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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.
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
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal
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 ear
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 mo
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