Open Access
Volume 56, Number 4, July-August 2022
Page(s) 1151 - 1172
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. (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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you