Width and extremal height distributions of fluctuating interfaces with window boundary conditions
Autor(a) principal: | |
---|---|
Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | LOCUS Repositório Institucional da UFV |
Texto Completo: | https://doi.org/10.1103/PhysRevE.93.012801 http://www.locus.ufv.br/handle/123456789/18848 |
Resumo: | 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 ξ l (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 w n c ∼ t γ n , with γ n = 2nβ + (n − 1)d s /z = [2n + (n − 1)d s /α]β. 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, β 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 ξ 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. |
id |
UFV_e2b5e4468d0a276d94679ccf85636f2f |
---|---|
oai_identifier_str |
oai:locus.ufv.br:123456789/18848 |
network_acronym_str |
UFV |
network_name_str |
LOCUS Repositório Institucional da UFV |
repository_id_str |
2145 |
spelling |
Carrasco, I. S. S.Oliveira, T. J.2018-04-19T14:14:01Z2018-04-19T14:14:01Z2016-01-0724700053https://doi.org/10.1103/PhysRevE.93.012801http://www.locus.ufv.br/handle/123456789/18848We 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 ξ l (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 w n c ∼ t γ n , with γ n = 2nβ + (n − 1)d s /z = [2n + (n − 1)d s /α]β. 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, β 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 ξ 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.engPhysical Review Ev. 93, Iss. 1, p. 012801, January 2016American Physical Societyinfo:eu-repo/semantics/openAccessDistributions of fluctuating interfacesBoundary conditionsWidth and extremal height distributions of fluctuating interfaces with window boundary conditionsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdfTexto completoapplication/pdf1114295https://locus.ufv.br//bitstream/123456789/18848/1/artigo.pdf34859f1ee8e9da8a0272810f14bbcd72MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/18848/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg5299https://locus.ufv.br//bitstream/123456789/18848/3/artigo.pdf.jpg30dfdc78640a8aec27fdfa160f79e10bMD53123456789/188482018-04-19 23:01:10.929oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-04-20T02:01:10LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false |
dc.title.en.fl_str_mv |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
title |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
spellingShingle |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions Carrasco, I. S. S. Distributions of fluctuating interfaces Boundary conditions |
title_short |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
title_full |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
title_fullStr |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
title_full_unstemmed |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
title_sort |
Width and extremal height distributions of fluctuating interfaces with window boundary conditions |
author |
Carrasco, I. S. S. |
author_facet |
Carrasco, I. S. S. Oliveira, T. J. |
author_role |
author |
author2 |
Oliveira, T. J. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Carrasco, I. S. S. Oliveira, T. J. |
dc.subject.pt-BR.fl_str_mv |
Distributions of fluctuating interfaces Boundary conditions |
topic |
Distributions of fluctuating interfaces Boundary conditions |
description |
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 ξ l (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 w n c ∼ t γ n , with γ n = 2nβ + (n − 1)d s /z = [2n + (n − 1)d s /α]β. 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, β 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 ξ 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. |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-01-07 |
dc.date.accessioned.fl_str_mv |
2018-04-19T14:14:01Z |
dc.date.available.fl_str_mv |
2018-04-19T14:14:01Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.1103/PhysRevE.93.012801 http://www.locus.ufv.br/handle/123456789/18848 |
dc.identifier.issn.none.fl_str_mv |
24700053 |
identifier_str_mv |
24700053 |
url |
https://doi.org/10.1103/PhysRevE.93.012801 http://www.locus.ufv.br/handle/123456789/18848 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.pt-BR.fl_str_mv |
v. 93, Iss. 1, p. 012801, January 2016 |
dc.rights.driver.fl_str_mv |
American Physical Society info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
American Physical Society |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Physical Review E |
publisher.none.fl_str_mv |
Physical Review E |
dc.source.none.fl_str_mv |
reponame:LOCUS Repositório Institucional da UFV instname:Universidade Federal de Viçosa (UFV) instacron:UFV |
instname_str |
Universidade Federal de Viçosa (UFV) |
instacron_str |
UFV |
institution |
UFV |
reponame_str |
LOCUS Repositório Institucional da UFV |
collection |
LOCUS Repositório Institucional da UFV |
bitstream.url.fl_str_mv |
https://locus.ufv.br//bitstream/123456789/18848/1/artigo.pdf https://locus.ufv.br//bitstream/123456789/18848/2/license.txt https://locus.ufv.br//bitstream/123456789/18848/3/artigo.pdf.jpg |
bitstream.checksum.fl_str_mv |
34859f1ee8e9da8a0272810f14bbcd72 8a4605be74aa9ea9d79846c1fba20a33 30dfdc78640a8aec27fdfa160f79e10b |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 |
repository.name.fl_str_mv |
LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV) |
repository.mail.fl_str_mv |
fabiojreis@ufv.br |
_version_ |
1801212941619429376 |