Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 98 - 129
Published online 10 August 2011
  1. H.C. Berg. Random walks in biology. Princeton University Press, Princeton, 1983.
  2. H.C. Berg. E. Coli in Motion. Springer Verlag, New York, 2004.
  3. B.M. Haines, I.S. Aranson, L. Berlyand and D.A. Karpeev. Effective viscosity of dilute bacterial suspensions: a two-dimensional model. Physical Biology, 5 (2008), No. 4.
  4. P. G. Ciarlet. Introduction à l’analyse numérique matricielle et à l’optimisation. Masson, Paris, 1990.
  5. L.H. Cisneros, R. Cortez, C. Dombrowski, R.E. Goldstein, J.O. Kessler. Fluid dynamics of self-propelled microorganisms. from individual to concentrated populations. Exp Fluids, 43 (2007), 737–753. [CrossRef]
  6. Darnton NC, Turner L, Rojevsky S, Berg HC. Dynamics of bacterial swarming. Biophys J. 98 (2010), No. 10, 2082–90. [CrossRef] [PubMed]
  7. A. Decoene, A. Lorz, S. Martin, B. Maury, M. Tang. Simulation of self-propelled chemotactic bacteria in a Stokes flow. ESAIM: Proc, 30 (2010), 104–123 . [CrossRef] [EDP Sciences]
  8. C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, J. O. Kessler. Self-concentration and large-scale coherence in bacteria dynamics. Phys. Rev. Lett., 93 (2004), No. 9.
  9. D. Gérard-Varet, M. Hillairet. Regularity Issues in the Problem of Fluid Structure Interaction. to appear in Arch. Rational Mech. Anal.
  10. R. Glowinski, T. W. Pan, T. I. Hesla, D. D. Joseph & J. Périaux. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comp. Phys., 169 (2001), 363–427. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
  11. R. Glowinski. Finite element methods for incompressible viscous flow. In: Handbook of Numerical Analysis, Vol. IX, P. G. Ciarlet and J.-L. Lions eds., Ed. North-Holland, Amsterdam, 2003.
  12. V. Gyrya, K. Lipnikov, I. Aranson, L. Berlyand. Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate suspensions. Journal of Mathematical Biology (accepted, 2011).
  13. Hernandez-Ortiz J.P., C. Stoltz and M.D. Graham. Transport and col lective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett., 95 (2005), pp. 204501.
  14. J. Happel, H. Brenner. Low Reynolds Number Hydrodynamics. Dordrecht, Kluwer, 1991.
  15. M. Hillairet. Lack of collision between solid bodies in a 2D constant-density incompressible flow. Communications in Partial Differential Equations 32 (2007), 1345-1371. [CrossRef] [MathSciNet]
  16. J. Janela, A. Lefebvre, B. Maury. A penalty method for the simulation of fluid-rigid body interaction. ESAIM: Proc., 1 (2007), 115–123.
  17. D. Kaiser. Bacterial swarming, a re-examination of cell movement patterns. Curr Biol, 17 (2007), R561-R570. [CrossRef] [PubMed]
  18. S. Kim, S.J. Karrila. Microhydrodynamics: Principles and Selected Applications. Dover, New York, 2005.
  19. E. Lauga and T.R. Powers. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys., 72 (2009).
  20. A. Lefebvre. Fluid-particle simulations with Freefem++. ESAIM: Proc., 18 (2007), 120–132. [CrossRef] [EDP Sciences]
  21. A. Lefebvre, B. Maury. Apparent viscosity of a mixture of a Newtonian fluid and interacting particles. Fluid-solid interactions: modeling, simulation, bio-mechanical applications. Comptes Rendus MŐcanique, 333 (2005), No. 12.
  22. B. Maury. A time-stepping scheme for inelastic collisions. Numerische Mathematik, 102 (2006), No. 4, 649–679. [CrossRef] [MathSciNet]
  23. B. Maury. Numerical Analysis of a Finite Element / Volume Penalty Method. SIAM J. Numer. Anal. 47 (2009), No. 2, 1126–1148. [CrossRef] [MathSciNet]
  24. J.T. Locsei, T.J. Pedley. Run and Tumble in Chemotaxis in a Shear Flow; The Effect of Temporal Comparisons, Persistence, Rotational Diffusion, and Cell Shape. Bulletin of Mathematical Biology, 71 (2009), 1089–1116. [CrossRef] [MathSciNet] [PubMed]
  25. J.O. Kessler, T.J. Pedley. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24 (1992), 313–58. [CrossRef]
  26. F. Peruani, L. G. Morelli. Self-propelled particles with fluctuating speed and direction of motion in two dimensions. PRL 99 (2007), 010602, 2007.
  27. S. Rafai, L. Jibuti, P. Peyla. Effective viscosity of microswimmer suspensions. Phys. Rev. Lett., 104 (2010), 098102. [CrossRef] [PubMed]
  28. D. Saintillan, M. J. Shelley. Orientational order and instabilities in suspensions of self-locomoting rods. Phys. Rev. Lett., 99 (2007), 058102. [CrossRef] [PubMed]
  29. J. E. Segall, S.M. Block, H.C. Berg. Temporal comparisons in bacterial chemotaxis. Proc. Natl . Acad. Sci. USA, 83 (1986), 8987–8991. [CrossRef]
  30. A. Sokolov, I. S. Aranson. Reduction of viscosity in suspension of swimming bacteria. Phys. Rev. Lett. 103 (2009), 148101. [CrossRef] [PubMed]
  31. A. Sokolov, R. E. Goldstein, F. I. Feldchtein, and I. S. Aranson. Enhanced mixing and spatial instability in concentrated bacterial suspensions. Phys. Rev. E 80 (2009), 031903. [CrossRef]
  32. R. Temam, A. Miranville. Mathematical modeling in continuum mechanics. Cambridge University press, 2001.
  33. L. Turner, W.S. Ryu, H.C. Berg. Real-time imaging of fluorescent flagellar filaments. J. Bacteriol., 182 (2000), No. 10, 2793–2801. [CrossRef] [PubMed]
  34. I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J.O. Kessler, R. E. Goldstein. Bacterial swimming and oxygen transport near contact lines. Proc. Natl. Acad. Sci. USA, 102 (2005), 2277–2282. [CrossRef]
  35. S. Vincent, J. P. Caltagirone, P. Lubin & T. N. Randrianarivelo. An adaptative augmented Lagrangian method for three-dimensional multimaterial flows. Computers and Fluids, 33 (2004), 1273–1289. [CrossRef] [MathSciNet]
  36. X.-L. Wu, A. Libchaber. Particle diffusion in a quasi-two-dimensional bacterial bath. Physical Review Letters, 84 (2000), 3017–3020. [CrossRef] [PubMed]
  37. Y. Wu, D. Kaiser, Y. Jiang, M. S. Alber. Periodic reversal of direction allows Myxobacteria to swarm. Proc. Natl. Acad. Sci. USA, 106 (2009), No. 4, 1222–1227. [CrossRef]

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