{"id":{"repo_id":"brazil-uff","oai_identifier":"oai:app.uff.br:1/18634"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-uff/oai:app.uff.br:1/18634","repository":{"repo_id":"brazil-uff","name":"Brazil UFF","base_url":"https://app.uff.br/oai/request"},"display":{"title":"Estudo numérico da equação de Kardar, Parisi e Zhang","abstract":"We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in one and two dimensions using the usual finite differences scheme and the replacement of |∇h|2 by exponentially decreasing functions of that quantity. In one dimension the study showed that the discretization scheme adopted by us was able to solve the two major problems found with the usual discretization: numerical instabilities and inconsistency between the parameters of the discretized and the continuum version. Our study advences over previous works on the KPZ equation, which usually treated those problems apart. In two dimensions, we evaluated and confirmed the universality of steady state height and roughness distributions in KPZ class by a sistematic variation of the equation s parameters. Estimates of kurtosis and skewness of steady state height and roughness distributions were provided. We also obtained roughness exponents estimates. We observed the weak scaling corrections behavior of steady state roughness distributions and verified the evidence of stretched exponentials tails of such distributions. Our results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.","abstract_html":"We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in one and two dimensions using the usual finite differences scheme and the replacement of |∇h|2 by exponentially decreasing functions of that quantity. In one dimension the study showed that the discretization scheme adopted by us was able to solve the two major problems found with the usual discretization: numerical instabilities and inconsistency between the parameters of the discretized and the continuum version. Our study advences over previous works on the KPZ equation, which usually treated those problems apart. In two dimensions, we evaluated and confirmed the universality of steady state height and roughness distributions in KPZ class by a sistematic variation of the equation s parameters. Estimates of kurtosis and skewness of steady state height and roughness distributions were provided. We also obtained roughness exponents estimates. We observed the weak scaling corrections behavior of steady state roughness distributions and verified the evidence of stretched exponentials tails of such distributions. Our results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.","abstract_has_math":false,"creators":["Miranda, Vladimir Gonçalves"],"institution":"Programa de Pós-graduação em Física","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-03-04","date_published":"2009-03-04","updated_at":"2026-07-27T19:00:47Z","subjects":["Integração numérica","Equação diferencial estocástica","Rugosidade (Superfície)","Numerical integration","Stochastic differential equation","Roughness (surface)"],"languages":["por"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://app.uff.br/riuff/handle/1/18634","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Miranda, Vladimir Gonçalves"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-03-10T20:45:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-12-07","2021-03-10T20:45:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2009-03-04"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Física"]},{"key":"dc:type","label":"Dc Type","values":["Dissertação"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Integração numérica","Equação diferencial estocástica","Rugosidade (Superfície)","Numerical integration","Stochastic differential equation","Roughness (surface)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["por"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://app.uff.br/riuff/handle/1/18634"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in one and two dimensions using the usual finite differences scheme and the replacement of |∇h|2 by exponentially decreasing functions of that quantity. In one dimension the study showed that the discretization scheme adopted by us was able to solve the two major problems found with the usual discretization: numerical instabilities and inconsistency between the parameters of the discretized and the continuum version. Our study advences over previous works on the KPZ equation, which usually treated those problems apart. In two dimensions, we evaluated and confirmed the universality of steady state height and roughness distributions in KPZ class by a sistematic variation of the equation s parameters. Estimates of kurtosis and skewness of steady state height and roughness distributions were provided. We also obtained roughness exponents estimates. We observed the weak scaling corrections behavior of steady state roughness distributions and verified the evidence of stretched exponentials tails of such distributions. Our results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Estudo numérico da equação de Kardar, Parisi e Zhang"]}]}],"canonical_facts":{"dc:creator":["Miranda, Vladimir Gonçalves"],"dc:date.accessioned":["2021-03-10T20:45:08Z"],"dc:date.available":["2009-12-07","2021-03-10T20:45:08Z"],"dc:date.issued":["2009-03-04"],"dc:description.abstract":["We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in one and two dimensions using the usual finite differences scheme and the replacement of |∇h|2 by exponentially decreasing functions of that quantity. In one dimension the study showed that the discretization scheme adopted by us was able to solve the two major problems found with the usual discretization: numerical instabilities and inconsistency between the parameters of the discretized and the continuum version. Our study advences over previous works on the KPZ equation, which usually treated those problems apart. In two dimensions, we evaluated and confirmed the universality of steady state height and roughness distributions in KPZ class by a sistematic variation of the equation s parameters. Estimates of kurtosis and skewness of steady state height and roughness distributions were provided. We also obtained roughness exponents estimates. We observed the weak scaling corrections behavior of steady state roughness distributions and verified the evidence of stretched exponentials tails of such distributions. Our results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://app.uff.br/riuff/handle/1/18634"],"dc:language":["por"],"dc:publisher.department":["Física"],"dc:rights":["Acesso Aberto"],"dc:subject":["Integração numérica","Equação diferencial estocástica","Rugosidade (Superfície)","Numerical integration","Stochastic differential equation","Roughness (surface)"],"dc:title":["Estudo numérico da equação de Kardar, Parisi e Zhang"],"dc:type":["Dissertação"]},"updated_at":"2026-07-27T19:00:47Z"}