The role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar-Parisi-Zhang growth process

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dc.contributor.authorPriyankaen
dc.contributor.authorTäuber, Uwe C.en
dc.contributor.authorPleimling, Michel J.en
dc.date.accessioned2021-11-01T16:14:12Zen
dc.date.available2021-11-01T16:14:12Zen
dc.date.issued2021-04-16en
dc.date.updated2021-11-01T16:14:09Zen
dc.description.abstractWe explore linear control of the one-dimensional non-linear Kardar-Parisi-Zhang (KPZ) equation with the goal to understand the effects the control process has on the dynamics and on the stationary state of the resulting stochastic growth kinetics. In linear control, the intrinsic non-linearity of the system is maintained at all times. In our protocol, the control is applied to only a small number nc of Fourier modes. The stationary-state roughness is obtained analytically in the small-nc regime with weak non-linear coupling wherein the controlled growth process is found to result in Edwards-Wilkinson dynamics. Furthermore, when the non-linear KPZ coupling is strong, we discern a regime where the controlled dynamics shows scaling in accordance to the KPZ universality class. We perform a detailed numerical analysis to investigate the controlled dynamics subject to weak as well as strong non-linearity. A first-order perturbation theory calculation supports the simulation results in the weak non-linear regime. For strong non-linearity, we find a temporal crossover between KPZ and dispersive growth regimes, with the crossover time scaling with the number nc of controlled Fourier modes. We observe that the height distribution is positively skewed, indicating that as a consequence of the linear control, the surface morphology displays fewer and smaller hills than in the uncontrolled growth process, and that the inherent size-dependent stationary-state roughness provides an upper limit for the roughness of the controlled system.en
dc.description.versionAccepted versionen
dc.format.extent18 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 154002 (Article number)en
dc.identifier.doihttps://doi.org/10.1088/1751-8121/abe753en
dc.identifier.eissn1751-8121en
dc.identifier.issn1751-8113en
dc.identifier.issue15en
dc.identifier.orcidTauber, Uwe [0000-0001-7854-2254]en
dc.identifier.urihttp://hdl.handle.net/10919/106480en
dc.identifier.volume54en
dc.language.isoenen
dc.publisherIOPen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000631804900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.relation.urihttps://doi.org/10.1088/1751-8121/abe753en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPhysics, Multidisciplinaryen
dc.subjectPhysics, Mathematicalen
dc.subjectPhysicsen
dc.subjectsurface roughnessen
dc.subjectControlen
dc.subjectKardar-Parisi-Zhang equationen
dc.subjectcond-mat.stat-mechen
dc.subject01 Mathematical Sciencesen
dc.subject02 Physical Sciencesen
dc.titleThe role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar-Parisi-Zhang growth processen
dc.title.serialJournal of Physics A-Mathematical and Theoreticalen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Physicsen
pubs.organisational-group/Virginia Tech/Faculty of Health Sciencesen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen

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