ArticlePhilosophical transactions. Series A, Mathematical, physical, and engineering sciences2020
The shape of dendritic tips.
Article in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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3 citing papers in PubMed, 63 citations in OpenAlex.
- Transport phenomena in complex systems (part 2).Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2022Article
- Thin interface limit of the double-sided phase-field model with convection.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
- Patterns in soft and biological matters.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
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Authors and funding
2 authors at 1 institution in 2 countries.
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No grant is acknowledged in the PubMed record.
Abstract
The 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. This article is part of the theme issue 'Patterns in soft and biological matters'.
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