Abstract

Colloidal particles in a liquid medium are transported with constant velocity, and dynamic light scattering experiments are performed on the samples by self-mixing laser Doppler velocimetry. The power spectrum of the modulated wave induced by the motion of the colloidal particles cannot be described by the well-known formula for flowing Brownian motion systems, i.e., a combination of Doppler shift, diffusion, and translation. Rather, the power spectrum was found to be described by the q-Gaussian distribution function. The molecular mechanism resulting in this anomalous line shape of the power spectrum is attributed to the anomalous molecular dynamics of colloidal particles in transported dilute samples, which satisfy a nonlinear Langevin equation.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  16. S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
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  21. U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
    [CrossRef]
  22. A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).
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    [CrossRef]
  24. L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
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  25. A. Razdan, “q-Gaussian representation of non-Lorentzian Mössbauer lineshapes,” Hyperfine Interact. 188, 103–106 (2009).
    [CrossRef]
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    [CrossRef]
  27. M. Ausloos and K. Ivanova, “Dynamical model and nonextensive statistical mechanics of a market index on large time windows,” Phys. Rev. E 68, 046122 (2003).
    [CrossRef]

2010 (1)

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

2009 (2)

T. Ohtomo, S. Sudo, and K. Otsuka, “Three-channel three-dimensional self-mixing thin-slice solid-state laser-Doppler measurements,” Appl. Opt. 48, 609–616 (2009).
[CrossRef]

A. Razdan, “q-Gaussian representation of non-Lorentzian Mössbauer lineshapes,” Hyperfine Interact. 188, 103–106 (2009).
[CrossRef]

2008 (1)

B. Liu and J. Goree, “Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma,” Phys. Rev. Lett. 100, 055003 (2008).
[CrossRef]

2007 (4)

U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
[CrossRef]

A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).

S. Sudo, Y. Miyasaka, K. Nemoto, K. Kamikariya, and K. Otsuka, “Detection of small particles in fluid flow using a self-mixing laser,” Opt. Express 15, 8135–8145 (2007).
[CrossRef]

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

2006 (5)

S. Sudo, Y. Miyasaka, K. Otsuka, Y. Takahashi, T. Oishi, and J.-Y. Ko, “Quick and easy measurement of particle size of Brownian particles and planktons in water using a self-mixing laser,” Opt. Express 14, 1044–1054 (2006).
[CrossRef]

L. G. Moyano, and C. Anteneodo, “Diffusive anomalies in a long-range Hamiltonian system,” Phys. Rev. E 74, 021118 (2006).
[CrossRef]

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

2003 (1)

M. Ausloos and K. Ivanova, “Dynamical model and nonextensive statistical mechanics of a market index on large time windows,” Phys. Rev. E 68, 046122 (2003).
[CrossRef]

2002 (1)

2001 (1)

C. Beck, “Dynamical foundations of nonextensive statistical mechanics,” Phys. Rev. Lett. 87, 180601 (2001).
[CrossRef]

1999 (1)

1998 (1)

C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized nonextensive statistics,” Physica A 261, 534–554 (1998).
[CrossRef]

1995 (1)

C. Tsallis, “Non-extensive thermostatistics: brief review and comments,” Physica A 221, 277–290 (1995).
[CrossRef]

1993 (1)

T. H. Solomon, E. R. Weeks, and H. L. Swinney, “Observations of anomalous diffusion and Lévy flights in a two-dimensional rotating flow,” Phys. Rev. Lett. 71, 3975–3978 (1993).
[CrossRef]

1988 (1)

C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” J. Stat. Phys. 52, 479–487 (1988).
[CrossRef]

1986 (1)

1984 (1)

1979 (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

Abe, K.

Anteneodo, C.

L. G. Moyano, and C. Anteneodo, “Diffusive anomalies in a long-range Hamiltonian system,” Phys. Rev. E 74, 021118 (2006).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, “Photocount distributions and field statistics,” in Quantum Optics, R. J. Glauber, ed. (Academic, 1969).

Asakawa, Y.

Ausloos, M.

M. Ausloos and K. Ivanova, “Dynamical model and nonextensive statistical mechanics of a market index on large time windows,” Phys. Rev. E 68, 046122 (2003).
[CrossRef]

Beck, C.

U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
[CrossRef]

C. Beck, “Dynamical foundations of nonextensive statistical mechanics,” Phys. Rev. Lett. 87, 180601 (2001).
[CrossRef]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley-Interscience, 1976), Chap. 5.

Chowdhury, D. P.

Dal Molin, J. P.

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, 1980).

Fuentes, M. A.

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

Fukazawa, T.

Givambattista, N.

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

Goree, J.

B. Liu and J. Goree, “Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma,” Phys. Rev. Lett. 100, 055003 (2008).
[CrossRef]

Ivanova, K.

M. Ausloos and K. Ivanova, “Dynamical model and nonextensive statistical mechanics of a market index on large time windows,” Phys. Rev. E 68, 046122 (2003).
[CrossRef]

Ivlev, A.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Kamikariya, K.

Kawai, R.

Khrapak, S.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Knapek, C.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Ko, J.-Y.

Lenza, E. K.

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

Lester, T. W.

Lim, T.-S.

Liu, B.

B. Liu and J. Goree, “Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma,” Phys. Rev. Lett. 100, 055003 (2008).
[CrossRef]

Malacarne, L. C.

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

Marsh, J. A.

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

Mazza, M. G.

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

Mendes, R. S.

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized nonextensive statistics,” Physica A 261, 534–554 (1998).
[CrossRef]

Merklin, J. F.

Milovanov, A. V.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Miyasaka, Y.

Morfill, G. E.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Moyano, L. G.

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

L. G. Moyano, and C. Anteneodo, “Diffusive anomalies in a long-range Hamiltonian system,” Phys. Rev. E 74, 021118 (2006).
[CrossRef]

Nemoto, K.

Ohtomo, T.

Oishi, T.

Otsuka, K.

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley-Interscience, 1976), Chap. 5.

Picoli, S.

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

Plastino, A. R.

C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized nonextensive statistics,” Physica A 261, 534–554 (1998).
[CrossRef]

Pluchino, A.

A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).

Rapisarda, A.

A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).

Rasmussen, J. J.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Ratynskaia, S.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Razdan, A.

A. Razdan, “q-Gaussian representation of non-Lorentzian Mössbauer lineshapes,” Hyperfine Interact. 188, 103–106 (2009).
[CrossRef]

Rypdal, K.

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Shen, J.

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Solomon, T. H.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, “Observations of anomalous diffusion and Lévy flights in a two-dimensional rotating flow,” Phys. Rev. Lett. 71, 3975–3978 (1993).
[CrossRef]

Sorensen, C. M.

Stankey, H. E.

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

Starr, F. W.

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

Sudo, S.

Swinney, H. L.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, “Observations of anomalous diffusion and Lévy flights in a two-dimensional rotating flow,” Phys. Rev. Lett. 71, 3975–3978 (1993).
[CrossRef]

Takahashi, Y.

Taylor, T. W.

Tirnakli, U.

U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
[CrossRef]

Tsallis, C.

A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).

U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
[CrossRef]

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized nonextensive statistics,” Physica A 261, 534–554 (1998).
[CrossRef]

C. Tsallis, “Non-extensive thermostatistics: brief review and comments,” Physica A 221, 277–290 (1995).
[CrossRef]

C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” J. Stat. Phys. 52, 479–487 (1988).
[CrossRef]

Wang, B.

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Wang, H.

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Weeks, E. R.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, “Observations of anomalous diffusion and Lévy flights in a two-dimensional rotating flow,” Phys. Rev. Lett. 71, 3975–3978 (1993).
[CrossRef]

Xu, Y.

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Yu, B.

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

H. Wang, J. Shen, B. Wang, B. Yu, and Y. Xu, “Laser diode feedback interferometry in flowing Brownian motion system: a novel theory,” Appl. Phys. B 101, 173–183 (2010).
[CrossRef]

Eur. Phys. J. E (1)

L. C. Malacarne, R. S. Mendes, E. K. Lenza, S. Picoli, and J. P. Dal Molin, “A non-Gaussian model in polymeric network,” Eur. Phys. J. E 20, 395 (2006).
[CrossRef]

Eur. Phys. Lett. (1)

A. Pluchino, A. Rapisarda, and C. Tsallis, “Nonergodicity and central-limit behavior for long-range Hamiltonians,” Eur. Phys. Lett. 80, 26002 (2007).

Hyperfine Interact. (1)

A. Razdan, “q-Gaussian representation of non-Lorentzian Mössbauer lineshapes,” Hyperfine Interact. 188, 103–106 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. QE-15, 655–663 (1979).
[CrossRef]

J. Stat. Phys. (1)

C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” J. Stat. Phys. 52, 479–487 (1988).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (4)

M. G. Mazza, N. Givambattista, H. E. Stankey, and F. W. Starr, “Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water,” Phys. Rev. E 76, 031203 (2007).
[CrossRef]

L. G. Moyano, and C. Anteneodo, “Diffusive anomalies in a long-range Hamiltonian system,” Phys. Rev. E 74, 021118 (2006).
[CrossRef]

U. Tirnakli, C. Beck, and C. Tsallis, “Central limit behavior of deterministic dynamical systems,” Phys. Rev. E 75, 040106 (2007).
[CrossRef]

M. Ausloos and K. Ivanova, “Dynamical model and nonextensive statistical mechanics of a market index on large time windows,” Phys. Rev. E 68, 046122 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

C. Beck, “Dynamical foundations of nonextensive statistical mechanics,” Phys. Rev. Lett. 87, 180601 (2001).
[CrossRef]

B. Liu and J. Goree, “Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma,” Phys. Rev. Lett. 100, 055003 (2008).
[CrossRef]

T. H. Solomon, E. R. Weeks, and H. L. Swinney, “Observations of anomalous diffusion and Lévy flights in a two-dimensional rotating flow,” Phys. Rev. Lett. 71, 3975–3978 (1993).
[CrossRef]

S. Ratynskaia, K. Rypdal, C. Knapek, S. Khrapak, A. V. Milovanov, A. Ivlev, J. J. Rasmussen, and G. E. Morfill, “Superdiffusion and viscoelastic vortex flows in a two-dimensional complex plasma,” Phys. Rev. Lett. 96, 105010 (2006).
[CrossRef]

Physica A (3)

C. Tsallis, “Non-extensive thermostatistics: brief review and comments,” Physica A 221, 277–290 (1995).
[CrossRef]

C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized nonextensive statistics,” Physica A 261, 534–554 (1998).
[CrossRef]

J. A. Marsh, M. A. Fuentes, L. G. Moyano, and C. Tsallis, “Influence of global correlations on central limit theorems and entropic extensivity,” Physica A 372, 183–202 (2006).
[CrossRef]

Other (3)

L. E. Drain, The Laser Doppler Technique (Wiley, 1980).

B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley-Interscience, 1976), Chap. 5.

F. T. Arecchi, “Photocount distributions and field statistics,” in Quantum Optics, R. J. Glauber, ed. (Academic, 1969).

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup. LD, laser diode; AP, anamorphic prism pair; OL, objective lens; SL, 0.3-mm-thick LiNdP4O12 (LNP); SG, slide glass; AOM, acousto-optic modulators; PD, photodiode receiver; PC, personal computer.

Fig. 2.
Fig. 2.

Power spectra for 200-nm-diameter PS particles in water and in PVA–water mixtures with various transportation velocities of the dilute samples. (a) Experimental results for PS particles in water; (b) calculation results with w=5μm for PS particles in water; (c) experimental results for PS particles in 6.3 wt. % PVA–water mixture; (d) calculation results with w=5μm for PS particles in 6.3 wt. % PVA–water mixture.

Fig. 3.
Fig. 3.

Half-widths of the spectra plotted against the Doppler shift frequency for 200-nm-diameter PS particles in water. Plots indicates the half-widths experimentally, solid circles, θ=10°; open circles, θ=20°; solid diamonds, θ=30°; open diamonds, θ=40°. The dashed and dotted curves indicate the half-width obtained by computation using the FFT of Eq. (2) with w=20 and 5 μm, respectively.

Fig. 4.
Fig. 4.

Power spectra for 200-nm-diameter PS particles in (a) water and (b) 6.3 wt. % PVA–water mixture with vz=0.0253m/s. The dashed curve indicates the computed power spectrum.

Fig. 5.
Fig. 5.

Power spectra for 200-nm-diameter PS particles in (a) water and (b) 6.3 wt. % PVA–water mixture with vz=0.0253m/s. The gray dashed curve is the power spectrum computed using the FFT of Eq. (2) with w=5μm, which only reproduces each spectrum around the peak frequency. The gray solid curve is the power spectrum calculated from Eq. (11), which can reproduce the whole of each spectrum extremely well.

Fig. 6.
Fig. 6.

(a) q and (b) x0 plotted against transportation velocity for 200-nm-diameter PS particles in PVA–water mixtures. Solid circles, 0 wt. %; open circles, 2.4 wt. %; solid squares, 6.3 wt. %; open squares, 19 wt. % of PVA. Note that q=2 corresponds to fully diffusional motion, while q=1 corresponds to fully translational motion.

Fig. 7.
Fig. 7.

αq and γq plotted against the diffusion constant for 110 (circles), 200 (squares), and 458 (diamonds) nm diameter PS particles in PVA–water mixtures with various concentrations.

Equations (15)

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fD=2vzλ=2vsinθλ.
G(t)=GD×Gdif×Gtrans=exp(jk·vt)×exp(Dk2t)×exp(v2t22w2).
k=4πnλsinϕ2,
D=kBT3πηd,
I(ω)=Dk2ω2+(Dk2)2.
I(ω)=exp[12(wωv)2].
p(x)=p0[1(1q)(xx0)]1/(1q),
Sq=1Piq1q,
pq1(x)=p0exp[(xx0)2].
pq=2(x)=p0[1+(xx0)2]1.
I(Δω)=I0[1(1q)(Δωx0)]1/(1q).
Δω=2π(ffAOMfD),
q=αqexp(γqvz),
dvdt=γv+σL(t).
dvdt=γF(v)+σL(t).

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