@inproceedings{4bcafab8daa84cd698b64645cdaf9e67,

title = "On the general analytical solution of the kinematic cosserat equations",

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.",

keywords = "Cosserat rods, Differential thomas decomposition, Flagellated microswimmers, General analytical solution, Kinematic equations, Lie symmetry analysis, Stokes flow, Symbolic computation",

author = "Michels, {Dominik L.} and Lyakhov, {Dmitry A.} and Gerdt, {Vladimir P.} and Zahid Hossain and Riedel-Kruse, {Ingmar H.} and Weber, {Andreas G.}",

note = "Funding Information: 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{\textquoteright} valuable comments are gratefully acknowledged. Publisher Copyright: {\textcopyright} Springer International Publishing AG 2016.; 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016 ; Conference date: 19-09-2016 Through 23-09-2016",

year = "2016",

doi = "10.1007/978-3-319-45641-6_24",

language = "English (US)",

isbn = "9783319456409",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "367--380",

editor = "Vorozhtsov, {Evgenii V.} and Gerdt, {Vladimir P.} and Wolfram Koepf and Seiler, {Werner M.}",

booktitle = "Computer Algebra in Scientific Computing - 18th International Workshop, CASC 2016, Proceedings",

}