Width and extremal height distributions of fluctuating interfaces with window boundary conditions.
Phys Rev E
; 93(1): 012801, 2016 Jan.
Article
em En
| MEDLINE
| ID: mdl-26871135
We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size l, for interfaces in several universality classes, in substrate dimensions d_{s}=1 and 2. We show that their cumulants follow a Family-Vicsek-type scaling, and, at early times, when ξâªl (ξ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their nth cumulant scaling as (ξ/l)^{(n-1)d_{s}}. This gives rise to an interesting temporal scaling for such cumulants as ãw_{n}ã_{c}â¼t^{γ_{n}}, with γ_{n}=2nß+(n-1)d_{s}/z=[2n+(n-1)d_{s}/α]ß. This scaling is analytically proved for the Edwards-Wilkinson (EW) and random deposition interfaces and numerically confirmed for other classes. In general, it is featured by small corrections, and, thus, it yields exponents γ_{n} (and, consequently, α,ß and z) in good agreement with their respective universality class. Thus, it is a useful framework for numerical and experimental investigations, where it is usually hard to estimate the dynamic z and mainly the (global) roughness α exponents. The stationary (for ξâ«l) SLRDs and LEHDs of the Kardar-Parisi-Zhang (KPZ) class are also investigated, and, for some models, strong finite-size corrections are found. However, we demonstrate that good evidence of their universality can be obtained through successive extrapolations of their cumulant ratios for long times and large l. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.
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01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2016
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos