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Volumn 67, Issue 1, 2003, Pages

Kinetics of phase separation in the driven lattice gas: Self-similar pattern growth under anisotropic nonequilibrium conditions

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; ARTICLE; EVAPORATION; GAS; KINETICS; LOW TEMPERATURE PROCEDURES; MONTE CARLO METHOD; PHASE SEPARATION; POLYMERIZATION;

EID: 0037285076     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.014206     Document Type: Article
Times cited : (12)

References (57)
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    • J. D. Gunton, M. San Miguel, and P. S. Shani, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983), Vol. 8.
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    • K. Binder and P. Fratzl, in, edited by G. Kostorz (Wiley-VCH, Weinheim, 2001), 409–480
    • K. Binder and P. Fratzl, Spinodal Decomposition, in Phase Transformations in Materials, edited by G. Kostorz (Wiley-VCH, Weinheim, 2001), pp. 409–480.
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    • S. K. Ma, (World Scientific, Singapore, 1985)
    • S. K. Ma, Statistical Mechanics (World Scientific, Singapore, 1985).
  • 23
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    • B. B. Mandelbrot, (formula presented), (Springer, New York, 1999)
    • B. B. Mandelbrot, Multifractals and(formula presented) Noise (Springer, New York, 1999).
  • 25
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    • J. Marro and R. Dickman, (Cambridge University, Cambridge, England, 1999)
    • J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University, Cambridge, England, 1999).
  • 29
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    • B. Schmittman and R. Zia, in, edited by C. Domb and J. L. Lebowitz (Academic, London, 1995), 17
    • B. Schmittman and R. Zia, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1995), Vol. 17.
  • 35
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    • Some partial, unconclusive studies about interfaces in the driven lattice gas (Ref. have been reviewed in Ref
    • Some partial, unconclusive studies about interfaces in the driven lattice gas (Ref. 31) have been reviewed in Ref. 21.
  • 38
    • 85038285021 scopus 로고    scopus 로고
    • This corresponds to the standard Monte Carlo method only if the time increment (formula presented) is drawn from a Poisson distribution. Taking constant (formula presented) involves some approximation. However, if the number of particle-hole pairs in the system is sufficiently large, the approximation is excellent. In particular, for a half filled system subject to an, drive (our model case), the minimum amount of particle-hole pairs present in the system will be of order (formula presented) which is large for large lattices
    • This corresponds to the standard Monte Carlo method only if the time increment (formula presented) is drawn from a Poisson distribution. Taking constant (formula presented) involves some approximation. However, if the number of particle-hole pairs in the system is sufficiently large, the approximation is excellent. In particular, for a half filled system subject to an infinite drive (our model case), the minimum amount of particle-hole pairs present in the system will be of order (formula presented) which is large for large lattices.
  • 40
    • 85038327284 scopus 로고    scopus 로고
    • See, for instance, N. T. J. Bailey, (Wiley, New York, 1964)
    • See, for instance, N. T. J. Bailey, The Elements of Stochastic Processes (Wiley, New York, 1964).
  • 41
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    • A. Guinier and G. Fournet, (Wiley, New York, 1955)
    • A. Guinier and G. Fournet, Small Angle Scattering of X-Rays (Wiley, New York, 1955).
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    • 85038326882 scopus 로고    scopus 로고
    • M. San Miguel and R. Toral, in, edited by E. Tirapegui, J. Martínez, and R. Tiemann (Kluwer Academic, New York, 2001)
    • M. San Miguel and R. Toral, in Instabilities and Nonequilibrium Structures VI, edited by E. Tirapegui, J. Martínez, and R. Tiemann (Kluwer Academic, New York, 2001).
  • 52
    • 0035939436 scopus 로고    scopus 로고
    • The (formula presented) behavior here is in contrast with the logarithmic growth that is assumed to govern a class of lattice models in which coarsening is not a direct consequence of surface tension. See, and
    • The (formula presented) behavior here is in contrast with the logarithmic growth that is assumed to govern a class of lattice models in which coarsening is not a direct consequence of surface tension. See I. Dornic, H. Chaté, J. Chave, and H. Hinrichsen, Phys. Rev. Lett.87, 045701 (2001).
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 45701
    • Dornic, I.1    Chaté, H.2    Chave, J.3    Hinrichsen, H.4
  • 53
    • 85038331689 scopus 로고    scopus 로고
    • More properly, one should speak here of “self-affinity,” given the underlying anisotropy (Ref
    • More properly, one should speak here of “self-affinity,” given the underlying anisotropy (Ref. 19).
  • 54
    • 85038331252 scopus 로고    scopus 로고
    • Extending some of our arguments to (formula presented) needs some care but the whole picture should still be valid, at least not far from (formula presented)
    • Extending some of our arguments to (formula presented) needs some care but the whole picture should still be valid, at least not far from (formula presented)
  • 55
    • 85038283872 scopus 로고    scopus 로고
    • Note that the Lifshitz-Slyozov-Wagner behavior is known to be valid in some cases in both (formula presented) and (formula presented) (Ref
    • Note that the Lifshitz-Slyozov-Wagner behavior is known to be valid in some cases in both (formula presented) and (formula presented) (Ref. 5).


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