Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which a random walker will generate a power-law travel displacement distribution with exponent -2. When considering the inhomogeneities of cities' locations and attractions, this model reproduces a power-law displacement distribution with an exponential cutoff, as well as a scaling behavior in the probability density of having traveled a certain distance at a certain time. Our results agree very well with the empirical observations reported in [D. Brockmann et al., Nature 439, 462 (2006)].PACS numbers: 89.75.Fb, 05.40.Fb, 89.75.Da Studies on the non-Poisson statistics of human behaviors have recently attracted much attention [1,2,3]. Besides the inter-event or waiting time distribution, the spatial movements of human also exhibit non-Poisson statistics. Brockmann et al. [4] investigated the bank note dispersal, as a proxy for human movements, and revealed indirectly a power-law distribution of human travel displacements. Gonzalez et al.[5] studied the human travel patterns by measuring the distance of mobile phone users' movements in different stations, and observed a similar scaling law. Actually, the mobility patterns of many animals also show power-law-like displacement distributions [6,7,8]. The ubiquity of such kind of distributions attracts scientists to dig into the underlying mechanism. Some interpretations, such as optimal search strategy [9, 10], olfactory-driven foraging [11] and deterministic walks [12], have already been raised for the power-law displacement distribution in animals mobility patterns, however, they are based on the prey processes and thus cannot be used to explain the observed scaling law in human trajectories, which is still an open problem. In this paper, we propose a model to mimic the human travel pattern, where the hierarchical organization of the real human traffic systems is taken into account. Our model can reproduce the power-law displacement distributions, as well as the scaling behavior in probability density of having traveled a certain distance at a certain time, agreeing very well with the empirical results reported in Ref. [4].Let's think about the real human traffic systems. Generally speaking, a district (e.g., a province or a state) usually has a core city, like its capital; around this core city, there are several big cities as the secondary centers (e.g., municipalities); then, each of these centers is rounded by some counties; and towns and villages will surround each of the counties. A hierarchical traffic system is built accordingly. Imaging people traveling from a town, a, subordinating to the central city, A, to another town b that is subordinated to the central city B. There is usually no direct way connecting a and b, and the typical route is a → A → B → b. This kind of hierarchical organization is not just inside a countr...

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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.

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This paper has studied spontaneous symmetry breaking (SSB) phenomenon in two types of two-channel asymmetric simple exclusion processes (ASEPs). One common feature of the two systems is that interactions for each species of particle happen at only one site, and the system reduces to two independent ASEPs when interaction vanishes. It is shown that with the weakening of interaction, the SSB is suppressed. More interestingly, the SSB disappears before the interaction is eliminated. Our work thus indicates that local interaction has to be strong enough to produce SSB. The mean-field analysis has been carried out, and the results are consistent with the simulation ones.

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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.