Construction, mathematical description and coding of reactive lattice-gas cellular automaton

Simulation Practice and Theory

Volumn 7, Issue 7, 2000, Pages 657-689

  Voroney, Jon Paul ^a   Lawniczak, Anna T ^b,c  

^a UNIVERSITY OF TORONTO   (Canada)

^b Flds Inst for Res in Math Sci   (Canada)

^c UNIVERSITY OF GUELPH   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

C (PROGRAMMING LANGUAGE); COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; DATA STRUCTURES; ENCODING (SYMBOLS); SOFTWARE ENGINEERING;

REACTIVE LATTICE-GAS CELLULAR AUTOMATON (LGCA);

AUTOMATA THEORY;

EID: 0033882070     PISSN: 09284869     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0928-4869(99)00029-4     Document Type: Article

References (31)

1. Boon J.P., Dab D., Kapral R., Lawniczak A. Lattice-gas automata for reactive systems. Phys. Rep. 273(2):1996;55-147.
2. W. Boyce, R. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, Toronto, New York, 1986 (for the Runge-Kutta and Euler approximations).
3. Castets V., Dulos E., Boissonade J., DeKepper P. Experimental evidence of a sustained standing Turing-type non-equilibrium chemical pattern. Phys. Rev. Lett. 64:1990;2953-2957.
4. Chen S., Dawson S.P., Doolen G.D., Janecky D.R., Lawniczak A. Lattice methods and their applications to reacting systems. Comput. Chem. Engrg. 19(6/7):1995;617-646.
5. Chopard B., Droz M. Cellular automata model for the diffusion equation. J. Stat. Phys. 64:1991;859-892.
6. Deutsch A. Orientation-induced pattern formation: swarm dynamics in a lattice-gas automaton model. Int. J. Bifurc. Chaos. 6:1996;1735-1752.
7. Deutsch A., Lawniczak A.T. Probabilistic lattice models of collective motion and aggregation from individual to collective dynamics. Math. Biosci. 156:1999;255-269.
8. G. Doolen (Ed.), Lattice-Gas Methods for Partial Differential Equations, Addison-Wesley, New York, 1990.
9. G. Doolen (Ed.), Lattice-Gas Methods for PDE's Theory, Applications and Hardware, North-Holland, Amsterdam, 1991.
10. Frisch U., Hasslacher B., Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56:1986;1505-1509.
11. Frisch U., d'Humières D., Hasslacher B., Pomeau Y., Rivet J.P. Lattice-gas hydrodynamics in two- and three-dimensions. Complex Syst. 1:1987;649-707.
12. Hasslacher B., Kapral R., Lawniczak A. Molecular Turing structures in the biochemistry of the cell. Chaos, Solitons & Fractals. 3:1993;7-13.
13. Hess B., Mikhailov A. Self-organization in living cells. Science. 264:1994;223-224.
14. Kapral R., Lawniczak A., Masiar P. Oscillations and waves in a reactive lattice-gas automaton. Phys. Rev. Lett. 66:1991;2539-2542.
15. Kapral R., Lawniczak A., Masiar P. Reactive dynamics in a multispecies lattice-gas automaton. J. Chem. Phys. 96(4):1992;2762-2776.
16. A.T. Lawniczak, in: R. Kapral (Ed.), Pattern Formation and Lattice Gas Automata. The Fields Institute Communications, American Mathematical Society, 1996.
17. A.T. Lawniczak, Lattice-Gas Automata for Diffusive-Convective Dynamics, CNLS Newsletter, Los Alamos National Laboratory, vol. 136, 1997, pp. 1-15.
18. A.T. Lawniczak, J.P. Voroney, LGCA modeling of spatio-temporal dynamics of reactive systems, in preparation.
19. Lengyel I., Epstein I.R. Modeling of turing structures in the chlorite-iodide-malonic acid-starch reaction system. Science. 251:1991;650-652.
20. Murray J.D. Mathematical Biology. 1989;Springer, New York.
21. Margolous N., Toffoli T. Cellular Automata Machines, A New Environment for Modeling. 1987;MIT Press, Cambridge, MA.
22. Marsaglia G., Narasimhan B., Zaman A. A random number generator for PC's. Comput. Phys. Comm. 60:1990;345-349.
23. Ouyang Q., Swinney H.L. Transitions from a uniform state to hexagonal and striped Turing patterns. Nature. 352:1991;610-612.
24. Rothman D.H., Zaleski S. Lattice-Gas Cellular Automata Simple Models of Complex Hydrodynamics. 1997;Cambridge University Press, Cambridge, UK.
25. Rovinsky A.B., Mezinger M. Chemical instability induced by a differential flow. Phys. Rev. Lett. 69:1992;1193-1197.
26. Richter P.H., Rehmus P., Ross J. Control and dissipation in oscillatory chemical engines. Prog. Theor. Phys. 66:1981;385-405.
27. Sel'kov E.E. Self-oscillations in glycolysis. 1. A simple kinetic model. Eur. J. Biochem. 4:1968;79-86.
28. Toffoli T. Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Physica D. 10:1984;117-127.
29. Turing A. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London. B 237:1952;37-72.
30. Voroney J.P., Lawniczak A., Kapral R. Turing pattern formation in heterogeneous media. Physica D. 99:1996;303-317.
31. J.P. Voroney, Spatial and Temporal Patterns in Chemical Systems: Theoretical and Computational Approaches, PhD thesis, Department of Mathematics and Statistics, University of Guelph, 1998.