreover, the generalization of the scheme to the qudit case is also outined.

Natural convection in an enclosure with different ratios are investigated with the lattice Boltzmann method, and double distribution functions (DDF) are proposed to simulate the velocity and the temperature fields. Meanwhile, compared with other existing results, we studied the effect of the different aspect ratios on heat transfer, and 2D numerical simulation of natural convection flow in a square cavity are performed at Rayleigh numbers 10³–10⁶ with fixed Prandtl number 0.71 in detail. The numerical results of the Nusselt number along the two sidewalls and the maximum velocities along the horizontal and vertical lines through the cavity center are in good agreement with existing results, which shows the accuracy of the present model.

In this paper, a two-lane traffic system consisting of a mixture of buses and cars is studied. The buses stop at each bus stop to pick up passengers and are not allowed to change lane. The cars may change lane when hindered by preceding vehicles. Our simulations show that with a fixed number of buses, four states of the traffic system are identified. The spatial-temporal plots of the four traffic states, and the trajectories of buses at different densities are presented. A gradual transition instead of sharp phase transition from bunching state to homogeneous state of the buses is found. Next, we study the system behavior at different number of bus stops, and an optimal number of stops is suggested. Finally, the influence of bus stops on the fundamental diagram is studied.

This paper proposes a study of the computational efficiency of a lattice Boltzmann model (LBM) solver to simulate the behavior of a generalized Newtonian fluid. We present recent progress concerning a 4-1 planar contraction considering a power-law and a Carreau-law model. First we compare the power-law model for a Poiseuille flow with the analytical solution, and show that our model is second-order accurate in space. Then we compare the results obtained with LBM for both laws to those obtained using a commercial finite element solver for the 4-1 plane sharp corner contraction.

Transition metals such as titanium are known to attract (molecular) H₂ in some complexes through Kubas interaction. This interaction involves coordination of sigma bonds of the H2 with the transition metal, and it is comparatively strong, allowing promising hydrogen storage applications. In this work, the impact of structural geometry on this coordination is investigated using a model titan–carbide structure (TiC₄H₄) by performing density functional theory calculations.

We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Lewy numbers. As a result, with our implicit-explicit finite-difference scheme the computational convergence rate can be significantly improved compared with previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of the Riemann problem, Taylor vortex flow, Couette flow, and oscillatory compressible flows with shock waves show that our implicit-explicit finite-difference lattice Boltzmann method is accurate and efficient. In addition, it is demonstrated that with the proposed scheme non-uniform meshes can also be implemented with ease.

We have calculated the relative density and crossing time through the fitness barrier by switching on an asymmetric sharply-peaked landscape, from the initial state which is the quasispecies in a sharply-peaked landscape. It is found that the increment of the relative density with the reversal sequence is a linearly increasing function of time unless a new stationary state in an asymmetric sharply-peaked landscape is reached. It is also found that the relative density with the reversal sequence at the new stationary state is in inverse proportion to the asymmetric parameter when the asymmetric parameter is greater than the saturation asymmetric parameter. We have derived the approximate formulae for the relaxation time, the saturation asymmetric parameter, and the relative density with the reversal sequence , which nicely fit computer simulation results. It is found that the crossing time diverges at the critical fitness parameter in the asymmetric sharply-peaked landscape, in contrast with the symmetric sharply-peaked landscape where the crossing time scales as a power law in the fitness parameter. It is also found that the critical fitness parameter decreases as the asymmetric parameter and sequence length increase.

We use a model whose rules were inspired by population genetics and language competition, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle plate-like objects, and in particular the existence of (i) composite scaling laws, (ii) small critical exponents τ associated with the power-law fragment-size distribution, and (iii) the typical pattern of cracks. The proposed computer simulations do not require numerical solutions of Newton's equations of motion, nor several additional assumptions normally used in discrete element models. The model is also able to predict some physical aspects which could be tested in new experiments of fragmentation of brittle systems.