Universal macroscopic background formation in surface super-roughening

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 3, 1997, Pages R2347-R2350

  Lee, H W ^a   Kim, Doochul ^a  

^a Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874917796     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.R2347     Document Type: Article

References (16)

1. Dynamics of Fractal Surfaces, edited by F. Family and T. Vicsek (World Scientific, Singapore, 1991), Chap. 3, p. 73.
2. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
3. F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).JPHAC5
4. J. G. Amar, P.-M. Lam, and F. Family, Phys. Rev. E 47, 3242 (1993).PLEEE8
5. L. A. N. Amaral, A. L. Barabasi, H. A. Makse, and H. E. Stanley, Phys. Rev. E 52, 4087 (1995).PLEEE8
6. M. Schroeder, M. Siegert, D. E. Wolf, J. D. Shore, and M. Plischke, Europhys. Lett. 24, 563 (1993).EULEEJ
7. S. Das Sarma, S. V. Ghaisas, and J. M. Kim, Phys. Rev. E 49, 122 (1994).PLEEE8
8. J. M. López, M. A. Rodríguez, and R. Cuerno, Report No. cond-mat/9703024.
9. J. M. López and M. A. Rodríguez, Phys. Rev. E 54, R2189 (1996).PLEEE8
10. as an origin of the anomalous roughening for the (Formula presented) uniform diffusion model, which they call groove instability.
11. The proportionality constant in front of the minimal discrepancy (Formula presented) decays as (Formula presented) However, this decay does not change the scaling of the minimal discrepancy since the relevant limiting procedure is to take (Formula presented) first and then allow (Formula presented)
12. For example, see M. Lücke, M. Mihelcic, B. Kowalski, and K. Wingerach, in The Physics of Structure Formation, edited by W. Güttinger and G. Dangelmayr (Springer-Verlag, Berlin, 1987).
13. For an integer α, the FV term (Formula presented) in Eq. (13) is modified to (Formula presented) where (Formula presented) is a constant of order 1. The modification occurs because the (Formula presented) limiting behavior of the scaling function (Formula presented) [Eq. (9)] is modified from (Formula presented) to (Formula presented) for an integer α. The new proportionality constant (Formula presented) is not zero and so the FV term survives even if α is an integer.
14. H. J. Jensen, J. Phys. A 28, 1861 (1995).JPHAC5
15. M. Dong, M. C. Marchetti, A. A. Middleton, and V. Vinokur, Phys. Rev. Lett. 70, 662 (1993).PRLTAO
16. O. Narayan and D. S. Fisher, Phys. Rev. B 48, 7030 (1993). PRBMDO