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Volumn 60, Issue 1, 1999, Pages 212-221

Dynamical scaling: The two-dimensional [Formula Presented] model following a quench

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[No Author keywords available]

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ARTICLE;

EID: 0000427869     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.212     Document Type: Article
Times cited : (48)

References (67)
  • 10
    • 0031234536 scopus 로고    scopus 로고
    • see also Formation and Interactions of Topological Defects, Vol. 349 of NATO Advanced study Institute, Series B: Physics, edited by A.-C. Davis and R. Brandenberger (Plenum, New York, 1995)
    • See, e.g., U.-L. Pen, U. Seljak, and N. Turok, Phys. Rev. Lett. 79, 1611 (1997);see also Formation and Interactions of Topological Defects, Vol. 349 of NATO Advanced study Institute, Series B: Physics, edited by A.-C. Davis and R. Brandenberger (Plenum, New York, 1995).
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 1611
    • Pen, U.-L.1    Seljak, U.2    Turok, N.3
  • 33
    • 85036316552 scopus 로고    scopus 로고
    • For multiple defect species, for instance, with a (Formula presented) ground-state degeneracy 38 or for (Formula presented) nematic quenches 6, multiple length scales may be common. It remains to be seen if these length scales are coupled through the dynamics, i.e., if scaling violations occur
    • For multiple defect species, for instance, with a (Formula presented) ground-state degeneracy 38 or for (Formula presented) nematic quenches 6, multiple length scales may be common. It remains to be seen if these length scales are coupled through the dynamics, i.e., if scaling violations occur.
  • 41
    • 85036377957 scopus 로고    scopus 로고
    • The analogy with an interacting particle system is not exact, since vortices in the 2D (Formula presented) model have effective mobilities that depend on the local structure (see discussion in 10
    • The analogy with an interacting particle system is not exact, since vortices in the 2D (Formula presented) model have effective mobilities that depend on the local structure (see discussion in 10).
  • 44
    • 85036336339 scopus 로고    scopus 로고
    • Existing correlation-closure schemes use the bare vortex configurations, while the logarithmic mobility and hence the logarithmic factor in the growth law comes from nonsingular corrections to the tails of bare vortices 27. This may be connected with the deviations between theory and simulation seen at large distances in Fig. 33, and also with the lack of logarithmic factors seen in correlation-closure schemes [R. Wickham, (private communication)]
    • Existing correlation-closure schemes use the bare vortex configurations, while the logarithmic mobility and hence the logarithmic factor in the growth law comes from nonsingular corrections to the tails of bare vortices 27. This may be connected with the deviations between theory and simulation seen at large distances in Fig. 33, and also with the lack of logarithmic factors seen in correlation-closure schemes [R. Wickham, (private communication)].
  • 51
    • 85036187528 scopus 로고    scopus 로고
    • While the exponent of the leading correction to a growth law is probably universal (between, for example, (Formula presented) and (Formula presented), a nonuniversal shift in the amplitude ratio between the growth law and the leading correction is sufficient to shift the effective exponent at finite times
    • While the exponent of the leading correction to a growth law is probably universal (between, for example, (Formula presented) and (Formula presented), a nonuniversal shift in the amplitude ratio between the growth law and the leading correction is sufficient to shift the effective exponent at finite times.
  • 53
    • 85036309235 scopus 로고    scopus 로고
    • Higher-point correlations that cannot be expressed in a simple scaling form 16 are subdominant, in that they only probe the vicinity of defects and thus have negligible weight compared to two-point correlations. It may be that multiple length scales can be found in any system with singular defects if sufficiently high-order correlations, restricted to the vicinity of the defects, are considered
    • Higher-point correlations that cannot be expressed in a simple scaling form 16 are subdominant, in that they only probe the vicinity of defects and thus have negligible weight compared to two-point correlations. It may be that multiple length scales can be found in any system with singular defects if sufficiently high-order correlations, restricted to the vicinity of the defects, are considered.
  • 54
    • 85036222852 scopus 로고    scopus 로고
    • One could argue that a scaling form for full two-time correlations, (Formula presented), is the most natural since it would include autocorrelations. However, this two-time correlation is impractical to measure and is not necessary to determine the scaling growth law. We use a less restrictive definition of dynamical scaling, using only (Formula presented) and (Formula presented)
    • One could argue that a scaling form for full two-time correlations, (Formula presented), is the most natural since it would include autocorrelations. However, this two-time correlation is impractical to measure and is not necessary to determine the scaling growth law. We use a less restrictive definition of dynamical scaling, using only (Formula presented) and (Formula presented).
  • 55
    • 6144240248 scopus 로고
    • Conserved dynamics have also been explored in the 2D (Formula presented) model, see M. Mondello and N. Goldenfeld, Phys. Rev. E 47, 2384 (1993)
    • (1993) Phys. Rev. E , vol.47 , pp. 2384
    • Mondello, M.1    Goldenfeld, N.2
  • 56
    • 4244027195 scopus 로고
    • No evidence of scaling violations is observed in these systems
    • Phys. Rev. ES. Puri, A.J. Bray, and F. Rojas, 52, 4699 (1995). No evidence of scaling violations is observed in these systems.
    • (1995) Phys. Rev. E , vol.52 , pp. 4699
    • Puri, S.1    Bray, A.J.2    Rojas, F.3
  • 57
    • 85036251079 scopus 로고    scopus 로고
    • Liquid-crystal films can have significant and discernible differences from 2D (Formula presented) systems (though see 35, Most obvious are the non-Abelian species of vortices seen in biaxial nematic films 22, Less obvious is the different vortex structure, resulting from the “headless” nature of nematics 21 or from varying bend and twist elastic constants, which will change the Porod amplitude contributed by each vortex
    • Liquid-crystal films can have significant and discernible differences from 2D (Formula presented) systems (though see 35).Most obvious are the non-Abelian species of vortices seen in biaxial nematic films 22.Less obvious is the different vortex structure, resulting from the “headless” nature of nematics 21 or from varying bend and twist elastic constants, which will change the Porod amplitude contributed by each
  • 58
    • 85036422506 scopus 로고    scopus 로고
    • While any scaling growth law must be the same in these systems, determined by the singular nature of the vortices 27 rather than their fine structure, it is possible that some planar systems with vortices do not dynamically scale
    • (M. Zapotocky and P.M. Goldbart, eprint cond-mat/9812235).While any scaling growth law must be the same in these systems, determined by the singular nature of the vortices 27 rather than their fine structure, it is possible that some planar systems with vortices do not dynamically scale.
    • Zapotocky, M.1    Goldbart, P.M.2
  • 65
    • 0003474751 scopus 로고
    • Cambridge University Press, Cambridge
    • W.H. Press , Numerical Recipes (Cambridge University Press, Cambridge, 1994).
    • (1994) Numerical Recipes
    • Press, W.H.1


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