翻訳待ち：Linear Motility Maps in Nonlinear Viscous Fluids
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。ソース概要：arXiv:2606.00063v1 Announce Type: new Abstract: Systems moving in low Reynolds number fluid regimes are known to be governed by a ``motility map'' which linearly relates their shape change rates to they body frame velocity moving through the fluid. A consequence of this is ``Purcell's Scallop Theorem'' -- a locomotion system that undergoes shape changes that follow the same path forward and backward in time (reciprocal body deformations) cannot achieve net displacement, regardless of pacing of those changes.We show that linear-in-velocity motility maps extend to any power law viscosity (a.k.a. Ostwald--de Waele fluid), and therefore to many biological fluids in intermediate shear ranges. We also show that the linear-in-velocity property can be violated in Carreau-Yasuda fluids to produce net motion using an ``inchworm'' model consisting of two unequal masses with unequal drag coefficients performing reciprocal motions. Interestingly, the direction of motion can be switched by changing speeds. Our results show that the linear motility map of geometric mechaincs can be used to analyze and design locomotion in power-law fluids, and that some nonlinear drag relationships such as Carreau-Yasuda can be exploited to generate net locomotion in seeming violation of the ``scallop theorem''.
AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。
[2606.00063] Linear Motility Maps in Nonlinear Viscous Fluids [Submitted on 19 May 2026] Title:Linear Motility Maps in Nonlinear Viscous Fluids View a PDF of the paper titled Linear Motility Maps in Nonlinear Viscous Fluids, by Yishun Zhou and 1 other authors View PDF HTML (experimental) Abstract:Systems moving in low Reynolds number fluid regimes are known to be governed by a `motility map'' which linearly relates their shape change rates to they body frame velocity moving through the fluid. A consequence of this is Purcell's Scallop Theorem'' -- a locomotion system that undergoes shape changes that follow the same path forward and backward in time (reciprocal body deformations) cannot achieve net displacement, regardless of pacing of those this http URL show that linear-in-velocity motility maps extend to any power law viscosity (a.k.a. Ostwald--de Waele fluid), and therefore to many biological fluids in intermediate shear ranges. We also show that the linear-in-velocity property can be violated in Carreau-Yasuda fluids to produce net motion using an inchworm'' model consisting of two unequal masses with unequal drag coefficients performing reciprocal motions. Interestingly, the direction of motion can be switched by changing speeds. Our results show that the linear motility map of geometric mechaincs can be used to analyze and design locomotion in power-law fluids, and that some nonlinear drag relationships such as Carreau-Yasuda can be exploited to generate net locomotion in seeming violation of the `scallop theorem''. Subjects: Robotics (cs.RO); Mathematical Physics (math-ph); Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2606.00063 [cs.RO] (or arXiv:2606.00063v1 [cs.RO] for this version) https://doi.org/10.48550/arXiv.2606.00063 arXiv-issued DOI via DataCite Submission history From: Yishun Zhou [view email] [v1] Tue, 19 May 2026 19:56:42 UTC (437 KB) Full-text links: Access Paper: View a PDF of the paper titled Linear Motility Maps in Nonlinear Viscous Fluids, by Yishun Zhou and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.RO new | recent | 2026-06 Change to browse by: cs math math-ph math.MP physics physics.flu-dyn References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)