Efficient Monte Carlo methods for the simulation of catalytic surface reactions

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 2, 1998, Pages 2598-2610

  Lukkien, J J ^a   Segers, J P L ^a   Hilbers, P A J ^a   Gelten, R J ^a   Jansen, A P J ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000364095     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.2598     Document Type: Article

References (35)

1. A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, J. Comput. Phys. 17, 10 (1975).JCTPAH
2. A. M. Bowler and E. S. Hood, J. Chem. Phys. 94, 5162 (1981).JCPSA6
3. H. C. Kang and W. H. Weinberg, Phys. Rev. B 38, 11543 (1988).PRBMDO
4. H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989).JCPSA6
5. P. A. Maksym, Semicond. Sci. Technol. 3, 594 (1988).SSTEET
6. R. M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986).PRLTAO
7. K. A. Fichthorn, E. Gulari, and R. M. Ziff, Phys. Rev. Lett. 63, 1527 (1989).PRLTAO
8. K. A. Fichthorn, E. Gulari, and R. M. Ziff, Chem. Eng. Sci. 44, 1403 (1989).CESCAC
9. Usually, a reaction changes only a small neighborhood on the lattice. In a Monte Carlo method this may be used to obtain a significantly faster algorithm. We come back to this later.
10. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
11. A. P. J. Jansen, Comput. Phys. Commun. 86, 1 (1995).CPHCBZ
12. A. P. J. Jansen, Appl. Catal. A. 160, 99 (1997).ACAGE4
13. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976).JCTPAH
14. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).JPCHAX
15. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, London, 1970).
16. M. T. M. Koper, J. J. Lukkien, A. P. J. Jansen, R. A. van Santen, and P. A. J. Hilbers, J. Chem. Phys. (to be published).
17. I. Mitrani, Simulation Techniques for Discrete Event Systems (Cambridge University Press, Cambridge, England, 1982).
18. D. E. Knuth, Seminumerical Algorithms, 2nd ed. (Addison-Wesley, Reading, MA, 1981).
19. A Bernoulli experiment with parameter p is an experiment that has two possible outcomes, usually called s(uccess) and f(ailure). The parameter gives the probability that the outcome is s.
20. The precise formulation is limopk→∞ Π i=0k[](1-λ/λi)=0.
21. K. Binder, in Monte Carlo Methods in Statistical Physics, edited by K. Binder, Topics in Current Physics Vol. 7 (Springer, Berlin, 1979).
22. J. P. L. Segers, Ph.D. dissertation, Eindhoven University of Technology, 1998.
23. J. P. Boon, D. Dab, R. Kapral, and A. Lawniczak, Phys. Rep. 273, 55 (1996).PRPLCM
24. This is indeed a simplifying assumption since this type of simulation is used in particular for systems not at equilibrium. We assume, however, that variations in the time evolution of the simulated system (like the occurrence of oscillations) occur at a much slower scale than the adaptation of the data structures to these phenomena. Then this analysis is applicable to a small (simulated) period.
25. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, Data Structures and Algorithms (Addison-Wesley, Reading, MA, 1983).
26. D. E. Knuth, Sorting and Searching (Addison-Wesley, Reading, MA, 1997).
27. Some information about the program can be obtained via http://www.win.tue.nl/cs/pa/johanl/carlos. We just started to create this web site.
28. R. J. Gelten, A. P. J. Jansen, R. A. van Santen, J. J. Lukkien, J. P. L. Segers, and P. A. J. Hilbers, J. Chem. Phys. 108, 5921 (1998).JCPSA6
29. R. Imbihl, M. P. Cox, G. Ertl, H. Muller, and W. Brenig, J. Chem. Phys. 83, 1578 (1985).JCPSA6
30. M. P. Cox, G. Ertl, R. Imbihl, and J. Rustig, Surf. Sci. 134, L517 (1983).SUSCAS
31. R. Danielak, Physica A 229, 428 (1996).PHYADX
32. M. Tammaro, M. Sabella, and J. W. Evans, J. Chem. Phys. 103, 10277 (1995).JCPSA6
33. J. Segers, J. J. Lukkien, and P. A. J. Hilbers, in High-Performance Computing and Networking, Proceedings HPCN Europe, 1996, edited by H. Liddell, A. Colbrook, B. Hertzberger, and P. Sloot, Lecture Notes in Computer Science Vol. 1067 (Springer, New York, 1996), p. 243.
34. N. Haider, A. K. Souheil, M. R. Wilby, and D. D. Vvedensky, Comput. Phys. 9, 85 (1995).CPHYE2
35. Advances in Parallel and Distributed Simulation, edited by V. Madisetti, D. Nicol, and R. Fujimoto, Simulation Series Vol. 23 (Society for Computer Simulation, 1990).