419 research outputs found
Exact results for one dimensional stochastic cellular automata for different types of updates
We study two common types of time-noncontinuous updates for one dimensional
stochastic cellular automata with arbitrary nearest neighbor interactions and
arbitrary open boundary conditions. We first construct the stationary states
using the matrix product formalism. This construction then allows to prove a
general connection between the stationary states which are produced by the two
different types of updates. Using this connection, we derive explicit relations
between the densities and correlation functions for these different stationary
states.Comment: 7 pages, Late
Density fluctuations and phase separation in a traffic flow model
Within the Nagel-Schreckenberg traffic flow model we consider the transition
from the free flow regime to the jammed regime. We introduce a method of
analyzing the data which is based on the local density distribution. This
analyzes allows us to determine the phase diagram and to examine the separation
of the system into a coexisting free flow phase and a jammed phase above the
transition. The investigation of the steady state structure factor yields that
the decomposition in this phase coexistence regime is driven by density
fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M.
Schreckenberg, Springer, Singapore (1998
The asymmetric exclusion process: Comparison of update procedures
The asymmetric exclusion process (ASEP) has attracted a lot of interest not
only because its many applications, e.g. in the context of the kinetics of
biopolymerization and traffic flow theory, but also because it is a
paradigmatic model for nonequilibrium systems. Here we study the ASEP for
different types of updates, namely random-sequential, sequential,
sublattice-parallel and parallel. In order to compare the effects of the
different update procedures on the properties of the stationary state, we use
large-scale Monte Carlo simulations and analytical methods, especially the
so-called matrix-product Ansatz (MPA). We present in detail the exact solution
for the model with sublattice-parallel and sequential updates using the MPA.
For the case of parallel update, which is important for applications like
traffic flow theory, we determine the phase diagram, the current, and density
profiles based on Monte Carlo simulations. We furthermore suggest a MPA for
that case and derive the corresponding matrix algebra.Comment: 47 pages (11 PostScript figures included), LATEX, Two misprints in
equations correcte
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