Brownian Motion after Einstein: Some New Applications and New Experiments

  • D. Selmeczi
  • S. Tolić-Nørrelykke
  • E. Schäffer
  • P.H. Hagedorn
  • S. Mosler
  • K. Berg-Sørensen
  • N.B. Larsen
  • H. Flyvbjerg
Part of the Lecture Notes in Physics book series (LNP, volume 711)


The first half of this chapter describes the development in mathematical models of Brownian motion after Einstein’s seminal papers [1] and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of precision that requires an understanding of Brownian motion beyond Einstein’s. This is illustrated with some applications, current and potential, and it is shown how addition of a controlled forced motion on the nano-scale of the tweezed object’s thermal motion can improve the calibration of the instrument in general, and make it possible also in complex surroundings. The second half of the present chapter, starting with Sect. 9.1, describes the co-evolution of biological motility models with models of Brownian motion, including very recent results for how to derive cell-type-specific motility models from experimental cell trajectories.


Power Spectrum Brownian Motion Brownian Particle Optical Tweezer Inertial Mass 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Einstein (1956). Investigations on the Theory of the Brownian movement. Edited and annotated by R. Fürth. Translated by A. D. Cowper. Dover Publications, Inc.Google Scholar
  2. 2.
    J. Renn (2005).Ann. Phys. (Leipzig), 14 (Suppl.), 23.CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    P. Langevin (1908). C. R. Acad. Sci. (Paris), 146, p. 530. Translated and commented in [4].zbMATHGoogle Scholar
  4. 4.
    D. S. Lemons and A. Gythiel (1997). Am. J. Phys., 65, pp. 1079.CrossRefADSGoogle Scholar
  5. 5.
    L. S. Ornstein (1918). Proc. Amst., 21, pp. 96–108.Google Scholar
  6. 6.
    G. E. Uhlenbeck and L. S. Ornstein (1930). Phys. Rev., 36, pp. 823–841.CrossRefADSGoogle Scholar
  7. 7.
    H. A. Lorentz (1921). Lessen over Theoretishe Natuurkunde. E. J. Brill, Leiden.Google Scholar
  8. 8.
    G. G. Stokes (1851). On the effect of the internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society, IX, pp. 8–106, Reprinted in Mathematical and Physical Papers, 2nd ed., vol. 3. New York: Johnson Reprint Corp., p. 1, 1966.ADSGoogle Scholar
  9. 9.
    L. L. Landau and E. M. Lifshitz (1959). Fluid Mechanics. Addison-Wesley, Reading, MA.Google Scholar
  10. 10.
    A. Rahman (1964). Phys. Rev., 136, p. A405.CrossRefADSGoogle Scholar
  11. 11.
    A. Rahman (1966). J. Chem. Phys., 45, p. 2585.CrossRefADSGoogle Scholar
  12. 12.
    B. J. Alder and T. E. Wainwright (1967). Phys. Rev. Lett., 18, pp. 988–990.CrossRefADSGoogle Scholar
  13. 13.
    B. J. Alder and T. E. Wainwright (1970). Phys. Rev., 1, pp. 18–21.CrossRefADSGoogle Scholar
  14. 14.
    R. Zwanzig and M. Bixon (1970). Phys. Rev. A, 2, pp. 2005–2012.CrossRefADSGoogle Scholar
  15. 15.
    J. Boussinesq (1903). Théorie Analytique de la Chaleur, vol. II Paris.Google Scholar
  16. 16.
    A. Widom (1971). Phys. Rev. A, 3, pp. 1394–1396.CrossRefADSGoogle Scholar
  17. 17.
    K. M. Case (1971). Phys. Fluid, 14, pp. 2091–2095.zbMATHCrossRefADSGoogle Scholar
  18. 18.
    D. Bedeaux and P. Mazur (1974). Physica, 76, pp. 247–258.CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Y. Pomeau and P. Résibois (1975). Phys. Rep., 19C, pp. 63–139.CrossRefADSGoogle Scholar
  20. 20.
    R. Kubo, M. Toda, and N. Hashitsume (1985). Statistical Physics II Nonequilibrium Statistical Mechanics. Springer Verlag, Berlin, Heidelberg.Google Scholar
  21. 21.
    K. Berg-Sørensen and H. Flyvbjerg (2004). Rev. Sci. Ins., 75, pp. 594–612.CrossRefADSGoogle Scholar
  22. 22.
    K. C. Neuman and S. M. Block (2004). Rev. Sci. Instr., 75, pp. 2782–2809.CrossRefADSGoogle Scholar
  23. 23.
    E. J. G. Petermann, M. van Dijk, L. G. Kapiteln, and C. F. Schmidt (2003). Rev. Sci. Instr., 74, pp. 3246–3249.CrossRefADSGoogle Scholar
  24. 24.
    B. Lukić et al. (2005). Phys. Rev. Lett., 95, p. 160601.CrossRefADSGoogle Scholar
  25. 25.
    J. P. Boon and A. Bouiller (1976). Phys. Lett., 55A, pp. 391–392.ADSGoogle Scholar
  26. 26.
    A. Bouiller, J. P. Boon, and P. Deguent (1978). J. Phys. (Paris), 39, pp. 159–165.Google Scholar
  27. 27.
    G. L. Paul and P. N. Pusey (1981). J. Phys. A: Math. Gen., 14, pp. 3301–3327.CrossRefADSGoogle Scholar
  28. 28.
    P. N. Pusey. Private communication.Google Scholar
  29. 29.
    K. Ohbayashi, T. Kohno, and H. Utiyama (1983). Phys. Rev. A, 27, pp. 2632–2641.CrossRefADSGoogle Scholar
  30. 30.
    K. Berg-Sørensen and H. Flyvbjerg (2005). New J. Phys., 7(38).Google Scholar
  31. 31.
    H. Faxén (1923). Ark. Mat. Astron. Fys., 17, p. 1.Google Scholar
  32. 32.
    J. Happel and H. Brenner. Low Reynolds Number Hydrodynamics. (Nijhoff, The Hague, 1983), p. 327.Google Scholar
  33. 33.
    S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg. arXiv: physics/0603037.Google Scholar
  34. 34.
    K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block (1993). Nature, 365(6448), 721–727.CrossRefADSGoogle Scholar
  35. 35.
    K. Przibram (1913). Pflügers Arch. Physiol., 153, pp. 401–405.CrossRefGoogle Scholar
  36. 36.
    R. Fürth (1917). Ann. Phys., 53, p. 177.CrossRefGoogle Scholar
  37. 37.
    R. Fürth (1920). Z. Physik, 2, pp. 244–256.CrossRefADSGoogle Scholar
  38. 38.
    M. H. Gail and C. W. Boone (1970). Biophys. J., 10, pp. 980–993.CrossRefADSGoogle Scholar
  39. 39.
    D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg (2005). Biophys. J., 89, pp. 912–931.CrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • D. Selmeczi
    • 1
    • 2
  • S. Tolić-Nørrelykke
    • 3
  • E. Schäffer
    • 4
  • P.H. Hagedorn
    • 5
  • S. Mosler
    • 1
  • K. Berg-Sørensen
    • 6
  • N.B. Larsen
    • 1
    • 5
  • H. Flyvbjerg
    • 1
    • 5
  1. 1.Danish Polymer CentreRisø National LaboratoryRoskildeDenmark
  2. 2.Department of Biological PhysicsEötvös Loránd University (ELTE)BudapestHungary
  3. 3.Max Planck Institute for the Physics of Complex SystemsDresdenGermany
  4. 4.Max Planck Institute for Molecular Cell Biology and GeneticsDresdenGermany
  5. 5.Biosystems DepartmentRisø National LaboratoryRoskildeDenmark
  6. 6.Department of PhysicsTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations