Skip to main content

Measuring the Instantaneous Velocity of a Brownian Particle in Air

  • Chapter
  • First Online:
  • 1134 Accesses

Part of the book series: Springer Theses ((Springer Theses))

Abstract

Chapter 4 covers the theory of Brownian motion in air at short time scales, a home-built detection system with ultrahigh resolution, and the results of our measurement of the instantaneous velocity of a Brownian particle in air.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. R. Brown, A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles containded in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Phil. Mag. 4, 161 (1828)

    Google Scholar 

  2. A. Einstein, Ann. D. Phys. 17, 549 (1905)

    Article  ADS  MATH  Google Scholar 

  3. A. Einstein, Theoretische bemerkungen über die Brownsche bewegung. Zeit. f. Elektrochemie. 13, 41 (1907)

    Article  Google Scholar 

  4. A. Einstein, in Investigations on the Theory of the Brownian Movement, ed. by R. Fürth, (Trans: A.D. Cowper) (Methuen, London, 1926), pp. 63–67

    Google Scholar 

  5. P. Langevin, C.R. Acad. Sci. (Paris). 146, 530 (1908)

    MATH  Google Scholar 

  6. D.S. Lemons, A. Gythiel, Paul Langevin’s 1908 paper “on the theory of Brownian motion". Am. J. Phys. 65, 1079 (1997)

    Article  ADS  Google Scholar 

  7. G.E. Uhlenbeck, L.S. Ornstein, On the theory of the Brownian motion. Phys. Rev. 36, 823 (1930)

    Article  ADS  MATH  Google Scholar 

  8. M.C. Wang, G.E. Uhlenbeck, On the theory of the Brownian motion II. Rev. Mod. Phys. 17, 323 (1945)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. S.F. Nørrelykke, H. Flyvbjerg, Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark, statistics. arXiv:1102.0524 (2011)

    Google Scholar 

  10. K. Berg-Sørensen, H. Flyvbjerg, Power spectrum analysis for optical tweezers. Rev. Sci. Instrum. 75, 594 (2004)

    Article  ADS  Google Scholar 

  11. P. Kwee, B. Willke, Automatic laser beam characterization of monolithic Nd:YAG nonplanar ring lasers. Appl. Opt. 47, 6022 (2008)

    Article  ADS  Google Scholar 

  12. I. Chavez, R. Huang, K. Henderson, E.-L. Florin, M.G. Raizen, Development of a fast position-sensitive laser beam detector. Rev. Sci. Instrum. 79, 105104 (2008)

    Article  ADS  Google Scholar 

  13. K.G. Libbrecht, E.D. Black, Toward quantum-limited position measurements using optically levitated microspheres. Phys. Lett. A. 321, 99 (2004)

    Article  ADS  MATH  Google Scholar 

  14. E.R.I. Abraham, E.A. Cornell, Teflon feedthrough for coupling optical fibers into ultrahigh vacuum systems. Appl. Opt. 37, 1762 (1998)

    Article  ADS  Google Scholar 

  15. R. Zwanzig, M. Bixon, Compressibility effects in the hydrodynamic theory of Brownian motion. J. Fluid Mech. 69, 21 (1975)

    Article  ADS  MATH  Google Scholar 

  16. A. Moshfegh, M. Shams, G. Ahmadi, R. Ebrahimi, A novel surface-slip correction for microparticles motion. Colloids Surf. A: Physicochem. and Eng. Aspects 345, 112 (2009)

    Article  Google Scholar 

  17. R. Kubo, Brownian motion and nonequilibrium statistical mechanics. Science 233, 330 (1986)

    Article  ADS  Google Scholar 

  18. G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles, D.J. Evans, Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys. Rev. Lett. 89, 050601 (2002)

    Article  ADS  Google Scholar 

  19. A. Hopkins, K. Jacobs, S. Habib, K. Schwab, Feedback cooling of a nanomechanical resonator. Phys. Rev. B. 68, 235328 (2003)

    Article  ADS  Google Scholar 

  20. D. Kleckner, D. Bouwmeester, Sub-kelvin optical cooling of a micromechanical resonator. Nature 444, 75 (2006)

    Article  ADS  Google Scholar 

  21. A. Ashkin, J.M. Dziedzic, Optical levitation in high vacuum. Appl. Phys. Lett. 28, 333 (1976)

    Article  ADS  Google Scholar 

  22. D.E. Chang et al., Cavity opto-mechanics using an optically levitated nanosphere. Proc. Natl. Acad. Sci. USA 07, 1005 (2010)

    Article  ADS  Google Scholar 

  23. O. Romero-Isart, M.L. Juan, R. Quidant, J. Ignacio Cirac, Toward quantum superposition of living organisms. New J. Phys. 12, 033015 (2010)

    Article  ADS  Google Scholar 

  24. N.L. Balazs, Brownian motion of a mirror in superfluid helium. Phys. Rev. 109, 232 (1958)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. D.G. Henshaw, A.D.B. Woods, Modes of atomic motions in liquid helium by inelastic scattering of neutrons. Phys. Rev. 121, 266 (1961)

    Article  ADS  Google Scholar 

  26. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, Transmission and reflection of phonons and rotons at the superfluid helium-solid interface. Phys. Rev. B 77, 174510 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tongcang Li .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Li, T. (2013). Measuring the Instantaneous Velocity of a Brownian Particle in Air. In: Fundamental Tests of Physics with Optically Trapped Microspheres. Springer Theses. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6031-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-6031-2_4

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6030-5

  • Online ISBN: 978-1-4614-6031-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics