We address a long-standing debate regarding the finite-size scaling (FSS) of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We ...prove that this model exhibits the same universal FSS behavior previously conjectured for the self-avoiding walk and Ising model on finite boxes in high-dimensional lattices. Our results show that the mean walk length of the random walk model controls the scaling behavior of the corresponding Green's function. We numerically demonstrate the universality of our rigorous findings by extensive Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices with free and periodic boundaries.
► We study Macroscopic Fundamental Diagrams in networks with traffic signals. ► We simulate these networks using an efficient cellular automata model. ► MFDs depend strongly on the specific control ...strategy of the traffic signals. ► MFDs do exist for biased demand, but their shapes depend on the bias. ► Hysteresis can be clockwise or anticlockwise, depending on heterogeneity.
Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.
•A Robust perimeter control based on an MFD-based traffic model with partial information feedback is developed.•H∞, observer-based P and PI robust controllers are designed.•Set-point accumulations & ...control values are obtained off-line using an optimization program.•Control parameters are obtained from an LMI problem derived based on the Lyapunov theory.•Control design addresses the correlation between different directions of the perimeter control signals.
Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and ...self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behavior for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial ...randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
We study the impact of disruptions on road networks, and the recovery process after the disruption is removed from the system. Such disruptions could be caused by vehicle breakdown or illegal ...parking. We analyze the transient behavior using domain wall theory, and compare these predictions with simulations of a stochastic cellular automaton model. We find that the domain wall model can reproduce the time evolution of flow and density during the disruption and the recovery processes, for both one-dimensional systems and two-dimensional networks.
•Domain wall model used to explain disruption and recovery processes in road networks.•Both one-dimensional systems and two-dimensional networks studied.•Domain wall model includes interactions of multiple walls during recovery.•Domain wall predictions in good agreement with cellular automata simulations.
Bond and site percolation in three dimensions Wang, Junfeng; Zhou, Zongzheng; Zhang, Wei ...
Physical review. E, Statistical, nonlinear and soft matter physics,
05/2013, Letnik:
87, Številka:
5
Journal Article
Odprti dostop
We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be p(c)(bond)=0.24881182(10) and ...p(c)(site)=0.3116077(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.47705(15), the leading correction exponent y(i)=-1.2(2), and the shortest-path exponent d(min)=1.3756(3). Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent ≈-2, rather than y(i)≈-1.2.
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