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Register a new userSimulation of pedestrian dynamics using a 2-dimensional cellular automaton
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We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor field which modifies the transition rates to neighbouring cells. This field, which can be discrete or continuous, is subject to diffusion and decay. Furthermore it can be modified by the motion of the pedestrians. Therefore the model uses an idea similar to chemotaxis, but with pedestrians following a virtual rather than a chemical trace. Our main goal is to show that the introduction of such a floor field is sufficient to model collective effects and self-organization encountered in pedestrian dynamics, e.g. lane formation in counterflow through a large corridor. As an application we also present simulations of the evacuation of a large room with reduced visibility, e.g. due to failure of lights or smoke.
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We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three classes of earthquakes with different underlying physical mechanisms. In addition to the events that exhibit scaling, there are larger ``breakout events that are not on the scaling plot. We discuss the interpretation of these events as fluctuations in the vicinity of a spinodal critical point.
Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations, 2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed new light on the relevant interactions in traffic flow.
Inspired by recent developments in the study of chaos in many-body systems, we construct a measure of local information spreading for a stochastic Cellular Automaton in the form of a spatiotemporally resolved Hamming distance. This decorrelator is a classical version of an Out-of-Time-Order Correlator studied in the context of quantum many-body systems. Focusing on the one-dimensional Kauffman Cellular Automaton, we extract the scaling form of our decorrelator with an associated butterfly velocity $v_b$ and a velocity-dependent Lyapunov exponent $lambda(v)$. The existence of the latter is not a given in a discrete classical system. Second, we account for the behaviour of the decorrelator in a framework based solely on the boundary of the information spreading, including an effective boundary random walk model yielding the full functional form of the decorrelator. In particular, we obtain analytic results for $v_b$ and the exponent $beta$ in the scaling ansatz $lambda(v) sim mu (v - v_b)^beta$, which is usually only obtained numerically. Finally, a full scaling collapse establishes the decorrelator as a unifying diagnostic of information spreading.
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We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase transition in the directed percolation universality class. Estimates for the stochastic time evolution, phase boundaries and critical exponents can be obtained with high precision. This is possible using only modest numerical effort since the thermodynamic limit can be taken analytically in our approach. We also point out further advantages of the TMRG over other numerical approaches, such as classical DMRG or Monte-Carlo simulations.
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