Open Access
Issue
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
Page(s) 1151 - 1172
DOI https://doi.org/10.1051/m2an/2022038
Published online 27 June 2022
  1. F. Alouges and M. Aussal, The sparse cardinal sine decomposition and its application for fast numerical convolution. Numer. Algorithms 70 (2015) 427–448. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Alouges, A. DeSimone, L. Giraldi and M. Zoppello, Can magnetic multilayers propel artificial microswimmers mimicking sperm cells? Soft Rob. 2 (2015) 117–128. [CrossRef] [Google Scholar]
  3. F. Alouges, M. Aussal, A. Lefebvre-Lepot, F. Pigeonneau and A. Sellier, Application of the sparse cardinal sine decomposition to 3d stokes flows. Int. J. Comput. Methods Exp. Meas. 5 (2017) 387–394. [Google Scholar]
  4. G. Alzetta, D. Arndt, W. Bangerth, V. Boddu, B. Brands, D. Davydov, R. Gassmoeller, T. Heister, L. Heltai, K. Kormann, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin and D. Wells, The deal.II Library, Version 9.0. J. Numer. Math. 26 (2018) 173–183. [Google Scholar]
  5. J. Archibald, Handbook of the Protists. Springer, Cham (2017). [Google Scholar]
  6. M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An “empirical interpolation’” method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339 (2004) 667–672. [CrossRef] [MathSciNet] [Google Scholar]
  7. Blender Online Community, Blender – A 3D Modelling and Rendering Package. Blender Foundation, Blender Institute, Amsterdam (2019). [Google Scholar]
  8. S. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 32 (2010) 2737–2764. [Google Scholar]
  9. C.M. Colciago and S. Deparis, Reduced numerical approximation of reduced fluid-structure interaction problems with applications in hemodynamics. Frontiers Appl. Math. Stat. 4 (2018) 18. [CrossRef] [Google Scholar]
  10. B. Dai, J. Wang, Z. Xiong, X. Zhan, W. Dai, C.-C. Li, S.-P. Feng and J. Tang, Programmable artificial phototactic microswimmer. Nat. Nanotechnol. 11 (2016) 1087–1092. [CrossRef] [PubMed] [Google Scholar]
  11. G. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled microswimmers. SIAM J. Math. Anal. 43 (2011) 1345–1368. [CrossRef] [MathSciNet] [Google Scholar]
  12. G. Dal Maso, A. DeSimone and M. Morandotti, One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls. ESAIM: Control Optim. Calc. Var. 21 (2015) 190–216. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  13. K. Drescher, K.C. Leptos and R.E. Goldstein, How to track protists in three dimensions. Rev. Sci. Instrum. 80 (2009) 014301. [CrossRef] [PubMed] [Google Scholar]
  14. K. Drescher, R.E. Goldstein, N. Michel, M. Polin and I. Tuval, Direct measurement of the flow field around swimming microorganisms. Phys. Rev. Lett. 105 (2010) 168101. [CrossRef] [PubMed] [Google Scholar]
  15. T. Fujita and T. Kawai, Optimum shape of a flagellated microorganism. JSME Int. J. Ser. C 44 (2001) 952–957. [CrossRef] [Google Scholar]
  16. I. Fumagalli, N. Parolini and M. Verani, Shape optimization for Stokes flows: a finite element convergence analysis. ESAIM: Math. Modell. Numer. Anal. 49 (2015) 921–951. [CrossRef] [EDP Sciences] [Google Scholar]
  17. V.F. Geyer, F. Jülicher, J. Howard and B.M. Friedrich, Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga. Proc. Nat. Acad. Sci. USA 110 (2013) 18058–18063. [CrossRef] [PubMed] [Google Scholar]
  18. N. Giuliani, Modelling fluid structure interaction problems using boundary element method. Ph.D. thesis, SISSA, Scuola Internazionale Superiore di Studi Avanzati (2017). [Google Scholar]
  19. N. Giuliani, L. Heltai and A. DeSimone, Predicting and optimizing microswimmer performance from the hydrodynamics of its components: the relevance of interactions. Soft Rob. 5 (2018) 410–424. [CrossRef] [PubMed] [Google Scholar]
  20. N. Giuliani, L. Heltai and A. DeSimone, BEMStokes: a boundary element method solver for micro-swimmers. https://github.com/mathLab/BEMStokes (2020). [Google Scholar]
  21. N. Giuliani, A. Mola and L. Heltai, π – BEM: a flexible parallel implementation for adaptive, geometry aware, and high order boundary element methods. Adv. Eng. Softw. 121 (2018) 39–58. [CrossRef] [Google Scholar]
  22. J. Gray and G.J. Hancock, The propulsion of sea-urchin spermatozoa. J. Exp. Biol 32 (1955) 802–814. [CrossRef] [Google Scholar]
  23. L. Greengard and V. Rokhlin, A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325–348. [Google Scholar]
  24. J.S. Guasto, K.A. Johnson and J.P. Gollub, Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105 (2010) 168102. [CrossRef] [PubMed] [Google Scholar]
  25. M. Gurtin, An Introduction to Continuum Mechanics (Mathematics in Science and Engineering). Academic Press (1982). [Google Scholar]
  26. E. Gutman and Y. Or, Optimizing an undulating magnetic microswimmer for cargo towing. Phys. Rev. E 93 (2016) 1–8. [CrossRef] [Google Scholar]
  27. B. Haasdonk and M. Ohlberger, Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Math. Modell. Numer. Anal. 42 (2008) 277–302. [CrossRef] [EDP Sciences] [Google Scholar]
  28. E. Harris, The Chlamydomonas Sourcebook: A Comprehensive Guide to Biology and Laboratory Use. Elsevier Science, Burlington (1989). [Google Scholar]
  29. M.A. Heroux, E.T. Phipps, A.G. Salinger, H.K. Thornquist, R.S. Tuminaro, J.M. Willenbring, A. Williams, S.S. Kendall, R.A. Bartlett, V.E. Howle, R.J. Hoekstra, J.J. Hu, T.G. Kolda, R.B. Lehoucq, K.R. Long and R.P. Pawlowski, An overview of the Trilinos project. ACM Trans. Math. Softw. 31 (2005) 397–423. [CrossRef] [Google Scholar]
  30. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer International Publishing (2016). [Google Scholar]
  31. K. Ishimoto, H. Gadêlha, E.A. Gaffney, D.J. Smith and J. Kirkman-Brown, Coarse-graining the fluid flow around a human sperm. Phys. Rev. Lett. 118 (2017) 1–5. [CrossRef] [Google Scholar]
  32. C. Josenhans and S. Suerbaum, Motility in bacteria. Int. J. Med. Microbiol. 291 (2002) 605–614. [CrossRef] [Google Scholar]
  33. G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20 (1998) 359–392. [Google Scholar]
  34. E.E. Keaveny, S.W. Walker and M.J. Shelley, Optimization of chiral structures for microscale propulsion. Nano Lett. 13 (2013) 531–537. [CrossRef] [PubMed] [Google Scholar]
  35. G.S. Klindt and B.M. Friedrich, Flagellar swimmers oscillate between pusher- and puller-type swimming. Phys. Rev. E – Stat. Nonlinear Soft Matter Phys. 92 (2015) 1–6. [Google Scholar]
  36. M. Kronbichler and T. Heister, W. Bangerth, High accuracy mantle convection simulation through modern numerical methods. Geophys. J. Int. 191 (2012) 12–29. [CrossRef] [Google Scholar]
  37. T. Lassila, A. Quarteroni and G. Rozza, A reduced basis model with parametric coupling for fluid-structure interaction problems. SIAM J. Sci. Comput. 34 (2012) A1187–A1213. [CrossRef] [Google Scholar]
  38. T. Lassila, A. Manzoni, A. Quarteroni and G. Rozza, Model order reduction in fluid dynamics: challenges and perspectives. In: Reduced Order Methods for Modelling and Computational Reduction, MS&A – Modeling, Simulation and Applications, edited by A. Quarteroni and G. Rozza. Vol. 9. Springer Cham (2014) 235–273. [Google Scholar]
  39. E. Lauga and T.R. Powers, The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (2009) 096601. [CrossRef] [Google Scholar]
  40. E. Lauga, W.R. DiLuzio, G.M. Whitesides and H.A. Stone, Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90 (2006) 400–12. [CrossRef] [Google Scholar]
  41. J. Lighthill, Flagellar hydrodynamics. SIAM Rev. 18 (1976) 161–230. [CrossRef] [MathSciNet] [Google Scholar]
  42. A. Manzoni, F. Salmoiraghi and L. Heltai, Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils. Comput. Methods Appl. Mech. Eng. 284 (2015) 1147–1180. [CrossRef] [Google Scholar]
  43. F. Negri, A. Manzoni and D. Amsallam, Efficient model reduction of parametrized systems by matrix discrete empirical interpolation. J. Comput. Phys. 303 (2015) 431–454. [CrossRef] [MathSciNet] [Google Scholar]
  44. N.C. Nguyen, G. Rozza and A.T. Patera, Reduced basis approximation and a posteriori errorestimation for the time-dependent viscous burgers equation. Calcolo 46 (2009) 157–185. [CrossRef] [MathSciNet] [Google Scholar]
  45. G. Noselli, A. Beran, M. Arroyo and A. DeSimone, Swimming euglena respond to confinement with a behavioural change enabling effective crawling. Nat. Phys. 15 (2019) 496–502. [CrossRef] [PubMed] [Google Scholar]
  46. E. Passov and Y. Or, Dynamics of Purcell’s three-link microswimmer with a passive elastic tail. Eur. Phys. J. E 35 (2012) 1–9. [CrossRef] [Google Scholar]
  47. N. Phan-Thien, T. Tran-Cong and M. Ramia, A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 184 (1987) 533. [CrossRef] [Google Scholar]
  48. D. Pimponi, M. Chinappi, P. Gualtieri and C.M. Casciola, Hydrodynamics of flagellated microswimmers near free-slip interfaces. J. Fluid Mech. 789 (2016) 514–533. [CrossRef] [MathSciNet] [Google Scholar]
  49. M.E. Porter and W.S. Sale, The 9 + 2 axoneme anchors multiple inner arm dyneins and a network of kinases and phosphatases that control motility. J. Cell Biol. 151 (2000) F37–F42. [CrossRef] [PubMed] [Google Scholar]
  50. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow. Vol 36. Cambridge University Press, Cambridge (1992). [CrossRef] [Google Scholar]
  51. E.M. Purcell, Life at low Reynolds number. Am. J. Phys. 45 (1977) 3–11. [Google Scholar]
  52. E.M. Purcell, The efficiency of propulsion by a rotating flagellum. Biophysics 94 (1997) 11307–11311. [Google Scholar]
  53. B. Rodenborn, C.-H. Chen, H.L. Swinney, B. Liu and H.P. Zhang, Propulsion of microorganisms by a helical flagellum. Proc. Nat. Acad. Sci. USA 110 (2013) E338–E347. [CrossRef] [PubMed] [Google Scholar]
  54. M. Rossi, G. Cicconofri, A. Beran, G. Noselli and A. DeSimone, Kinematics of flagellar swimming in euglena gracilis: helical trajectories and flagellar shapes. Proc. Nat. Acad. Sci. 114 (2017) 13085–13090. [CrossRef] [PubMed] [Google Scholar]
  55. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 229–275. [Google Scholar]
  56. R. Sevilla, L. Borchini, M. Giacomini and A. Huerta, Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows. Comput. Methods Appl. Mech. Eng. 372 (2020) 113397. [CrossRef] [Google Scholar]
  57. L. Shi, S. Čanić, A. Quaini and T.W. Pan, A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation. J. Comput. Phys. 314 (2016) 264–286. [CrossRef] [MathSciNet] [Google Scholar]
  58. H. Shum and E.A. Gaffney, Hydrodynamic analysis of flagellated bacteria swimming near one and between two no-slip plane boundaries. Phys. Rev. E 91 (2015) 033012. [CrossRef] [PubMed] [Google Scholar]
  59. H. Shum, E.A. Gaffney and D.J. Smith, Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry. Proc. R. Soc. A: Math. Phys. Eng. Sci. 466 (2010) 1725–1748. [Google Scholar]
  60. K. Son, J.S. Guasto and R. Stocker, Bacteria can exploit a flagellar buckling instability to change direction. Nat. Phys. 9 (2013) 494–498. [CrossRef] [Google Scholar]
  61. O. Steinbach, Numerical Approximation Methods for Elliptic Boundary Value Problems. Springer New York, New York, NY (2008). [CrossRef] [Google Scholar]
  62. T.T.M. Ta, V.C. Le and H.T. Pham, Shape optimization for stokes flows using sensitivity analysis and finite element method. Appl. Numer. Math. 126 (2018) 160–179. [CrossRef] [MathSciNet] [Google Scholar]
  63. A.C.H. Tsang, A.T. Lam and I.H. Riedel-Kruse, Polygonal motion and adaptable phototaxis via flagellar beat switching in the microswimmer Euglena gracilis. Nat. Phys. 14 (2018) 1216–1222. [CrossRef] [Google Scholar]
  64. D. Walker, M. Kübler, K.I. Morozov, P. Fischer and A.M. Leshansky, Optimal length of low Reynolds number nanopropellers. Nano Lett. 15 (2015) 4412–4416. [CrossRef] [PubMed] [Google Scholar]

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