Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram

@article{Okumura2013MaxminplusEF,
  title={Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram},
  author={Takazumi Okumura and Junta Matsukidaira and Daisuke A. Takahashi},
  journal={Journal of Physics A},
  year={2013},
  volume={46},
  pages={295101}
}
We study one-dimensional neighborhood-five conservative cellular automata (CA), referred to as particle cellular automata five (particle CA5). We show that evolution equations for particle CA5s that belong to certain types can be obtained in the form of max–min-plus expressions from a fundamental diagram. The obtained equations are transformed into other max–min-plus expressions by ultradiscrete Cole–Hopf transformations, which enable us to analyze the asymptotic behaviors of general solutions… 

Figures from this paper

On fundamental diagram of stochastic cellular automata with a quadratic conserved quantity
We report the exact analysis of asymptotic behavior for some stochastic cellular automata with a quadratic conserved quantity. There exists a reduction from the cellular automaton with a quadratic
Delay Bound: Fractal Traffic Passes through Network Servers
TLDR
A concise method of delay computation for hard real-time systems as shown in this paper is proposed and the delay computation of fractal traffic passing through servers is presented.

References

SHOWING 1-10 OF 10 REFERENCES
Max-plus analysis on some binary particle systems
We are concerned with a special class of binary cellular automata, i.e. the so-called particle cellular automata (PCA) in this paper. We first propose max-plus expressions to PCA of four neighbors.
Euler-lagrange correspondence of cellular automaton for traffic-flow models.
TLDR
It is shown that the Burgers CA, which is a corresponding CA of the continuous Burgers equation, plays a central role in considering this relation and is obtained the Lagrange representation of a traffic model.
Euler–Lagrange Correspondence Of Generalized Burgers Cellular Automaton
Recently, we have proposed a Euler–Lagrange transformation for cellular automata (CA) by developing new transformation formulas. Applying this method to the Burgers CA (BCA), we have succeeded in
Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton
In this paper, we propose an ultradiscrete Burgers equation of which all the variables are discrete. The equation is derived from a discrete Burgers equation under an ultradiscrete limit and reduces
Additive conserved quantities in discrete-time lattice dynamical systems
Abstract We give a necessary and sufficient condition for the existence of additive conserved quantities for one-dimensional discrete-time lattice dynamical systems such as cellular automata (CA) and
Toda-type Cellular Automaton and its $N$-soliton Solution(Discretizations of Integrable Systems : Theory and Applications)
Abstract We show that the cellular automaton proposed by two of the authors (D.T. and J.M.) is obtained from the discrete Toda lattice equation through a special limiting procedure. Also by applying
From soliton equations to integrable cellular automata through a limiting procedure.
TLDR
A direct connection between a cellular automaton and integrable nonlinear wave equations is shown and a general method for constructing suchintegrable cellular automata and their $N$-soliton solutions is proposed.
Cellular automaton rules conserving the number of active sites
This paper shows how to determine all of the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a
A New Kind of Science (Champaign: Wolfram Media
  • 2002
Theory and Applications of Cellular Automata (Singapore: World Scientific
  • 1986