Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 4, 2012, Pages

  Wang, Chi Jen ^a,b   Liu, Da Jiang ^a   Evans, J W ^a,b  

^a IOWA STATE UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOCATALYTIC; HYPERCUBIC LATTICES; INTERFACE DYNAMIC; KINETIC MONTE CARLO SIMULATION; MASTER EQUATIONS; NON EQUILIBRIUM; PLANAR INTERFACE; PROPAGATION FAILURE; REACTION DIFFUSION EQUATIONS; SPINODALS; STATIONARY POINTS; VACANT SITES; VACUUM STATE;

CRYSTAL LATTICES; LINEAR EQUATIONS; MONTE CARLO METHODS;

INTERFACE STATES;

EID: 84860523534     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.041109     Document Type: Article

References (28)

1. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, UK, 1999).
2. G. Odor, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.76.663 76, 663 (2004). (Pubitemid 40176839)
3. J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, UK, 1996).
4. F. Schloegl, Z. Phys. 1434-6001 10.1007/BF01379769 253, 147 (1972).
5. P. Grassberger, Z. Phys. B: Condens. Matter 0722-3277 10.1007/BF01313803 47, 365 (1982).
6. J. P. Boon, D. Dab, R. Kapral, and A. Lawniczak, Phys. Rep. 0370-1573 10.1016/0370-1573(95)00080-1 273, 55 (1996). (Pubitemid 126170079)
7. S. Prakash and G. Nicolis, J. Stat. Phys. 0022-4715 10.1007/BF02183624 86, 1289 (1997).
8. R. Durrett, SIAM Rev. 0036-1445 10.1137/S0036144599354707 41, 677 (1999).
9. D.-J. Liu, X. Guo, and J. W. Evans, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.98.050601 98, 050601 (2007). (Pubitemid 46203539)
10. X. Guo, J. W. Evans, and D.-J. Liu, Physica A 0378-4371 10.1016/j.physa.2007.09.002 387, 177 (2008). Sites in the last two loss terms in Eq. (B1) are mislabeled. One should replace i with i - 1. (Pubitemid 350051271)
11. X. Guo, D.-J. Liu, and J. W. Evans, J. Chem. Phys. 0021-9606 10.1063/1.3074308 130, 074106 (2009).
12. X. Guo, Y. de Decker, and J. W. Evans, Phys. Rev. E 1539-3755 10.1103/PhysRevE.82.021121 82, 021121 (2010).
13. C.-J. Wang, X. Guo, D.-J. Liu, and J. W. Evans, J. Stat. Phys. 0022-4715 10.1007/s10955-011-0288-6 144, 1308 (2011).
14. A. L. Toom, in Multicomponent Random Systems, edited by, R. L. Dobrushin, and, Y. G. Sinai, (Dekker, New York, 1980).
15. C. H. Bennett and G. Grinstein, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.55.657 55, 657 (1985).
16. R. S. MacKay, Nonlinearity 0951-7715 10.1088/0951-7715/21/12/T03 21, T273 (2008).
17. For systems with finite linear size L, an alternative criterion is to balance rates for transitions between states due to homogeneous fluctuations. See G. Nicolis and J. W. Turner, Ann. N.Y. Acad. Sci. 0077-8923 10.1111/j.1749-6632.1979.tb29473.x 316, 251 (1979);
18. J. Ross, K. L. C. Hunt, and M. O. Vlad, J. Phys. Chem. C 106, 10951 (2002).
19. R. M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.56.2553 56, 2553 (1986).
20. P. Fischer and U. M. Titulaer, Surf. Sci. 0039-6028 10.1016/0039-6028(89) 90589-X 221, 409 (1989).
21. J. W. Evans and T. R. Ray, Phys. Rev. E 1539-3755 10.1103/PhysRevE.50. 4302 50, 4302 (1994).
22. R. H. Goodman, D. S. Graff, L. M. Sander, P. Leroux-Hugon, and E. Clément, Phys. Rev. E 1539-3755 10.1103/PhysRevE.52.5904 52, 5904 (1995).
23. Y. De Decker, G. A. Tsekouras, A. Provata, T. Erneux, and G. Nicolis, Phys. Rev. E 1539-3755 10.1103/PhysRevE.69.036203 69, 036203 (2004).
24. R. M. Ziff and B. J. Brosilow, Phys. Rev. A 1050-2947 10.1103/PhysRevA.46.4630 46, 4630 (1992).
25. J. W. Evans, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.65.1281 65, 1281 (1993). (Pubitemid 24752340)
26. J. P. Keener, SIAM J. Appl. Math. 0036-1399 10.1137/0147038 47, 556 (1987).
27. S.-N. Chow, J. Mallet-Paret, and E. S. Van Vleck, Int. J. Bifurcation Chaos 0218-1274 10.1142/S0218127496000977 6, 1605 (1996). (Pubitemid 126311087)
28. G. Fath, Physica D 0167-2789 10.1016/S0167-2789(97)00251-0 116, 176 (1998).