On the General Analytical Solution of the Kinematic Cosserat Equations

Handle URI:
http://hdl.handle.net/10754/621970
Title:
On the General Analytical Solution of the Kinematic Cosserat Equations
Authors:
Michels, Dominik L.; Lyakhov, Dmitry ( 0000-0001-8034-9568 ) ; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.
Abstract:
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Springer Nature
Journal:
Computer Algebra in Scientific Computing
Conference/Event name:
International Workshop on Computer Algebra in Scientific Computing
Issue Date:
Sep-2016
DOI:
10.1007/978-3-319-45641-6_24
ARXIV:
arXiv:1610.03369
Type:
Conference Paper
Sponsors:
This work has been partially supported by the Max Planck Society (FKZ-01IMC01/FKZ-01IM10001), the Russian Foundation for Basic Research (16-01-00080), and a BioX Stanford Interdisciplinary Graduate Fellowship. The reviewers’ valuable comments are gratefully acknowledged.
Additional Links:
http://link.springer.com/chapter/10.1007%2F978-3-319-45641-6_24; https://arxiv.org/abs/1610.03369
Appears in Collections:
Conference Papers

Full metadata record

DC FieldValue Language
dc.contributor.authorMichels, Dominik L.en
dc.contributor.authorLyakhov, Dmitryen
dc.contributor.authorGerdt, Vladimir P.en
dc.contributor.authorHossain, Zahiden
dc.contributor.authorRiedel-Kruse, Ingmar H.en
dc.contributor.authorWeber, Andreas G.en
dc.date.accessioned2016-12-08T05:25:56Z-
dc.date.available2016-12-08T05:25:56Z-
dc.date.issued2016-09-
dc.identifier.doi10.1007/978-3-319-45641-6_24-
dc.identifier.urihttp://hdl.handle.net/10754/621970-
dc.description.abstractBased on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.en
dc.description.sponsorshipThis work has been partially supported by the Max Planck Society (FKZ-01IMC01/FKZ-01IM10001), the Russian Foundation for Basic Research (16-01-00080), and a BioX Stanford Interdisciplinary Graduate Fellowship. The reviewers’ valuable comments are gratefully acknowledged.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/chapter/10.1007%2F978-3-319-45641-6_24en
dc.relation.urlhttps://arxiv.org/abs/1610.03369en
dc.rightsThe final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-45641-6_24en
dc.subjectCosserat Rods, Differential Thomas Decomposition, Flagellated Microswimmers, General Analytical Solution, Kinematic Equations, Lie Symmetry Analysis, Stokes Flow, Symbolic Computationen
dc.titleOn the General Analytical Solution of the Kinematic Cosserat Equationsen
dc.typeConference Paperen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalComputer Algebra in Scientific Computingen
dc.conference.dateSeptember 19 - 23, 2016en
dc.conference.nameInternational Workshop on Computer Algebra in Scientific Computingen
dc.conference.locationBucharest, Romaniaen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Computer Science, Stanford University, Stanford, USAen
dc.contributor.institutionGroup of Algebraic and Quantum Computations, Joint Institute for Nuclear Research, Dubna, Russiaen
dc.contributor.institutionDepartment of Bioengineering, Stanford University, Stanford, USAen
dc.contributor.institutionInstitute of Computer Science II, University of Bonn, Bonn, Germanyen
dc.identifier.arxividarXiv:1610.03369en
kaust.authorLyakhov, Dmitry A.en
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