- Editors' Suggestion
- Access by Xinjiang University
Pros and cons of swimming in a noisy environment
Phys. Rev. E 89, 032136 – Published 28 March, 2014
DOI: https://doi.org/10.1103/PhysRevE.89.032136
Abstract
The problem of optimal microscopic swimming in a noisy environment is analyzed. A simplified model in which propulsion is generated by the relative motion of three spheres connected by immaterial links has been considered. We show that an optimized noisy microswimmer requires less power for propulsion (on average) than an optimal noiseless counterpart migrating with identical mean velocity and swimming stroke amplitude. We also show that noise can be used to overcome some of the limitations of the scallop theorem and have a swimmer that is able to propel itself with control over just one degree of freedom.
Article Text
References (42)
- S. Childress, Mechanics of Swimming and Flying (Cambridge University Press, Cambridge, UK, 1981).
- E. M. Purcell, Am. J. Phys. 45, 3 (1977).
- A. Shapere and F. Wilczek, J. Fluid Mech. 198, 557 (1989).
- R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, Nature (London) 437, 862 (2005).
- T. S. Yu, E. Lauga, and A. E. Hosoi, Phys. Fluids 18, 091701 (2006).
- B. Behkam and M. Sitti, J. Dyn. Sys. Meas. Control 128, 36 (2006).
- M. Leoni, J. Kotar, B. Bassetti, P. Cicuta, and M. C. Lagomarsino, Soft Matter 5, 472 (2009).
- J. Lighthill, Mathematical Biofluid Dynamics (SIAM, Philadelphia, 1975).
- J. R. Blake, Math. Methods Appl. Sci. 24, 1469 (2001).
- H. A. Stone and A. D. T. Samuel, Phys. Rev. Lett. 77, 4102 (1996).
- L. E. Becker, S. A. Koehler, and H. A. Stone, J. Fluid Mech. 490, 15 (2003).
- A. Najafi and R. Golestanian, Phys. Rev. E 69, 062901 (2004).
- J. E. Avron, O. Gat, and O. Kenneth, Phys. Rev. Lett. 93, 186001 (2004).
- F. Schweitzer, W. Ebeling, and B. Tilch, Phys. Rev. Lett. 80, 5044 (1998).
- T. Vicsek, Fluctuations and Scaling in Biology (Oxford University Press, Oxford, 2001).
- V. Lobaskin, D. Lobaskin, and I. Kulic, Eur. J. Phys. Spec. Topics 157, 149 (2008).
- R. Golestanian and A. Ajdari, J. Phys. Condens. Matter 21, 204104 (2009).
- J. Dunkel and I. M. Zaid, Phys. Rev. E 80, 021903 (2009).
- R. Golestanian, T. B. Liverpool, and A. Ajdari, Phys. Rev. Lett. 94, 220801 (2005).
- W. E. Paxton, S. Sundararajan, T. E. Mallouk, and A. Sen, Angew. Chem. Int. Ed. 45, 5420 (2006).
- C. M. Pooley and A. C. Balazs, Phys. Rev. E 76, 016308 (2007).
- R. Ma, G. S. Klindt, I. H. Riedel-Kruse, F. Jülicher, and B. Friedrich, arXiv:1401.7036.
- A. B. Kolomeisky and M. E. Fisher, Ann. Rev. Phys. Chem. 58, 675 (2007).
- D. J. Earl, C. M. Pooley, J. F. Ryder, I. Bredberg, and J. M. Yeomans, J. Chem. Phys. 126, 064703 (2007).
- P. Olla, Phys. Rev. E 82, 015302(R) (2010).
- B. M. Friedrich and F. Yülicher, Phys. Rev. Lett. 109, 138102 (2012).
- G. P. Alexander, C. M. Pooley, and J. M. Yeomans, Phys. Rev. E 78, 045302(R) (2008).
- V. B. Putz and J. M. Yeomans, J. Stat. Phys. 137, 1001 (2009).
- T. J. Murphy and J. L. Aguirre, J. Chem. Phys. 57, 2098 (1972).
- R. Golestanian and A. Ajdari, Phys. Rev. E 77, 036308 (2008).
- P. Olla, Eur. Phys. J. B 80, 263 (2011).
- J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, Boston, 1973).
- J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998).
- A. Shapere and F. Wilczek, Phys. Rev. Lett. 58, 2051 (1987).
- D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012).
- T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 (2007).
- E. Aurell, C. Mejia-Monasterio, and P. Muratore-Ginanneschi, Phys. Rev. E 85, 020103(R) (2012).
- E. Aurell, K. Gawedzki, C. Mejia-Monasterio, R. Mohayaee, and P. Muratore-Ginanneschi, J. Stat. Phys. 147, 487 (2012).
- E. Aurell, C. Mejia-Monasterio, and P. Muratore-Ginanneschi, Phys. Rev. Lett. 106, 250601 (2011).
- It is possible to see, from Eq. (2), that the kinetic energy of the trimer is diagonal in the center-of-mass velocity and the deformation rates : (to lowest order in , we disregard the contribution from to the bead velocities). The standard argument that each degree of freedom contributes to the energy fluctuations then applies, and leads to Eqs. (20) and (21).
- K. Sekimoto, Prog. Theor. Phys. Supp. 130, 17 (1998).
- Z. Schuss, Theory and Application of Stochastic Differential Equations (Wiley, New York, 1981).