In order to exhibit the meta-stable states, several slow-to-start rules have been investigated as modification to Nagel-Schreckenberg （NS） model. These models can reproduce some realistic phenomena which are absent ...In order to exhibit the meta-stable states, several slow-to-start rules have been investigated as modification to Nagel-Schreckenberg （NS） model. These models can reproduce some realistic phenomena which are absent in the original NS model. But in these models, the size of cluster is still not considered as a useful parameter. In real traffic, the slow-to-start motion of a standing vehicle often depends on the degree of congestion which can be measured by the clusters＇ size. According to this idea, we propose a cluster-size dependent slow-to-start model based on the speed- dependent slow-to-start rule （VDR） model. It gives expected results through simulations. Comparing with the VDR model, our new model has a better traffic efficiency and shows richer complex characters.展开更多
We extend the Achlioptas percolation （AP） process （Achlioptas et al. Science 323 （2009） 1453） to two generalized Achlioptas percolation processes named GAP1 and GAP2. GAP1 induces a weighted probability factor a...We extend the Achlioptas percolation （AP） process （Achlioptas et al. Science 323 （2009） 1453） to two generalized Achlioptas percolation processes named GAP1 and GAP2. GAP1 induces a weighted probability factor a in the node sampling process and excludes the intracluster links. Based on GAP1, GAP2 requires m pairs of nodes sampled to add m candidate links that should be residing in 2m different clusters at each step. In the evolution of GAP1, the phase transition can evolve from the continuous to the ＇most explosive＇ percolation as the value of the factor a is decreasing to a certain negative number. It indicates that there might be a type of discontinuous transition induced by the probability modulation effect even in the thermodynamic limit, and the most explosive percolation is only one of its extreme cases. We analyze the characteristics of the evolving process of the twonodes-clusters and the cluster-size distribution at the transformation point for different a; the numerical results suggest that there might be a critical value ao and the phase transition should be discontinuous （α〉 α0） or continuous （α ≤ α0）. In the evolution of GAP2, twice phase transitions are observed successively and the time duration between them becomes shorter till they amalgamate into the ＇most explosive＇ percolation. The first transition is induced by the probability modulation effect analyzed in GAP1, the second transition, induced by the three coexisting giant clusters, is always discontinuous and the maximum jump of order parameter approaches N /3 while the value of the factor a is increasing to 1.4 approximately. In this work, two typical discontinuous transitions induced respectively by the probability modulation and the extended local competition are exhibited in GAP2, which might provide references to analyze the discontinuous phase transition in networks further.展开更多
We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER ne...We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 < qc< 0.25 separating the two phase transition types.展开更多
基金Project supported by the State Key Development Program for Basic Research of China （Grant No 2006CB705500）, the National Natural Science Foundation of China （Grant Nos 10472116, 10532060, and 70571074）, the Special Research Funds for Theoretical Physics Frontier Problems （Grant Nos 10547004 and A0524701）, the Presidential Foundation of the Chinese Academy of Sciences, and the Specialized Rescarch Fund for the Doctoral Program of High Education of China.
文摘In order to exhibit the meta-stable states, several slow-to-start rules have been investigated as modification to Nagel-Schreckenberg （NS） model. These models can reproduce some realistic phenomena which are absent in the original NS model. But in these models, the size of cluster is still not considered as a useful parameter. In real traffic, the slow-to-start motion of a standing vehicle often depends on the degree of congestion which can be measured by the clusters＇ size. According to this idea, we propose a cluster-size dependent slow-to-start model based on the speed- dependent slow-to-start rule （VDR） model. It gives expected results through simulations. Comparing with the VDR model, our new model has a better traffic efficiency and shows richer complex characters.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61172115 and 60872029the High-Tech Research and Development Program of China under Grant No 2008AA01Z206+2 种基金the Aeronautics Foundation of China under Grant No 20100180003the Fundamental Research Funds for the Central Universities under Grant No ZYGX2009J037the Project 9140A07030513DZ02098
文摘基于簇生长机制，在簇被分到重量概率功能， intracluster 边被排除的地方，我们学习一个过滤模型。重量概率函数包括一个悦耳的参数。模型能认识到阶段转变从对连续多重象价值不连续、不连续被调节。根据重量概率功能的性质，对应于不同的簇生长机制的三个典型盒子被分析。当系统尺寸 N 等于 1/ 时，概率调整效果显示过滤过程产生类似于古典 Erd 的连续阶段转变 ? sR ? 浩異楲祴挠湯散瑮慲楴湯氠慥獤琠? 桴 ? 敤牣慥敳漠 ? 潭楢楬祴眠瑩 ? 牰獥?
文摘We extend the Achlioptas percolation （AP） process （Achlioptas et al. Science 323 （2009） 1453） to two generalized Achlioptas percolation processes named GAP1 and GAP2. GAP1 induces a weighted probability factor a in the node sampling process and excludes the intracluster links. Based on GAP1, GAP2 requires m pairs of nodes sampled to add m candidate links that should be residing in 2m different clusters at each step. In the evolution of GAP1, the phase transition can evolve from the continuous to the ＇most explosive＇ percolation as the value of the factor a is decreasing to a certain negative number. It indicates that there might be a type of discontinuous transition induced by the probability modulation effect even in the thermodynamic limit, and the most explosive percolation is only one of its extreme cases. We analyze the characteristics of the evolving process of the twonodes-clusters and the cluster-size distribution at the transformation point for different a; the numerical results suggest that there might be a critical value ao and the phase transition should be discontinuous （α〉 α0） or continuous （α ≤ α0）. In the evolution of GAP2, twice phase transitions are observed successively and the time duration between them becomes shorter till they amalgamate into the ＇most explosive＇ percolation. The first transition is induced by the probability modulation effect analyzed in GAP1, the second transition, induced by the three coexisting giant clusters, is always discontinuous and the maximum jump of order parameter approaches N /3 while the value of the factor a is increasing to 1.4 approximately. In this work, two typical discontinuous transitions induced respectively by the probability modulation and the extended local competition are exhibited in GAP2, which might provide references to analyze the discontinuous phase transition in networks further.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61172115 and 60872029the High-Tech Research and Development Program of China under Grant No.2008AA01Z206+1 种基金the Aeronautics Foundation of China under Grant No.20100180003the Fundamental Research Funds for the Central Universities under Grant No.ZYGX2009J037,and Project No.9140A07030513DZ02098
文摘We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 < qc< 0.25 separating the two phase transition types.
