Abstract
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.
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References
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.
J. Renn (2005).Ann. Phys. (Leipzig), 14 (Suppl.), 23.
P. Langevin (1908). C. R. Acad. Sci. (Paris), 146, p. 530. Translated and commented in [4].
D. S. Lemons and A. Gythiel (1997). Am. J. Phys., 65, pp. 1079.
L. S. Ornstein (1918). Proc. Amst., 21, pp. 96–108.
G. E. Uhlenbeck and L. S. Ornstein (1930). Phys. Rev., 36, pp. 823–841.
H. A. Lorentz (1921). Lessen over Theoretishe Natuurkunde. E. J. Brill, Leiden.
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.
L. L. Landau and E. M. Lifshitz (1959). Fluid Mechanics. Addison-Wesley, Reading, MA.
A. Rahman (1964). Phys. Rev., 136, p. A405.
A. Rahman (1966). J. Chem. Phys., 45, p. 2585.
B. J. Alder and T. E. Wainwright (1967). Phys. Rev. Lett., 18, pp. 988–990.
B. J. Alder and T. E. Wainwright (1970). Phys. Rev., 1, pp. 18–21.
R. Zwanzig and M. Bixon (1970). Phys. Rev. A, 2, pp. 2005–2012.
J. Boussinesq (1903). Théorie Analytique de la Chaleur, vol. II Paris.
A. Widom (1971). Phys. Rev. A, 3, pp. 1394–1396.
K. M. Case (1971). Phys. Fluid, 14, pp. 2091–2095.
D. Bedeaux and P. Mazur (1974). Physica, 76, pp. 247–258.
Y. Pomeau and P. Résibois (1975). Phys. Rep., 19C, pp. 63–139.
R. Kubo, M. Toda, and N. Hashitsume (1985). Statistical Physics II Nonequilibrium Statistical Mechanics. Springer Verlag, Berlin, Heidelberg.
K. Berg-Sørensen and H. Flyvbjerg (2004). Rev. Sci. Ins., 75, pp. 594–612.
K. C. Neuman and S. M. Block (2004). Rev. Sci. Instr., 75, pp. 2782–2809.
E. J. G. Petermann, M. van Dijk, L. G. Kapiteln, and C. F. Schmidt (2003). Rev. Sci. Instr., 74, pp. 3246–3249.
B. Lukić et al. (2005). Phys. Rev. Lett., 95, p. 160601.
J. P. Boon and A. Bouiller (1976). Phys. Lett., 55A, pp. 391–392.
A. Bouiller, J. P. Boon, and P. Deguent (1978). J. Phys. (Paris), 39, pp. 159–165.
G. L. Paul and P. N. Pusey (1981). J. Phys. A: Math. Gen., 14, pp. 3301–3327.
P. N. Pusey. Private communication.
K. Ohbayashi, T. Kohno, and H. Utiyama (1983). Phys. Rev. A, 27, pp. 2632–2641.
K. Berg-Sørensen and H. Flyvbjerg (2005). New J. Phys., 7(38).
H. Faxén (1923). Ark. Mat. Astron. Fys., 17, p. 1.
J. Happel and H. Brenner. Low Reynolds Number Hydrodynamics. (Nijhoff, The Hague, 1983), p. 327.
S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg. arXiv: physics/0603037.
K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block (1993). Nature, 365(6448), 721–727.
K. Przibram (1913). Pflügers Arch. Physiol., 153, pp. 401–405.
R. Fürth (1917). Ann. Phys., 53, p. 177.
R. Fürth (1920). Z. Physik, 2, pp. 244–256.
M. H. Gail and C. W. Boone (1970). Biophys. J., 10, pp. 980–993.
D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg (2005). Biophys. J., 89, pp. 912–931.
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Selmeczi, D. et al. (2007). Brownian Motion after Einstein: Some New Applications and New Experiments. In: Linke, H., Månsson, A. (eds) Controlled Nanoscale Motion. Lecture Notes in Physics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49522-3_9
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DOI: https://doi.org/10.1007/3-540-49522-3_9
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