Improvements in simulating discrete deposition models

dc.contributor.advisorİlday, Fatih Ömer
dc.contributor.authorHashemi, Batoul
dc.departmentDepartment of Physicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (M.S.): Bilkent University, Department of Physics, İhsan Doğramacı Bilkent University, 2021.en_US
dc.descriptionIncludes bibliographical references (leaves 60-64).en_US
dc.description.abstractThe main purpose of this work is to describe the surface growth phenomena. Initially, we give a brief introduction to the analytical studies, in particular, done by di erential equations such as Edward-Wilkinson and Kardar-Parisi-Zhang equations, and then introduce the discrete surface growth models as a means to describe these phenomena with a restricted number of rules. The universality properties of these models help us categorize them in three di erent classes, namely Gaussian, Edward-Wilkinson, and Kardar-Parisi-Zhang universality classes. Five di erent numerical growth models are explained, and the statistical properties of the growing interfaces in 1D systems are examined via computational studies. Growth properties of 1D structures are viewed in two di erent ways, one being the scaling exponent of roughness changing with respect to time, and the other the distribution of height uctuations. In this research, we show that our numerical simulation findings are in accord with the theoretical and analytical predictions. In addition, for the ballistic deposition and restricted solid-on-solid models, we introduce a binning method [1] which improves our numerical results. Moreover, we propose a novel modification on the ballistic deposition model by detecting the thin-deep wells on the interface and average them out which enables us to report an improvement in our numerical results with a noteworthy development on physical properties of the system. Furthermore, we investigate the e ect of the change of the deposition rate on the universal behavior of the system, as a result, we introduce critical values for the deposition rate with respect to the size of the system. With these modifications, we are one step closer to defining the complex behavior of the growth phenomena.en_US
dc.description.statementofresponsibilityby Batoul Hashemien_US
dc.format.extentxiii, 105 leaves : charts ; 30 cm.en_US
dc.publisherBilkent Universityen_US
dc.subjectSurface growthen_US
dc.subjectKPZ equationen_US
dc.subjectBallistic depositionen_US
dc.subjectRandom depositionen_US
dc.subjectRandom deposition with surface diffusionen_US
dc.subjectEden modelen_US
dc.subjectRestricted solid-on-solid modelen_US
dc.subjectTracy-Widom distributionen_US
dc.titleImprovements in simulating discrete deposition modelsen_US
dc.title.alternativeAyrık biriktirme modellerinin simülasyonunda gelişmeleren_US
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