Traffic-driven epidemic spreading in multiplex networks.

Recent progress on multiplex networks has provided a powerful way to abstract the diverse interaction of a network system with multiple layers. In this paper, we show that a multiplex structure can greatly affect the spread of an epidemic driven by traffic dynamics. One of the interesting findings is that the multiplex structure could suppress the outbreak of an epidemic, which is different from the typical finding of spread dynamics in multiplex networks. In particular, one layer with dense connections can attract more traffic flow and eventually suppress the epidemic outbreak in other layers. Therefore, the epidemic threshold will be larger than the minimal threshold of the layers. With a mean-field approximation, we provide explicit expressions for the epidemic threshold and for the onset of suppressing epidemic spreading in multiplex networks. We also provide the probability of obtaining a multiplex configuration that suppresses the epidemic spreading when the multiplex is composed of: (i) two Erdos-Rényi layers and (ii) two scale-free layers. Therefore, compared to the situation of an isolated network in which a disease may be able to propagate, a larger epidemic threshold can be found in multiplex structures.

History-dependent percolation on multiplex networks.

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, study of the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state, and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks.

Theoretical analysis and simulation of phase separation in a driven bidirectional two-lane system.

The two-lane driven system is a type of important model to research some transport systems, and also a powerful tool to investigate properties of nonequilibrium state systems. This paper presents a driven bidirectional two-lane model. The dynamic characteristics of the model with periodic boundary are investigated by Monte Carlo simulation, simple mean field, and cluster mean field methods, respectively. By simulations, phase separations are observed in the system with some values of model parameters. When the phase separation does not occur, cluster mean field results are in good agreement with simulation results. According to the cluster mean field analysis and simulations, a conjecture about the condition that the phase separation happens is proposed. Based on the conjecture, the phase boundary distinguishing phase separation state and homogeneous state is determined, and a corresponding phase diagram is drawn. The conjecture is validated through observing directly the spatiotemporal diagram and investigating the coarsening process of the system by simulation, and a possible mechanism causing the phase separation is also discussed. These outcomes maybe contribute to understand deeply transport systems including the congestion and efficiency of the transport, and enrich explorations of nonequilibrium state systems.

Transportation dynamics on coupled networks with limited bandwidth.

The communication networks in real world often couple with each other to save costs, which results in any network does not have a stand-alone function and efficiency. To investigate this, in this paper we propose a transportation model on two coupled networks with bandwidth sharing. We find that the free-flow state and the congestion state can coexist in the two coupled networks, and the free-flow path and congestion path can coexist in each network. Considering three bandwidth-sharing mechanisms, random, assortative and disassortative couplings, we also find that the transportation capacity of the network only depends on the coupling mechanism, and the fraction of coupled links only affects the performance of the system in the congestion state, such as the traveling time. In addition, with assortative coupling, the transportation capacity of the system will decrease significantly. However, the disassortative coupling has little influence on the transportation capacity of the system, which provides a good strategy to save bandwidth. Furthermore, a theoretical method is developed to obtain the bandwidth usage of each link, based on which we can obtain the congestion transition point exactly.

Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state.

Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.

Phase transition and flow-rate behavior of merging granular flows.

Merging of granular flows is ubiquitous in industrial, mining, and geological processes. However, its behavior remains poorly understood. This paper studies the phase transition and flow-rate behavior of two granular flows merging into one channel. When the main channel is wider than the side channel, the system shows a remarkable two-sudden-drops phenomenon in the outflow rate when gradually increasing the main inflow. When gradually decreasing the main inflow, the system shows obvious hysteresis phenomenon. We study the flow-rate-drop phenomenon by measuring the area fraction and the mean velocity at the merging point. The phase diagram of the system is also presented to understand the occurrence of the phenomenon. We find that the dilute-to-dense transition occurs when the area fraction of particles at the joint point exceeds a critical value ϕ(c)=0.65±0.03.

Bulk induced phase transition in driven diffusive systems.

This paper studies a weakly and asymmetrically coupled three-lane driven diffusive system. A non-monotonically changing density profile in the middle lane has been observed. When the extreme value of the density profile reaches ρ = 0.5, a bulk induced phase transition occurs which exhibits a shock and a continuously and smoothly decreasing density profile which crosses ρ = 0.5 upstream or downstream of the shock. The existence of double shocks has also been observed. A mean-field approach has been used to interpret the numerical results obtained by Monte Carlo simulations. The current minimization principle has excluded the occurrence of two or more bulk induced shocks in the general case of nonzero lane changing rates.

Traffic experiment reveals the nature of car-following.

As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation pattern of disturbances. However, the traffic theories have been controversial due to a lack of precise traffic data. We have studied traffic flow from a new perspective by carrying out large-scale car-following experiment on an open road section, which overcomes the intrinsic deficiency of empirical observations. The experiment has shown clearly the nature of car-following, which runs against the traditional traffic flow theory. Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.

Phase diagrams of the Katz-Lebowitz-Spohn process on lattices with a junction.

This paper studies the Katz-Lebowitz-Spohn (KLS) process on lattices with a junction, where particles move on parallel lattice branches that combine into a single lattice at the junction. It is shown that 11 kinds of phase diagrams could be observed, depending on the two parameters ε and δ in the KLS process. We have investigated the phase diagrams as well as bulk density analytically based on flow rate conservation and the extremal current principle. Extensive Monte Carlo computer simulations are performed, and it is found that they are in excellent agreement with theoretical prediction.

Phase diagram structures in a periodic one-dimensional exclusion process.

This paper studies a periodic one-dimensional exclusion process composed of a driven part and a biased diffusive part in a mesoscopic limit. It is shown that, depending on the biased diffusion parameter δ, rich phase diagram structures appear in which diverse phases have been exhibited and the density profile in the diffusive part is qualitatively different. This is because the domain wall is behaving differently. Our analytical results are in good agreement with Monte Carlo simulations.

Stop and restart of granular clock in a vibrated compartmentalized bidisperse granular system.

This paper studies a bidisperse granular mixture consisting of two species of stainless steel spheres in a vertically vibrated compartmentalized container. The experiments show that with proper vibration acceleration, the granular clock stops when horizontal segregation of the large spheres residing in the far end from the barrier wall occurs. When the segregation is broken, the granular clock restarts. We present the phase diagrams of vibration acceleration versus container width and small particle number, which exhibits three different regions, namely, clustering state, stop-restart of the granular clock, and the granular clock. A generalized flux model is proposed to reproduce the phenomenon of stop and restart of the granular clock.

Phase transitions induced by competition of two driven parts in a periodic system.

This paper studies a periodic driven diffusive system, which separates into two equal-sized parts with different values of hopping rates. Competition of the two different driven parts leads to various bulk-driven phase transitions, including shock and antishock. More interestingly, for the symmetric scenario, one can observe shock and antishock simultaneously in the system. We have explained the coexistence of shock and antishock via the effective boundary reservoir density. Theoretical analysis has been carried out to characterize the emerging nonequilibrium steady states, which is in good agreement with Monte Carlo simulations.

Pedestrian flow dynamics in a lattice gas model coupled with an evolutionary game.

This paper studies unidirectional pedestrian flow by using a lattice gas model with parallel update rules. Game theory is introduced to deal with conflicts that two or three pedestrians want to move into the same site. Pedestrians are either cooperators or defectors. The cooperators are gentle and the defectors are aggressive. Moreover, pedestrians could change their strategy. The fundamental diagram and the cooperator fraction at different system width W have been investigated in detail. It is found that a two-lane system exhibits a first-order phase transition while a multilane system does not. A microscopic mechanism behind the transition has been provided. Mean-field analysis is carried out to calculate the critical density of the transition as well as the probability of games at large value of W. The spatial distribution of pedestrians is investigated, which is found to be dependent (independent) on the initial cooperator fraction when W is small (large). Finally, the influence of the evolutionary game rule has been discussed.

Mean-field analysis for parallel asymmetric exclusion process with anticipation effect.

This paper studies an extended parallel asymmetric exclusion process, in which the anticipation effect is taken into account. The fundamental diagram of the model has been investigated via cluster mean field analysis. Different from previous mean field analysis, in which the n -cluster probabilities P(σ{i},…,σ{i+n-1}) involve the (n+2) -cluster probabilities P(τ{i-1},…,τ{i+n}) , our mean-field analysis is asymmetric because the three-cluster probabilities P(σ{i},σ{i+1},σ{i+2}) involve the six-cluster probabilities P(τ{i-1},…,τ{i+4}) . We find an excellent agreement between Monte Carlo simulations and cluster mean field analysis, which indicates that the mean field analysis might give the exact expression.

Pedestrian flow in a lattice gas model with parallel update.

This paper studies unidirectional pedestrian flow in a channel using the lattice gas model with parallel update rule. The conflict (i.e., several pedestrians intend to move to the same site) is solved by introducing probabilities as in floor field models. The fundamental diagram (FD) is investigated and it is found that when the drift strength D≲0.5, the FD is a concave curve. With the further increase in drift strength, a turning point appears on FD. The empirical findings show that both concave FD and FD with a turning point exist. Thus, the model might be able to reproduce both by tuning drift strength. It is also shown that in the special case D=1, two congested branches exist in the FD. We have carried out mean-field analysis of the FD and the mean-field results are in approximate agreement with simulations when the drift strength D is small. A comparison with random sequential update rule model is also made.

Global dynamic routing for scale-free networks.

Traffic is essential for many dynamic processes on networks. The efficient routing strategy [G. Yan, T. Zhou, B. Hu, Z. Q. Fu, and B. H. Wang, Phys. Rev. E 73, 046108 (2006)] can reach a very high capacity of more than ten times of that with shortest path strategy. In this paper, we propose a global dynamic routing strategy for network systems based on the information of the queue length of nodes. Under this routing strategy, the traffic capacity is further improved. With time delay of updating node queue lengths and the corresponding paths, the system capacity remains constant, while the travel time for packets increases.

Dynamical hysteresis phenomena in complex network traffic.

In this Brief Report, the dynamical hysteresis is investigated in constant-density traffic system of scale-free, small-world, and lattice networks. With the local-searching strategy, hysteresis persists for scale-free networks, while it disappears for small-world networks and lattice grids when the handling ability of nodes is higher than a certain threshold. With the shortest-path-routing strategy, hysteresis persists for all three networks investigated. When using shortest-path strategy, the system is easy to congest and difficult to recover to free-flow state.

Pheromone routing protocol on a scale-free network.

This paper proposes a routing strategy for network systems based on the local information of "pheromone." The overall traffic capacity of a network system can be evaluated by the critical packet generating rate R(c). Under this critical generating rate, the total packet number in the system first increases and then decreases to reach a balance state. The system behaves differently from that with a local routing strategy based on the node degree or shortest path routing strategy. Moreover, the pheromone routing strategy performs much better than the local routing strategy, which is demonstrated by a larger value of the critical generating rate. This protocol can be an alternation for superlarge networks, in which the global topology may not be available.

Spatial three-player prisoners' dilemma.

This paper extends traditional two-player prisoners' dilemma (PD) to three-player PD. We have studied spatial patterns of cooperation behaviors, growth patterns of cooperator clusters and defector clusters, and cooperation frequency of the players. It is found while three-player PD exhibits many properties similar to two-player PD, some new features arise. Specifically, (i) a new region appears, in which neither a 3x3 cooperator cluster nor a 3x3 defector cluster could grow; (ii) more growth patterns of cooperator clusters and defector clusters are identified; (iii) multiple cooperation frequencies exist in the region that exhibits dynamic chaos. Some theoretical analysis of these features is presented.