Abstract

If coherent light is incident on a suspension containing nanoparticles, they act as scattering centers and the result of the far-field interference is a “speckled” image. The scattering centers have a complex movement of both sedimentation and Brownian motion. Consequently the speckle image is not static but presents time fluctuations. A computer code to simulate the dynamics of the coherent light scattering on nanofluids was written, tested, and used to calculate the far-field intensity variation for nanofluids having different particle size. The results are discussed and an alternative experimental method for fast nanoparticle size assessing is suggested as a possible application.

© 2008 Optical Society of America

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References

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  1. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fed. 231, 99-103 (1995).
  2. P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer 128, 465-477 (2006).
    [CrossRef]
  3. S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. 84, 4316-4318 (2004).
    [CrossRef]
  4. W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
    [CrossRef]
  5. Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer 43, 3701-3707 (2000).
    [CrossRef]
  6. R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
    [CrossRef] [PubMed]
  7. B. Chu, Laser Light Scattering: Basic Principles and Practice, 2nd ed. (Academic, 1992).
  8. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier, 2000).
  9. L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214-3221(1999).
    [CrossRef]
  10. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed., (Springer-Verlag, 1984).
  11. J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22, R35-R66 (2001).
    [CrossRef]
  12. W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
    [CrossRef]
  13. D. Chicea and M. Racuciu, “On magnetic fluid synthesis and light scattering anisotropy parameter,” J. Optoelectron. Adv. Mater. 9, 2738-2742, (2007).
  14. M. Qian, J. Liu, M. S. Yan, Z. H. Shen, J. Lu, and X. Ni, “Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids,” Opt. Express 14, 7559-7566, (2006).
    [CrossRef] [PubMed]
  15. E. J. McCartey, Optics of the Atmosphere--Scattering by Molecules and Particles (Wiley1976).
  16. M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
    [CrossRef] [PubMed]
  17. “Physical characteristics of water,” http://www.thermexcel.com/english/tables/eau_atm.htm.
  18. D. Chicea, “A simple algorithm for nanoparticle Brownian motion computer simulation,” (submitted to Mod. Phys. Lett. B ).
  19. D. Chicea and M. Racuciu, “On low concentration aqueous magnetic fluid light scattering properties,” J. Optoelectron. Adv. Mater. 9, 3843-3846 (2007).
  20. Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
    [CrossRef]
  21. C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  22. D. Chicea, “Speckle size, intensity and contrast measurement application in micron-size particle concentration assessment,” Eur. Phys. J.: App. Physi. 40, 305-310 (2007).
    [CrossRef]
  23. R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999), pp. 40-45.
  24. W. Tscharnuter, “Photon correlation spectroscopy in particle sizing,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed, (Wiley, 2000), p. 5469.
  25. http://www.malvern.co.uk.
  26. http://www.bic.com/Particle_Sizers_overview.html.

2007

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

D. Chicea and M. Racuciu, “On magnetic fluid synthesis and light scattering anisotropy parameter,” J. Optoelectron. Adv. Mater. 9, 2738-2742, (2007).

D. Chicea and M. Racuciu, “On low concentration aqueous magnetic fluid light scattering properties,” J. Optoelectron. Adv. Mater. 9, 3843-3846 (2007).

D. Chicea, “Speckle size, intensity and contrast measurement application in micron-size particle concentration assessment,” Eur. Phys. J.: App. Physi. 40, 305-310 (2007).
[CrossRef]

2006

M. Qian, J. Liu, M. S. Yan, Z. H. Shen, J. Lu, and X. Ni, “Investigation on utilizing laser speckle velocimetry to measure the velocities of nanoparticles in nanofluids,” Opt. Express 14, 7559-7566, (2006).
[CrossRef] [PubMed]

P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer 128, 465-477 (2006).
[CrossRef]

W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
[CrossRef]

2005

R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
[CrossRef] [PubMed]

2004

S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. 84, 4316-4318 (2004).
[CrossRef]

2003

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

2001

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
[CrossRef] [PubMed]

J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

2000

Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer 43, 3701-3707 (2000).
[CrossRef]

1999

L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214-3221(1999).
[CrossRef]

1995

U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fed. 231, 99-103 (1995).

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier, 2000).

Bohren, C. F.

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999), pp. 40-45.

Brattacharya, P.

R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
[CrossRef] [PubMed]

Briers, J. D.

J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Chicea, D.

D. Chicea and M. Racuciu, “On magnetic fluid synthesis and light scattering anisotropy parameter,” J. Optoelectron. Adv. Mater. 9, 2738-2742, (2007).

D. Chicea, “Speckle size, intensity and contrast measurement application in micron-size particle concentration assessment,” Eur. Phys. J.: App. Physi. 40, 305-310 (2007).
[CrossRef]

D. Chicea and M. Racuciu, “On low concentration aqueous magnetic fluid light scattering properties,” J. Optoelectron. Adv. Mater. 9, 3843-3846 (2007).

D. Chicea, “A simple algorithm for nanoparticle Brownian motion computer simulation,” (submitted to Mod. Phys. Lett. B ).

Choi, S. U. S.

S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. 84, 4316-4318 (2004).
[CrossRef]

Choi, U. S.

U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fed. 231, 99-103 (1995).

Chu, B.

B. Chu, Laser Light Scattering: Basic Principles and Practice, 2nd ed. (Academic, 1992).

Cipelletti, L.

L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214-3221(1999).
[CrossRef]

Connolly, J.

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

Dobson, J.

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

Evans, W.

W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
[CrossRef]

Fang, W. X.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

Fish, J.

W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed., (Springer-Verlag, 1984).

Hammer, M.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
[CrossRef] [PubMed]

He(a), Z.-H.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

Huffman, D.

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jang, S. P.

S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. 84, 4316-4318 (2004).
[CrossRef]

Jones, S. K.

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

Keblinski, P.

W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
[CrossRef]

Liu, J.

Lu, J.

Mao, Z.-Q.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

McCartey, E. J.

E. J. McCartey, Optics of the Atmosphere--Scattering by Molecules and Particles (Wiley1976).

Ni, X.

Pankhurst, Q. A.

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier, 2000).

Phelan, P. E.

R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
[CrossRef] [PubMed]

Prasher, R.

R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
[CrossRef] [PubMed]

Qian, M.

Racuciu, M.

D. Chicea and M. Racuciu, “On magnetic fluid synthesis and light scattering anisotropy parameter,” J. Optoelectron. Adv. Mater. 9, 2738-2742, (2007).

D. Chicea and M. Racuciu, “On low concentration aqueous magnetic fluid light scattering properties,” J. Optoelectron. Adv. Mater. 9, 3843-3846 (2007).

Roetzel, W.

Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer 43, 3701-3707 (2000).
[CrossRef]

Schweitzer, D.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
[CrossRef] [PubMed]

Shen, H.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

Shen, Z. H.

Tscharnuter, W.

W. Tscharnuter, “Photon correlation spectroscopy in particle sizing,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed, (Wiley, 2000), p. 5469.

Vadasz, P.

P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer 128, 465-477 (2006).
[CrossRef]

Weitz, D. A.

L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214-3221(1999).
[CrossRef]

Xu, X.-Q.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

Xuan, Y. M.

Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer 43, 3701-3707 (2000).
[CrossRef]

Yan, M. S.

Yaroslavsky, A. N.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett.

S. P. Jang and S. U. S. Choi, “Role of Brownian motion in the enhanced thermal conductivity of nanofluids,” Appl. Phys. Lett. 84, 4316-4318 (2004).
[CrossRef]

W. Evans, J. Fish, and P. Keblinski, “Role of Brownian motion hydrodynamics on nanofluid thermal conductivity,” Appl. Phys. Lett. 88, 093116 (2006).
[CrossRef]

ASME Fed.

U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fed. 231, 99-103 (1995).

Eur. Phys. J.: App. Physi.

D. Chicea, “Speckle size, intensity and contrast measurement application in micron-size particle concentration assessment,” Eur. Phys. J.: App. Physi. 40, 305-310 (2007).
[CrossRef]

Europhysi. Lett.

W. X. Fang, Z.-H. He(a), X.-Q. Xu, Z.-Q. Mao, and H. Shen, “Magnetic-field-induced chainlike assembly structures of Fe3O4 nanoparticles,” Europhysi. Lett. 77, 68004-68009, (2007).
[CrossRef]

Int. J. Heat Mass Transfer

Y. M. Xuan and W. Roetzel, “Conceptions for heat transfer correlation of nanofluids,” Int. J. Heat Mass Transfer 43, 3701-3707 (2000).
[CrossRef]

J. Heat Transfer

P. Vadasz, “Heat conduction in nanofluid suspensions,” J. Heat Transfer 128, 465-477 (2006).
[CrossRef]

J. Optoelectron. Adv. Mater.

D. Chicea and M. Racuciu, “On magnetic fluid synthesis and light scattering anisotropy parameter,” J. Optoelectron. Adv. Mater. 9, 2738-2742, (2007).

D. Chicea and M. Racuciu, “On low concentration aqueous magnetic fluid light scattering properties,” J. Optoelectron. Adv. Mater. 9, 3843-3846 (2007).

J. Phys. D

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” J. Phys. D 36, R167-R181 (2003).
[CrossRef]

Mod. Phys. Lett. B

D. Chicea, “A simple algorithm for nanoparticle Brownian motion computer simulation,” (submitted to Mod. Phys. Lett. B ).

Opt. Express

Phys. Med. Biol.

M. Hammer, A. N. Yaroslavsky, and D. Schweitzer, “A scattering phase function for blood with physiological haematocrit,” Phys. Med. Biol. , 46, N65-N69, (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. Prasher, P. Brattacharya, and P. E. Phelan, “Thermal conductivity of nanoscale colloidal solutions (nanofluids),” Phys. Rev. Lett. 94, 025901 (2005).
[CrossRef] [PubMed]

Physiol. Meas.

J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging,” Physiol. Meas. 22, R35-R66 (2001).
[CrossRef]

Rev. Sci. Instrum.

L. Cipelletti and D. A. Weitz, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator,” Rev. Sci. Instrum. 70, 3214-3221(1999).
[CrossRef]

Other

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed., (Springer-Verlag, 1984).

B. Chu, Laser Light Scattering: Basic Principles and Practice, 2nd ed. (Academic, 1992).

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier, 2000).

“Physical characteristics of water,” http://www.thermexcel.com/english/tables/eau_atm.htm.

E. J. McCartey, Optics of the Atmosphere--Scattering by Molecules and Particles (Wiley1976).

C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999), pp. 40-45.

W. Tscharnuter, “Photon correlation spectroscopy in particle sizing,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed, (Wiley, 2000), p. 5469.

http://www.malvern.co.uk.

http://www.bic.com/Particle_Sizers_overview.html.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the computer simulation.

Fig. 2
Fig. 2

Variation of the computed diffusion coefficient (crosses) with the Brownian motion time step for 10 nm nanoparticles in water at 293.15 K .

Fig. 3
Fig. 3

Brownian motion velocity versus particle radius in the range 0.2 18.5 nm at 293.15 K .

Fig. 4
Fig. 4

Sedimentation motion velocity versus particle radius in the range 0.2 18.5 nm at 293.15 K .

Fig. 5
Fig. 5

Computed far-field image having 7 nm diameter nanoparticles as target.

Fig. 6
Fig. 6

Contour plot of the intensity distribution of the bitmap in Fig. 5.

Fig. 7
Fig. 7

Typical, experimental far-field speckle.

Fig. 8
Fig. 8

Average intensity variation with the nanoparticles’ volume ratio.

Fig. 9
Fig. 9

Average intensity variation with the particle diameter, for samples having a volume ratio equal to 5.0 * 10 13 .

Fig. 10
Fig. 10

0.2 s sequence of a computed time series for 10 nm diameter nanoparticles.

Fig. 11
Fig. 11

Autocorrelation time variation with the SC diameter, at constant SC number.

Fig. 12
Fig. 12

Variation of the autocorrelation time with the absolute temperature.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

E y = E c x 0 y 0 + x 0 2 + z 0 2 R 3 cos θ .
ν s = 2 r 2 g 9 η ( ρ ρ 0 ) ,
f v ( ν i ) = m 2 π k T exp ( m ν 2 i 2 k T ) ,
n t D · 2 n = 0 ,
P t D · 2 P = 0.
D = k B T μ ,
F ext = 6 π η R ν drift ,
ν drift = μ · F μ = 1 6 π η R .
D = k B T 6 π η R .
P ( 0 , 0 ) = δ ( r ) .
p ( r , t ) = ( 4 π D t ) 3 / 2 exp ( r 2 4 D t ) .
r 2 ( t ) = 0 0 π 0 2 π r 2 P ( r , t ) r 2 sin θ d θ d ϕ = 6 D comp t .
ν t = 3 k T m .
h = h 0 + ν s t exp ,
x 2 ( t exp ) = y 2 ( t exp ) = z 2 ( t exp ) = + + + x 2 · P ( r , t exp ) · d x d y d z = 2 D t exp .
N = V nano 4 π 3 ( d 2 ) 3 ,
σ s = 2 π 5 3 d 6 λ 4 ( n 2 1 n 2 + 2 ) 2 .
I N σ s ( d 2 ) 3 .
A ( τ ) = I ( r , t ) · I ( r , t + τ ) I ( r , t ) · I ( r , t ) ,
τ c = A k ν ,

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