Probabilistic cellular automata with conserved quantities

Nonlinearity

Volumn 17, Issue 1, 2004, Pages 159-173

  Fukś, Henryk ^a  

^a BROCK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346040353     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/1/010     Document Type: Article

References (27)

1. Hattori T and Takesue S 1991 Additive conserved quantities in discrete-time lattice dynamical systems Physica D 49 295-322
2. Fukś H 2000 A class of cellular automata equivalent to deterministic particle systems Hydrodynamic Limits and Related Topics (Fields Institute Communications Series) ed A T L S Feng and R S Varadhan (Providence, RI: AMS) (Preprint nlin.CG/0207047)
3. Boccara N and Fukś H 1998 Cellular automaton rules conserving the number of active sites J. Phys. A: Math. Gen. 31 6007-18 (Preprint adap-org/9112003)
4. Boccara N and Fukś H 2002 Number-conserving cellular automaton rules Fundamenta Informaticae 52 1-13 (Preprint adap-org/9905004)
5. Fukś H and Boccara N 2001 Convergence to equilibrium in a class of interacting particle systems Phys. Rev. E 64 016117 (Preprint nlin.CG/0101037)
6. Krug J and Spohn H 1988 Universality classes for deterministic surface growth Phys. Rev. A 38 4271-83
7. Nagatani T 1999 Creation and annihilation of traffic jams in a stochastic assymetric exclusion model with open boundaries: a computer simulation J. Phys. A: Math. Gen. 28 7079-88
8. Nagel K 1996 Particle hopping models and traffic flow theory Phys. Rev. E 53 4655-72 (Preprint cond-mat/9509075)
9. Belitsky V and Ferrari P A Invariant measures and convergence for cellular automaton 184 and related processes Preprint math.PR/9811103
10. Capcarrere M S, Sipper M and Tomassini M 1996 Two-state, r = 1 cellular automaton that classifies density Phys. Rev. Lett. 77 4969-71
11. Fukś H 1999 Exact results for deterministic cellular automata traffic models Phys. Rev. E 60 197-202 (Preprint comp-gas/9902001)
12. Nishinari K and Takahashi D 1998 Analytical properties of ultradiscrete burgers equation and rule-184 cellular automaton J. Phys. A: Math. Gen. 31 5439-50
13. Belitsky V, Krug J, Neves E J and Schutz G M 2001 A cellular automaton model for two-lane traffic J. Stat. Phys. 103 945-71
14. Blank M 2003 Ergodic properties of a simple deterministic traffic flow model J. Stat. Phys. 111 903-30
15. Pivato M 2002 Conservation laws in cellular automata Nonlinearity 15 1781-93 (Preprint math.DS/0111014)
16. Moreira A 2003 Universality and decidability of number-conserving cellular automata Theor. Comput. Sci. 292 711-21
17. Durand B, Formenti E and Róka Z 2003 Number-conserving cellular automata I: decidability Theor. Comput. Sci. 299 523-35
18. Formenti E and Grange A 2003 Number conserving cellular automata II: dynamics Theor. Comput. Sci. 304 269-90
19. Monta K and Imai K 2001 Number-conserving reversible cellular automata and their computation-universality Theor. Inform. Appl. 35 239-58
20. Kujala J V and Lukka T J 2002 Solutions for certain number-conserving deterministic cellular automata Phys. Rev. E 65 026115 (Preprint nlin.CG/0105045)
21. Boccara N and Fukś H 2000 Critical behavior of a cellular automaton highway traffic model J. Phys. A: Math. Gen. 33 3407-15 (Preprint cond-mat/9911039)
22. Fukś H 2002 Non-deterministic density classification with diffusive probabilistic cellular automata Phys. Rev. E 66 066106 (Preprint nlin.CG/0302015)
23. de Braijn N G 1946 A combinatorial problem Nederl. Akad. Wetensch. Proc. 49 746-58
24. Ralston A 1982 De Bruijn sequences - a model example of the interaction of discrete mathematics and computer science Math. Mag. 55 131-43
25. Gutowitz H A, Victor J D and Knight B W 1987 Local structure theory for cellular automata Physica D 28 18-48
26. Gutowitz H 1990 A hierarchical classification of cellular automata Physica D 45 136-56
27. Matsokidaira J and Nishinari K 2003 Euler-Lagrange correspondence of cellular automaton for traffic-flow models Phys. Rev. Lett. 90 088701