Handle URI:
http://hdl.handle.net/10754/599812
Title:
Surface growth kinematics via local curve evolution
Authors:
Moulton, Derek E.; Goriely, Alain
Abstract:
A mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process. © 2012 Springer-Verlag Berlin Heidelberg.
Citation:
Moulton DE, Goriely A (2012) Surface growth kinematics via local curve evolution. Journal of Mathematical Biology 68: 81–108. Available: http://dx.doi.org/10.1007/s00285-012-0625-7.
Publisher:
Springer Nature
Journal:
Journal of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
18-Nov-2012
DOI:
10.1007/s00285-012-0625-7
PubMed ID:
23161474
Type:
Article
ISSN:
0303-6812; 1432-1416
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), and based in part upon work supported by the National Science Foundation under grant DMS-0907773 (AG). AG is a Wolfson/Royal Society Merit Award Holder.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMoulton, Derek E.en
dc.contributor.authorGoriely, Alainen
dc.date.accessioned2016-02-28T06:10:23Zen
dc.date.available2016-02-28T06:10:23Zen
dc.date.issued2012-11-18en
dc.identifier.citationMoulton DE, Goriely A (2012) Surface growth kinematics via local curve evolution. Journal of Mathematical Biology 68: 81–108. Available: http://dx.doi.org/10.1007/s00285-012-0625-7.en
dc.identifier.issn0303-6812en
dc.identifier.issn1432-1416en
dc.identifier.pmid23161474en
dc.identifier.doi10.1007/s00285-012-0625-7en
dc.identifier.urihttp://hdl.handle.net/10754/599812en
dc.description.abstractA mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process. © 2012 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), and based in part upon work supported by the National Science Foundation under grant DMS-0907773 (AG). AG is a Wolfson/Royal Society Merit Award Holder.en
dc.publisherSpringer Natureen
dc.subjectBiological growthen
dc.subjectMathematical modelen
dc.subjectMorphologyen
dc.subjectSeashellen
dc.titleSurface growth kinematics via local curve evolutionen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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