Abstract
A scaling hypothesis for the standard deviation σ of the height of growing interfaces is proposed by extending the Family-Vicsek (FV) scaling hypothesis. A data-collapsing method is adopted for estimating values of three exponents α, β, and z, which characterize, respectively, the roughness, growth, and dynamic properties of growing interfaces. The estimation is carried out through σ, which is a function of both the time and the width of the interfaces. The advantages of the present extended scaling hypothesis are as follows: (A) The value of β can be obtained even if the data for σ in terms of t are few so that its value is not determined precisely from the slope of the ln σ vs ln t plot. (B) Different scaling relations can be obtained during the time evolution of interface growth. (C) By introducing a new exponent, which represents the time dependence of σ for a short width, a scaling argument is possible even for growing interfaces that do not satisfy the FV scaling relation. Successful applications are carried out to a few numerical models and a paper-wetting experiment.
| Original language | English |
|---|---|
| Article number | 104002 |
| Journal | Journal of the Physical Society of Japan |
| Volume | 76 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2007 Oct |
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Keywords
- Data-collapsing
- Extended scaling hypothesis
- Growth exponent
- Interface growth
- Roughness
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Reconstruction and extension of the Family-Vicsek scaling hypothesis for growing rough interfaces. / Yamazaki, Yoshihiro; Saito, Kazuaki; Kobayashi, Naoki; Ozawa, Tatsuya; Matsushita, Mitsugu.
In: Journal of the Physical Society of Japan, Vol. 76, No. 10, 104002, 10.2007.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Reconstruction and extension of the Family-Vicsek scaling hypothesis for growing rough interfaces
AU - Yamazaki, Yoshihiro
AU - Saito, Kazuaki
AU - Kobayashi, Naoki
AU - Ozawa, Tatsuya
AU - Matsushita, Mitsugu
PY - 2007/10
Y1 - 2007/10
N2 - A scaling hypothesis for the standard deviation σ of the height of growing interfaces is proposed by extending the Family-Vicsek (FV) scaling hypothesis. A data-collapsing method is adopted for estimating values of three exponents α, β, and z, which characterize, respectively, the roughness, growth, and dynamic properties of growing interfaces. The estimation is carried out through σ, which is a function of both the time and the width of the interfaces. The advantages of the present extended scaling hypothesis are as follows: (A) The value of β can be obtained even if the data for σ in terms of t are few so that its value is not determined precisely from the slope of the ln σ vs ln t plot. (B) Different scaling relations can be obtained during the time evolution of interface growth. (C) By introducing a new exponent, which represents the time dependence of σ for a short width, a scaling argument is possible even for growing interfaces that do not satisfy the FV scaling relation. Successful applications are carried out to a few numerical models and a paper-wetting experiment.
AB - A scaling hypothesis for the standard deviation σ of the height of growing interfaces is proposed by extending the Family-Vicsek (FV) scaling hypothesis. A data-collapsing method is adopted for estimating values of three exponents α, β, and z, which characterize, respectively, the roughness, growth, and dynamic properties of growing interfaces. The estimation is carried out through σ, which is a function of both the time and the width of the interfaces. The advantages of the present extended scaling hypothesis are as follows: (A) The value of β can be obtained even if the data for σ in terms of t are few so that its value is not determined precisely from the slope of the ln σ vs ln t plot. (B) Different scaling relations can be obtained during the time evolution of interface growth. (C) By introducing a new exponent, which represents the time dependence of σ for a short width, a scaling argument is possible even for growing interfaces that do not satisfy the FV scaling relation. Successful applications are carried out to a few numerical models and a paper-wetting experiment.
KW - Data-collapsing
KW - Extended scaling hypothesis
KW - Growth exponent
KW - Interface growth
KW - Roughness
UR - http://www.scopus.com/inward/record.url?scp=35348904388&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=35348904388&partnerID=8YFLogxK
U2 - 10.1143/JPSJ.76.104002
DO - 10.1143/JPSJ.76.104002
M3 - Article
AN - SCOPUS:35348904388
VL - 76
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 10
M1 - 104002
ER -