TY - JOUR
T1 - Surface growth kinematics via local curve evolution
AU - Moulton, Derek E.
AU - Goriely, Alain
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/11/18
Y1 - 2012/11/18
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/599812
UR - http://link.springer.com/10.1007/s00285-012-0625-7
UR - http://www.scopus.com/inward/record.url?scp=84891737172&partnerID=8YFLogxK
U2 - 10.1007/s00285-012-0625-7
DO - 10.1007/s00285-012-0625-7
M3 - Article
C2 - 23161474
SN - 0303-6812
VL - 68
SP - 81
EP - 108
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
IS - 1-2
ER -