International Journal of Modern Physics C

By utilizing the molecular dynamics code SPaSM on Livermore's BlueGene/L architecture, consisting of 212 992 IBM PowerPC440 700 MHz processors, a molecular dynamics simulation was run with one trillion atoms. To demonstrate the practicality and future potential of such ultra large-scale simulations, the onset of the mechanical shear instability occurring in a system of Lennard-Jones particles arranged in a simple cubic lattice was simulated. The evolution of the instability was analyzed on-the-fly using the in-house developed massively parallel graphical object-rendering code MD_render.

We proposed a new car-following model named as total generalized optimal velocity model (TGOVM) based on the analysis of the previous models. TGOVM is superior to the previous models in stabilizing the uniform traffic flow by considering all the front influencing factors: headways, relative velocities, and interactions. The linear analysis result showed its superiority to the GOVM, FLOVM, and FLRVM. The nonlinear analysis method is adopted to analyze this model, which described by a differential-difference equation. The modified Korteweg-de Vries (KdV) equation is derived and the kink-antikink soliton solution is obtained near the critical point. The simulation results show that the stabilization is enhanced by the improvement.

Many real systems can be regarded as complex networks. In this paper, we investigate the influence of traffic assignments on transportation dynamics in complex networks with different topologies. The sequential problem is motivated by the fact that some previous works are only on traffic assignment of user equilibrium (UE). We introduce traffic assignments of system equilibrium (SE) and system optimization (SO) to analyze the relationship between traffic assignments and network topologies. In terms of these traffic assignments, some interesting results concerning system total cost are obtained. Simulation results demonstrate that load distribution also exhibits a power-law behavior for SE and SO assignments in scale-free networks. Furthermore, the exponents for SE and SO assignments are much larger than that for UE assignment. It indicates that traffic assignments play an important role in determining the transportation dynamics in scale-free networks. Finally, cascading failures of link removal in different topologies are discussed.

A many-body system with co-existing attractive and repulsive interactions is considered on a ring. The competing interactions lead to a frustration similar with the one existing in Correlation Clustering (CC). The optimal mechanical equilibrium of the system is searched by molecular dynamics simulations. As a function of the disorder quenched in the interactions, the system exhibits the phase-transition recently reported in CC. The simulated system can be considered as a continuous and efficient approach to the otherwise discrete, NP hard CC problem.

In this paper, we numerically investigate the structural characteristics that affect the synchronizability of coupled identical oscillators on scale-free networks. By using the edge-exchange method, we can change the network structure with degree sequence fixed. An optimal algorithm, namely Tabu Search, is applied, respectively, to enhance and weaken the synchronizability. The numerical results indicate that the synchronizability is most sensitive to the maximal betweenness. By tracking the optimization process, most previous works suggest that the synchonizability can be enhanced by reducing assortative coefficient and clustering coefficient; however, interestingly, our numerical simulations show that the depression of synchronizability also corresponds to the reduction process of those two coefficients.

In this paper, we use the speed-gradient model proposed by Jiang et al. [Transp. Res. B36, 405 (2002)] to study the effects that various perturbations have on the stability of traffic flow. Our numerical tests show that the effects of perturbations on the stability of traffic flow are related to the initial density, i.e., when the initial density is very low (ρ₀ ≤ 0.02) or very high (ρ₀ > 0.08), any perturbation has little effect on the stability of traffic flow; when the initial density is relatively low (0.02 < ρ₀ ≤ 0.04), small perturbations have little effect on the stability of traffic flow and large perturbations will have effect on it and produce local cluster; when the initial density is relatively high (0.04 < ρ₀ ≤ 0.08), any perturbation will have great effect on the stability of traffic flow and produce stop-and-go traffic. These results are completely accordant with the real traffic, which just shows that the speed-gradient model can be used to perfectly explore the consequences caused by various perturbations.

We study the evolutionary Prisoner's Dilemma game under individual learning activity mechanism on small-world and scale-free networks, respectively. Each player updates its strategy with quenched learning rate which characterizes the strength of individual learning activity during the evolutionary process. Simulation results show that the mechanism of learning activity presents nontrivial phenomena on both the two networks: optimal intermediate levels of learning activity can promote or sustain cooperation. Specifically, there exists an interesting resonance-like manner in the evolutionary game when the intermediate level of learning activity promotes cooperation, and there exists a plateau for cooperation in the favorable moderate region of learning activity when the intermediate level of learning activity sustains cooperation. Moreover, these interesting phenomena are not sensitive to the two networks with other topological parameters. Our work can be helpful in reflecting the effects of individual learning mechanism on cooperative behavior in social systems.

The characteristic of the fixed points of the Carotid–Kundalini (C–K) map is investigated and the boundary equation of the first bifurcation of the C–K map in the parameter plane is given. Based on the studies of the phase graph, the power spectrum, the correlation dimension and the Lyapunov exponents, the paper reveals the general features of the C–K map transforming from regularity. Meanwhile, using the periodic scanning technology proposed by Welstead and Cromer, a series of Mandelbrot–Julia (M–J) sets of the complex C–K map are constructed. The symmetry of M–J set and the topological inflexibility of distributing of periodic region in the Mandelbrot set are investigated. By founding the whole portray of Julia sets based on Mandelbrot set qualitatively, we find out that Mandelbrot sets contain abundant information of structure of Julia sets.

For each celestial body of multi-planet systems, there are two slowly varying quantities or quasi-integrals, Kepler energy and Laplace integral, which are closely associated with the orbital semimajor axis and eccentricity, respectively. To correct numerical errors of the quantities, we give an extension of Nacozy's approach and develop a new manifold correction method, where corresponding reference values of the quantities at every integration step are obtained from integral invariant relations, and only velocity corrections are used to approximately satisfy the two quasi-integrals. As a result, the scheme does enhance the quality of the integration by significantly raising the accuracy of the two elements. Especially, it is superior to the existing dual scaling method in the improvement of eccentricity in general when the adopted integrator provides a sufficient precision to the eccentricity.

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

Tsallis entropy introduced in 1988 is considered to have obtained new possibilities to construct generalized thermodynamical basis for statistical physics expanding classical Boltzmann–Gibbs thermodynamics for nonequilibrium states. During the last two decades this q-generalized theory has been successfully applied to considerable amount of physically interesting complex phenomena. The authors would like to present a new view on the problem of algorithms computational complexity analysis by the example of the possible thermodynamical basis of the sorting process and its dynamical behavior. A classical approach to the analysis of the amount of resources needed for algorithmic computation is based on the assumption that the contact between the algorithm and the input data stream is a simple system, because only the worst-case time complexity is considered to minimize the dependency on specific instances. Meanwhile the article shows that this process can be governed by long-range dependencies with thermodynamical basis expressed by the specific shapes of probability distributions. The classical approach does not allow to describe all properties of processes (especially the dynamical behavior of algorithms) that can appear during the computer algorithmic processing even if one takes into account the average case analysis in computational complexity. The importance of this problem is still neglected especially if one realizes two important things. The first one: nowadays computer systems work also in an interactive mode and for better understanding of its possible behavior one needs a proper thermodynamical basis. The second one: computers from mathematical point of view are Turing machines but in reality they have physical implementations that need energy for processing and the problem of entropy production appears. That is why the thermodynamical analysis of the possible behavior of the simple insertion sort algorithm will be given here.

We propose a model that extends the binary "united we stand, divided we fall" opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions on a linear chain. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.