Maxminplus expressions for onedimensional particle cellular automata obtained from a fundamental diagram
Abstract
We study onedimensional neighborhoodfive 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 maxminplus expressions from a fundamental diagram. The obtained equations are transformed into other maxminplus expressions by ultradiscrete ColeHopf transformations, which enable us to analyze the asymptotic behaviors of general solutions. The equations in the Lagrange representation, which describe particle motion, are also presented, which can also be obtained from a fundamental diagram. Finally, we discuss the generalization to a onedimensional conservative neighborhoodn CA, i.e., particle CAn.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 July 2013
 DOI:
 10.1088/17518113/46/29/295101
 arXiv:
 arXiv:1303.4045
 Bibcode:
 2013JPhA...46C5101O
 Keywords:

 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Mathematics  Numerical Analysis;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 doi:10.1088/17518113/46/29/295101