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dc.contributor.authorAlexandrov, D. V.en
dc.contributor.authorGalenko, P. K.en
dc.date.accessioned2020-10-20T16:36:42Z-
dc.date.available2020-10-20T16:36:42Z-
dc.date.issued2020-
dc.identifier.citationAlexandrov D. V. The shape of dendritic tips / D. V. Alexandrov, P. K. Galenko. — DOI 10.1098/rsta.2019.0243 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2020. — Vol. 2171. — Iss. 378. — 243.en
dc.identifier.issn1364503X-
dc.identifier.otherhttps://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0243pdf
dc.identifier.other1good_DOI
dc.identifier.otherc192a8a9-c1ae-44ee-ad95-6440cc68c520pure_uuid
dc.identifier.otherhttp://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85083337744m
dc.identifier.urihttp://elar.urfu.ru/handle/10995/92660-
dc.description.abstractThe present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. © 2020 The Author(s) Published by the Royal Society. All rights reserved.en
dc.description.sponsorshipRussian Science Foundation, RSF: 16-11-10095en
dc.description.sponsorshipCompeting interests. We declare we have no competing interests. Funding. Authors thank Efim Brener and Mathis Plapp for the fruitful discussions. This work was supported by the Russian Science Foundation (grant no. 16-11-10095).en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherRoyal Society Publishingen
dc.relationinfo:eu-repo/grantAgreement/RSF//16-11-10095en
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourcePhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.subjectBOUNDARY INTEGRAL METHODen
dc.subjectDENDRITESen
dc.subjectDENDRITIC TIPSen
dc.subjectHEAT AND MASS TRANSFERen
dc.subjectPHASE TRANSFORMATIONSen
dc.subjectBINARY SYSTEMSen
dc.subjectDENDRITIC GROWTHen
dc.subjectFRACTIONAL POWERen
dc.subjectLIMITING CASEen
dc.subjectENGINEERINGen
dc.subjectARTICLEen
dc.subjectCOMPUTER SIMULATIONen
dc.subjectDENDRITEen
dc.subjectHEATen
dc.titleThe shape of dendritic tipsen
dc.typeReviewen
dc.typeinfo:eu-repo/semantics/reviewen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.1098/rsta.2019.0243-
dc.identifier.scopus85083337744-
local.affiliationDepartment of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
local.affiliationPhysikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, Jena, 07743, Germany
local.contributor.employeeAlexandrov, D.V., Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
local.contributor.employeeGalenko, P.K., Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation, Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, Jena, 07743, Germany
local.issue378-
local.volume2171-
dc.identifier.wos000526681700017-
local.identifier.pure12664930-
local.description.order243-
local.identifier.eid2-s2.0-85083337744-
local.fund.rsf16-11-10095-
local.identifier.wosWOS:000526681700017-
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