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Title: Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures
Authors: Dallaston, Michael C.
Fontelos, Marco
Tseluiko, Dmitri
Kalliadasis, Serafim
Issue Date: 2018
Publisher: American Physical Society
Citation: DALLASTON, M.C. ... et al, 2018. Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures. Physical Review Letters, 120(3): paper 034505.
Abstract: The formation of iterated structures, such as satellite and sub-satellite drops, filaments and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.
Description: This is an Open Access Article. It is published by American Physical Society under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
Sponsor: We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the UK through Grants No. EP/K041134/1, EP/K008595/1 and EP/L020564/1 and from the Spanish government through Grant No. MTM2014-57158-R.
Version: Published version
DOI: 10.1103/PhysRevLett.120.034505
URI: https://dspace.lboro.ac.uk/2134/27804
Publisher Link: https://doi.org/10.1103/PhysRevLett.120.034505
ISSN: 0031-9007
Appears in Collections:Published Articles (Maths)

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