Kink dynamics in a one-dimensional growing surface

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

Volumn 58, Issue 1, 1998, Pages 281-294

  Politi, Paolo ^a,b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010607901     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.281     Document Type: Article

References (42)

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8. We leave out the possibility of a current that is periodic in z [j=j0sin(2πz)] because it would be an effect of the discrete nature of the lattice, which may be important only in the very early stages of growth.
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16. Here jES must be read as the “slope-dependent current,” i.e., the current due to the Ehrlich-Schwoebel effect, and also to all possible different mechanisms that depend on m (see above). Current (4) has been used in the context of surface growth by Stroscio et al. 18. The fact that it diverges whenm →∞ is not relevant, because m=m0 is a “stable fixed point.” Current (5), which is correct only in the limit of a strong Ehrlich-Schwoebel effect [see Eq. (3)], has been introduced in 2+1 dimensions by M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, J. Sudijono, L. M. Sander, and B. G. Orr, Phys. Rev. Lett. 72, 116 (1994).PRLTAO
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27. In a different context [O. Pierre-Louis, C. Misbah, Y. Saito, J. Krug, and P. Politi, Phys. Rev. Lett. 80, 4221 (1998)] it is indeed possible to observe no coarsening because the period is a decreasing function of the amplitude.PRLTAO
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40. This value is a bit surprising: if compared to n≃0.22 it would lead one to conclude that (in 1+1 dimensions) deterministic coarsening is not slower than the noisy one; if compared to the noiseless coarsening of model I [L(t)∼lnt], we should conclude that steepening (due to the absence of finite zeros in jES) favors the coarsening.
41. The reason is simply that jSB (the cause of angular points) would contribute to the growth velocity with a term proportional to ∂x2A(m2), which diverges in the angular points. More details are given in Ref. 6.
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