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Feedback Control of Colloidal Transport

  • Robert Gernert
  • Sarah A. M. Loos
  • Ken Lichtner
  • Sabine H. L. KlappEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target for an ensemble of colloidal particles, and the systems are investigated via the Fokker-Planck equation for overdamped Brownian particles. Topics include the reversal of current and the emergence of current oscillations, transport in ratchet systems, and the enhancement of mobility by a co-moving trap. Beyond the commonly considered case of non-interacting systems, we also discuss the treatment of colloidal interactions via (dynamical) density functional theory and provide new results for systems with attractive interactions.

Keywords

Feedback Control Langevin Equation Particle Position Feedback Force Colloidal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft through SFB 910 (project B2).

References

  1. 1.
    J. Bechhoefer, Rev. Mod. Phys. 77, 783 (2005)ADSCrossRefGoogle Scholar
  2. 2.
    H. Löwen, Eur. Phys. J. Spec. Topics 222, 2727 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    T. Sagawa, M. Ueda, Phys. Rev. E 85, 021104 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    B. Qian, D. Montiel, A. Bregulla, F. Cichos, H. Yang, Chem. Sci. 4, 1420 (2013)CrossRefGoogle Scholar
  6. 6.
    A.P. Bregulla, H. Yang, F. Cichos, Acs Nano 8, 6542 (2014)CrossRefGoogle Scholar
  7. 7.
    M. Braun, A. Würger, F. Cichos, Phys. Chem. Chem. Phys. 16, 15207 (2014)CrossRefGoogle Scholar
  8. 8.
    J. Fisher, J. Cummings, K. Desai, L. Vicci, B. Wilde, K. Keller, C. Weigle, G. Bishop, R. Taylor, C. Davis, Rev. Sci. Instrum. 76, 053711 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    A.E. Cohen, Phys. Rev. Lett. 94, 118102 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Jun, J. Bechhoefer, Phys. Rev. E 86, 061106 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    J. Gieseler, L. Novotny, C. Moritz, C. Dellago, New. J. Phys. 17, 045011 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Nat. Phys. 6, 988 (2010)CrossRefGoogle Scholar
  13. 13.
    Y. Jun, M. Gavrilov, J. Bechhoefer, Phys. Rev. Lett. 113, 190601 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    J.J. Juarez, M.A. Bevan, Adv. Funct. Mat. 22, 3833 (2012)CrossRefGoogle Scholar
  15. 15.
    C. Prohm, H. Stark, Lab Chip 14, 2115 (2014)CrossRefGoogle Scholar
  16. 16.
    D.A. Strehober, E. Schöll, S.H.L. Klapp, Phys. Rev. E 88, 062509 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    S.H.L. Klapp, S. Hess, Phys. Rev E 81, 051711 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    T.A. Vezirov, S. Gerloff, S.H.L. Klapp, Soft Matter 11, 406 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    P. Reimann, Phys. Rep. 361 (2002)Google Scholar
  21. 21.
    R. Gernert, C. Emary, S.H.L. Klapp, Phys. Rev. E 90, 062115 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    F.J. Cao, L. Dinis, J.M.R. Parrondo, Phys. Rev. Lett. 93, 040603 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    M. Feito, F.J. Cao, Phys. Rev. E 76, 061113 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    E.M. Craig, B.R. Long, J.M.R. Parrondo, H. Linke, EPL 81, 10002 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    B.J. Lopez, N.J. Kuwada, E.M. Craig, B.R. Long, H. Linke, Phys. Rev. Lett. 101, 220601 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    E.M. Craig, N.J. Kuwada, B.J. Lopez, H. Linke, Ann. Phys. (Berlin) 17, 115 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    F.J. Cao, M. Feito, Entropy 14, 834 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    T. Munakata, M.L. Rosinberg, Phys. Rev. Lett. 112, 180601 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    C. Emary, Phil. Trans. R. Soc. A 371, 20120468 (2013)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    D. Hennig, L. Schimansky-Geier, and P. Hnggi, Phys. Rev. E 79, 041117 (2009)Google Scholar
  31. 31.
    K. Lichtner, S.H.L. Klapp, EPL 92, 40007 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    K. Lichtner, A. Pototsky, S.H.L. Klapp, Phys. Rev. E 86, 051405 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    S.V. Gurevich, R. Friedrich, Phys. Rev. Lett. 110, 014101 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    K. Pyragas, Phys. Lett. A 170, 421 (1992)ADSCrossRefGoogle Scholar
  35. 35.
    E. Schöll, H.G. Schuster (eds.), Handbook of Chaos Control (Wiley, 2007)Google Scholar
  36. 36.
    M.L. Rosinberg, T. Munakata, G. Tarjus, Phys. Rev. E 91, 042114 (2015)Google Scholar
  37. 37.
    T. Munakata, S. Iwama, M. Kimizuka, Phys. Rev. E 79, 031104 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    H. Jiang, T. Xiao, Z. Hou, Phys. Rev. E 83, 061144 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    H. Risken, The Fokker-Planck Equation (Springer, 1984)Google Scholar
  40. 40.
    U.M.B. Marconi, P. Tarazona, J. Chem. Phys. 110, 8032 (1999)ADSCrossRefGoogle Scholar
  41. 41.
    U.M.B. Marconi, P. Tarazona, J. Phys.: Condens. Matter 12, 413 (2000)ADSGoogle Scholar
  42. 42.
    S.A.M. Loos, R. Gernert, S.H.L. Klapp, Phys. Rev. E 89, 052136 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    R. Gernert, S.H.L. Klapp, Phys. Rev. E 92, 022132 (2015)Google Scholar
  44. 44.
    S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 59, 3970 (1999)ADSCrossRefGoogle Scholar
  45. 45.
    T.D. Frank, P.J. Beek, R. Friedrich, Phys. Rev. E 68, 021912 (2003)ADSCrossRefGoogle Scholar
  46. 46.
    C. Zeng, H. Wang, Chem. Phys. 402, 1 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    C. Dalle-Ferrier, M. Krüger, R.D.L. Hanes, S. Walta, M.C. Jenkins, S.U. Egelhaaf, Soft Matter 7, 2064 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    S.-H. Lee, D.G. Grier, Phys. Rev. Lett. 96, 190601 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    M. Feito, J.P. Baltanás, F.J. Cao, Phys. Rev. E 80, 031128 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    E.L. Florin, A. Pralle, E.H.K. Stelzer, J.K.H. Hörber, Appl. Phys. A 66, 75 (1998)ADSCrossRefGoogle Scholar
  51. 51.
    D.G. Cole, J.G. Pickel, J. Dyn. Syst. Meas. Control 134, 011020 (2012)CrossRefGoogle Scholar
  52. 52.
    T. Brandes, Phys. Rev. Lett. 105, 060602 (2010)ADSCrossRefGoogle Scholar
  53. 53.
    R.L. Stratonovich, Radiotekh. Elektron. 3, 497 (1958)Google Scholar
  54. 54.
    H. Kamegawa, T. Hondou, F. Takagi, Phys. Rev. Lett. 80, 5251 (1998)ADSCrossRefGoogle Scholar
  55. 55.
    C. Marquet, A. Begun, L. Talini, P. Silberzan, Phys. Rev. Lett. 88, 168301 (2002)ADSCrossRefGoogle Scholar
  56. 56.
    R. Bartussek, P. Hänggi, J.G. Kissner, EPL 28, 459 (1994)ADSCrossRefGoogle Scholar
  57. 57.
    M.O. Magnasco, Phys. Rev. Lett. 71, 1477 (1993)ADSCrossRefGoogle Scholar
  58. 58.
    A.J. Archer, R. Evans, J. Chem. Phys. 121, 4246 (2004)ADSCrossRefGoogle Scholar
  59. 59.
    C.N. Likos, Phys. Rep. 348, 267 (2001)ADSCrossRefGoogle Scholar
  60. 60.
    A.A. Louis, P.G. Bolhuis, J.P. Hansen, Phys. Rev. E 62, 7961 (2000)ADSCrossRefGoogle Scholar
  61. 61.
    D. Hennig, Phys. Rev. E 79, 041114 (2009)ADSCrossRefGoogle Scholar
  62. 62.
    J.K. Percus, J. Stat. Phys. 15, 505 (1976)ADSMathSciNetCrossRefGoogle Scholar
  63. 63.
    R. Roth, J. Phys.: Cond. Mat. 22, 063102 (2010)Google Scholar
  64. 64.
    A.E. Cohen, W.E. Moerner, PNAS 103, 4362 (2006)ADSCrossRefGoogle Scholar
  65. 65.
    K.J.M. Bishop, C.E. Wilmer, S. Soh, B.A. Grzybowski, Small 5, 1600 (2009)CrossRefGoogle Scholar
  66. 66.
    M.E. Leunissen, C.G. Christova, A.-P. Hynninen, C.P. Royall, A.I. Campbell, A. Imhof, M. Dijkstra, R. van Roij, A. van Blaaderen, Nature 437, 235 (2005)ADSCrossRefGoogle Scholar
  67. 67.
    C. Caccamo, Phys. Rep. 274, 1 (1996)ADSCrossRefGoogle Scholar
  68. 68.
    M.H.J. Hagen, D. Frenkel, J. Chem. Phys. 101, 4093 (1994)ADSCrossRefGoogle Scholar
  69. 69.
    M. Dijkstra, Phys. Rev. E 66, 021402 (2002)ADSCrossRefGoogle Scholar
  70. 70.
    L. Mederos, G. Navascues, J. Chem. Phys. 101, 9841 (1994)ADSCrossRefGoogle Scholar
  71. 71.
    F. Martinez-Pedrero, A. Straube, T.H. Johansen, P. Tierno, Lab Chip 15, 1765 (2015)CrossRefGoogle Scholar
  72. 72.
    A.J. Archer, A.M. Rucklidge, E. Knobloch, Phys. Rev. Lett. 111, 165501 (2013)ADSCrossRefGoogle Scholar
  73. 73.
    K. Lichtner, S.H.L. Klapp, Europhys. Lett. 106, 56004 (2014)ADSCrossRefGoogle Scholar
  74. 74.
    M. Selmke, A. Heber, M. Braun, F. Cichos, Appl. Phys. Lett. 105, 013511 (2014)ADSCrossRefGoogle Scholar
  75. 75.
    J.R. Gomez-Solano, C. July, J. Mehl, C. Bechinger, New. J. Phys. 17, 045026 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Robert Gernert
    • 1
  • Sarah A. M. Loos
    • 1
  • Ken Lichtner
    • 1
  • Sabine H. L. Klapp
    • 1
    Email author
  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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