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0031234536
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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)
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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).
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Pen, U.-L.1
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B. Yurke, A.N. Pargellis, T. Kovacs, and D.A. Huse, Phys. Rev. E 47, 1525 (1993).
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Huse, D.A.4
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33
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85036316552
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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
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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.
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41
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85036377957
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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
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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).
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44
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85036336339
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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)]
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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)].
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47
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5344277543
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Phys. Rev. EJ.-R. Lee, S.J. Lee, B. Kim, and I. Chang, 54, 3257 (1996)
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Phys. Rev. E
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Lee, J.-R.1
Lee, S.J.2
Kim, B.3
Chang, I.4
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51
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85036187528
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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
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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.
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53
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85036309235
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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
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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.
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54
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85036222852
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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)
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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).
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55
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6144240248
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Conserved dynamics have also been explored in the 2D (Formula presented) model, see M. Mondello and N. Goldenfeld, Phys. Rev. E 47, 2384 (1993)
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Phys. Rev. E
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Mondello, M.1
Goldenfeld, N.2
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56
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4244027195
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No evidence of scaling violations is observed in these systems
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Phys. Rev. ES. Puri, A.J. Bray, and F. Rojas, 52, 4699 (1995). No evidence of scaling violations is observed in these systems.
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Phys. Rev. E
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Puri, S.1
Bray, A.J.2
Rojas, F.3
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57
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85036251079
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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
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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
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58
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85036422506
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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
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(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.
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Zapotocky, M.1
Goldbart, P.M.2
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65
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0003474751
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Cambridge University Press, Cambridge
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W.H. Press , Numerical Recipes (Cambridge University Press, Cambridge, 1994).
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Press, W.H.1
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