{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-integral-based-spectral-method-for","title":"An integral-based spectral method for inextensible slender fibers in Stokes flow","arxiv_id":"2007.11728","date":"2020-07-23","proceeding":null,"authors":["Ondrej Maxian","Alex Mogilner","Aleksandar Donev"],"abstract":"Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible fibers, such as microtubules, actin fibers, and intermediate filaments, all suspended in a viscous fluid. Numerical simulation of this gel is challenging because the fiber aspect ratios can be as large as $10^4$. We describe a new method for rapidly computing the dynamics of inextensible slender filaments in periodically-sheared Stokes flow. The dynamics of the filaments are governed by a nonlocal slender body theory which we partially reformulate in terms of the Rotne-Prager-Yamakawa hydrodynamic tensor. To enforce inextensibility, we parameterize the space of inextensible fiber motions and strictly confine the dynamics to the manifold of inextensible configurations. To do this, we introduce a set of Lagrange multipliers for the tensile force densities on the filaments and impose the constraint of no virtual work in an $L^2$ weak sense. We augment this approach with a spectral discretization of the local and nonlocal slender body theory operators which is linear in the number of unknowns and gives improved spatial accuracy over approaches based on solving a line tension equation. For dynamics, we develop a second-order semi-implicit temporal integrator which requires at most a few evaluations of nonlocal hydrodynamics and a few block diagonal linear solves per time step. After demonstrating the improved accuracy and robustness of our approach through numerical examples, we apply our formulation to a permanently cross-linked actin mesh in a background oscillatory shear flow. We observe a characteristic frequency at which the network transitions from quasi-static, primarily elastic behavior to dynamic, primarily viscous behavior. We find that nonlocal hydrodynamics increases the viscous modulus by as much as 25%, even for semi-dilute fiber suspensions.","url_abs":"https://arxiv.org/abs/2007.11728v1","url_pdf":"https://arxiv.org/pdf/2007.11728v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-integral-based-spectral-method-for","repo_url":"https://github.com/stochasticHydroTools/SlenderBody","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}