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to mitigate any confusion, we note that the convention in defining the primed and unprimed variables in this reference is opposite to that used here.
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to mitigate any confusion, we note that the convention in defining the primed and unprimed variables in this reference is opposite to that used here.
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The same is true for all the higher order linear models of the [Formula Presented] type with n ge2, all of which have α'=1 and α = (n - 1/2), making kappa = (2n -d -1) for n ge 2 and d = 1+1 or 2+1. Note that in d=2+1 the [Formula Presented] linear model has a logarithmic anomalous scaling exponent with kappa = [Formula Presented].
-
The same is true for all the higher order linear models of the nabla2n type with n ge2, all of which have α'=1 and α = (n - 1/2), making kappa = (2n -d -1) for n ge 2 and d = 1+1 or 2+1. Note that in d=2+1 the nabla4 linear model has a logarithmic anomalous scaling exponent with kappa = 0+.
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While the scaling collapse of Fig. 6 for the BD model does not have the high quality of the corresponding SOS scaling collapses in Figs. 3 and 4, saturation of the scaling function is clear in Fig. 6 and the deviations for y= 0.1 to 1.0 are attributed to the intrinsic width and defect formation effects, well known to be important for non conservative growth, and demonstrate a problem of using a single valued height function to describe BD growth. See Refs. citedlgk,cjl_lag,krugspohn, for example. par
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While the scaling collapse of Fig. 6 for the BD model does not have the high quality of the corresponding SOS scaling collapses in Figs. 3 and 4, saturation of the scaling function is clear in Fig. 6 and the deviations for y= 0.1 to 1.0 are attributed to the intrinsic width and defect formation effects, well known to be important for non conservative growth, and demonstrate a problem of using a single valued height function to describe BD growth. See Refs. citedlgk,cjl_lag,krugspohn, for example. par
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We note that the correlation lengths in the simulations yielding α' and z' are small [ξ([Formula Presented]) sim 30 60 for the data of Fig. 5(a)] compared to the largest system size (L=200) used to extract an L independent value for γ in Fig. 7(a), so the comparison between γ and z' may not be completely justified due to finite size effects. In particular, we note that for L=50 in the d=1+1 results for S(k) [so that L approx ξ([Formula Presented])], γ approx 2.3, the finite size effect making γ more consistent with z'. Because growth in 2+1 dimensions is not as constrained as it is for d=1+1 (there are more diffusional opportunities for an atom in higher dimensions), it seems reasonable that such effects are reduced.
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We note that the correlation lengths in the simulations yielding α' and z' are small [ξ(tmax) sim 30 60 for the data of Fig. 5(a)] compared to the largest system size (L=200) used to extract an L independent value for γ in Fig. 7(a), so the comparison between γ and z' may not be completely justified due to finite size effects. In particular, we note that for L=50 in the d=1+1 results for S(k) [so that L approx ξ(tmax)], γ approx 2.3, the finite size effect making γ more consistent with z'. Because growth in 2+1 dimensions is not as constrained as it is for d=1+1 (there are more diffusional opportunities for an atom in higher dimensions), it seems reasonable that such effects are reduced.
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We attempted to fit the P(s) distribution to the stretched exponential form, but very few step height values occur even for very long simulations both in the D=10,20 DT model and the Family model, and such an exercise is not statistically meaningful.
-
We attempted to fit the P(s) distribution to the stretched exponential form, but very few step height values occur even for very long simulations both in the D=10,20 DT model and the Family model, and such an exercise is not statistically meaningful.
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