Skip to main content
SpringerLink
Log in

Monte Carlo studies of a driven lattice gas. I. Growth and asymmetry during phase segregation

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We investigate the effects of an external field on the kinetics of phase segregation in systems with conservative diffusive dynamics. We find that, in contrast to the situation without a field, there are now qualitative differences between the results of microscopic simulations of a 2D lattice model with biased Kawasaki exchanges and those obtained from various modifications of the macroscopic Cahn-Hilliard equation (mCH). While both microscopic simulations and numerical solutions of MCH yield triangular domains, we find that in the former the triangles mainly pointopposite to the field, while in the latter and in new calculations with the mCH they pointalong the field. On the other hand, the rate of growth of the clusters and their final state, bands parallel to the field, are similar. This issue and the question of the mesoscopic behavior of cell dynamical systems is discussed but not resolved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow,J. Stat. Phys. 66:1071 (1992); see also C. Yeung, J. L. Mozos, A. Hernandez-Machado, and D. Jasnow,J. Stat. Phys. 70:1149 (1993).

    Google Scholar 

  2. J. D. Gunton, M. San Miguel, and P. S. Sahni, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1983); H. Furukawa,Adv. Phys. 34:703 (1985); K. Binder,Rep. Prog. Phys. 50:783 (1987); J. S. Langer, inSolids far from Equilibrium, C. Godreche, (ed.)(Cambridge University Press, Cambridge, 1992); A. J. Bray,Adv. Phys. 43:357 (1994).

    Google Scholar 

  3. B. D. Gaulin, S. Spooner, and Y. Morii,Phys. Rev. Lett. 59:668 (1987).

    Google Scholar 

  4. K. Kawasaki and T. Ohta,Physica A 118:75 (1982).

    Google Scholar 

  5. S. Katz, J. L. Lebowitz, and H. Spohn,Phys. Rev. B 28:1655 (1983);J. Stat. Phys. 34:497 (1984).

    Google Scholar 

  6. B. Schmittmann and R. K. P. Zia, inPhase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1995).

    Google Scholar 

  7. J. Amar, F. E. Sullivan, and R. D. Mountain,Phys. Rev. B 37:196 (1988).

    Google Scholar 

  8. C. Roland and M. Grant,Phys. Rev. B 39:11971 (1989).

    Google Scholar 

  9. J. Marro, J. L. Lebowitz, and M. H. Kalos,Phys. Rev. Lett. 43:282 (1979); J. L. Lebowitz, J. Marro, and M. H. Kalos,Acta Metall 30:297 (1982).

    Google Scholar 

  10. J. W. Cahn and J. E. Hilliard,J. Chem. Phys. 28:258 (1958);31:668 (1959); J. W. Cahn,Acta Metall. 9:795 (1961);Trans. Metall. Soc. AIME 242:166 (1968).

    Google Scholar 

  11. T. M. Rogers, K. R. Elder, and R. Desai,Phys. Rev. B 37:9638 (1989).

    Google Scholar 

  12. A. Chakrabarti, R. Toral, and J. D. Gunton,Phys. Rev. B 39:4386 (1989).

    Google Scholar 

  13. Y. Oono and S. Puri,Phys. Rev. Lett. 58:836 (1987).

    Google Scholar 

  14. S. Puri and Y. Oono,Phys. Rev. A 38, 434:1542 (1988).

    Google Scholar 

  15. A. Shinozaki and Y. Oono,Phys. Rev. E 48:2622 (1993).

    Google Scholar 

  16. K. Kitahara, Y. Oono, and D. Jasnow,Mod. Phys. Lett. B 2:765 (1988).

    Google Scholar 

  17. J. S. Langer, N. Bar-On, and H. D. Miller,Phys. Rev. A 11:1417 (1975).

    Google Scholar 

  18. K. Kitahara and M. Imada,Prog. Theor. Phys. Suppl. 64:65 (1978).

    Google Scholar 

  19. S. Puri, K. Binder, and S. Dattagupta,Phys. Rev. B 46:98 (1992).

    Google Scholar 

  20. S. Puri, N. Parekh, and S. Dattagupta,J. Stat. Phys. 75:839 (1994).

    Google Scholar 

  21. F. J. Alexander, C. A. Laberge, J. L. Lebowitz, and R. K. P. Zia, to be published.

  22. K.-T. Leung,Phys. Rev. Lett. 66:453 (1991);Int. J. Mod. Phys. C3:367 (1992).

    Google Scholar 

  23. J. S. Wang,J. Stat. Phys., to be published.

  24. G. Giacomin, Ph.D. thesis, Department of Mathematics, Rutgers University;G. Giacomin and J. L. Lebowitz, to be published.

  25. J. L. Valles and J. Marro,J. Stat. Phys. 49:89, 121 (1987).

    Google Scholar 

  26. D. A. Huse,Phys. Rev. B 34:7845 (1986).

    Google Scholar 

  27. P. Fratzl, J. L. Lebowitz, O. Penrose, and J. Amar,Phys. Rev. B 44:4794 (1991).

    Google Scholar 

  28. P. Fratzl and J. L. Lebowitz,Acta Metall. 37:3245 (1989).

    Google Scholar 

  29. K. Hwang, B. Schmittmann, and R. K. P. Zia,Phys. Rev. Lett. 67:326 (1991);Phys. Rev. E 48:800 (1993).

    Google Scholar 

  30. W. W. Mullins and R. F. Sekerka,J. Appl. Phys. 34:323 (1963);35:444 (1964).

    Google Scholar 

  31. H. Guo and D. Jasnow,Phys. Rev. A 34:5027 (1986).

    Google Scholar 

  32. H. E. Cook,Acta Metall. 18:297 (1970).

    Google Scholar 

  33. S. Puri and Y. Oono,J. Phys. A 21:L755–762 (1988).

    Google Scholar 

  34. R. K. P. Zia, K. Hwang, B. Schmittmann, and K.-T. Leung,Physica A 194:183 (1993).

    Google Scholar 

  35. G. Eyink, J. L. Lebowitz, and H. Spohn, To be published.

  36. Y. Oono and C. Yeung, Unpublished.

Download references

Author information

Author notes

  1. F. J. Alexander

    Present address: Center for Computational Science, Boston University, 02215, Boston, Massachusetts

Authors and Affiliations

  1. Institute for Scientific Computing Research L-416, Lawrence Livermore National Laboratory, 94550, Livermore, California

    F. J. Alexander

  2. Departments of Physics and Mathematics, Rutgers University, 08855-0849, Piscataway, New Jersey

    C. A. Laberge & J. L. Lebowitz

  3. Center for Stochastic Processes in Science and Engineering and Department of Physics, Virginia Polytechnic Institute and State University, 24061-0435, Blacksburg, Virginia

    R. K. P. Zia

Authors
  1. F. J. Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. A. Laberge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. L. Lebowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. K. P. Zia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alexander, F.J., Laberge, C.A., Lebowitz, J.L. et al. Monte Carlo studies of a driven lattice gas. I. Growth and asymmetry during phase segregation. J Stat Phys 82, 1133–1158 (1996). https://doi.org/10.1007/BF02179806

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02179806

Key Words

Search

Navigation