Abstract

Comprehensive experimental research on the fundamental optical properties of dust pollution in a coal mine is presented. Rock dust generated in a tunneling roadway was sampled and the spectral complex refractive index within an infrared range of 2.5–25 μm was obtained by Fourier transform infrared spectroscopy measurement and Kramers–Kronig relation. Experimental results were validated to be consistent with equivalent optical constants simulated by effective medium theory based on component analysis of x-ray fluorescence, which illustrates that the top three mineral components are SiO2 (62.06%), Al2O3 (21.26%), and Fe2O3 (4.27%). The complex refractive index and the spatial distribution tested by a filter dust and particle size analyzer were involved in the simulation of extinction properties of rock dust along the tunneling roadway solved by the discrete ordinates method and Mie scattering model. The compared results illustrate that transmission is obviously enhanced with the increase of height from the floor but weakened with increasing horizontal distance from the air duct.

© 2015 Optical Society of America

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References

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    [Crossref]
  29. H. W. Pfefferkorn and J. Wang, “Early Permian coal-forming floras preserved as compressions from the Wuda District (Inner Mongolia, China),” Int. J. Coal Geol. 69, 90–102 (2007).
    [Crossref]
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    [Crossref]
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  32. S. E. Allaire and L. E. Parent, “Size guide number and Rosin-Rammler approaches to describe particle size distribution of granular organic-based fertilisers,” Biosystems Eng. 86, 503–509 (2003).
  33. L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
    [Crossref]
  34. H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).
  35. L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
    [Crossref]
  36. R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182, 273–279 (2000).
    [Crossref]
  37. L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
    [Crossref]

2015 (5)

L. X. Ma, F. Q. Wang, C. A. Wang, C. C. Wang, and J. Y. Tan, “Monte Carlo simulation of spectral reflectance and BRDF of the bubble layer in the upper ocean,” Opt. Express 23, 24274–24289 (2015).
[Crossref]

W. Z. Wang, Y. M. Wang, and G. Q. Shi, “Forward research on transmission characteristics of near-surface particulate-matter-polluted atmosphere in mining area combined with CFD method,” Opt. Express 23, A1010–A1023 (2015).
[Crossref]

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

2014 (3)

Y. Liang, H. Liang, and S. Zhu, “Mercury emission from coal seam fire at Wuda, Inner Mongolia, China,” Atmos. Environ. 83, 176–184 (2014).
[Crossref]

K. J. Candra, S. A. Pulung, and M. A. Sadashiv, “Dust dispersion and management in underground mining faces,” Int. J. Min. Sci. Technol. 24, 39–44 (2014).

P. Rai, B. Chutia, and S. Patil, “Monitoring of spatial variations of particulate matter (PM) pollution through bio-magnetic aspects of roadside plant leaves in an Indo-Burma hot spot region,” Urban Forestry Urban Greening 13, 761–770 (2014).

2013 (1)

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

2012 (2)

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

S. J. Schatzel and B. W. Stewart, “A provenance study of mineral matter in coal from Appalachian Basin coal mining regions and implications regarding the respirable health of underground coal workers: a geochemical and Nd isotope investigation,” Int. J. Coal Geol. 94, 123–136 (2012).
[Crossref]

2011 (2)

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

J. Lee, “Estimation of emission properties for silica particles using thermal radiation spectroscopy,” Appl. Opt. 50, 4262–4267 (2011).
[Crossref]

2010 (2)

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

2009 (2)

M. Onder and S. Onder, “Evaluation of occupational exposures to respirable dust in underground coal mines,” Ind. Health. 47, 43–49 (2009).

S. J. Schatzel, “Identifying sources of respirable quartz and silica dust in underground coal mines in southern West Virginia, western Virginia, and eastern Kentucky,” Int. J. Coal Geol. 78, 110–118 (2009).
[Crossref]

2007 (2)

H. W. Pfefferkorn and J. Wang, “Early Permian coal-forming floras preserved as compressions from the Wuda District (Inner Mongolia, China),” Int. J. Coal Geol. 69, 90–102 (2007).
[Crossref]

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

2006 (1)

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

2005 (1)

E. Petavratzi, S. Kingman, and I. Lowndes, “Particulates from mining operations: a review of sources, effects and regulations,” Miner. Eng. 18, 1183–1199 (2005).

2003 (1)

S. E. Allaire and L. E. Parent, “Size guide number and Rosin-Rammler approaches to describe particle size distribution of granular organic-based fertilisers,” Biosystems Eng. 86, 503–509 (2003).

2002 (2)

L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
[Crossref]

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

2001 (1)

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

2000 (2)

V. Castranova and V. Vallyathan, “Silicosis and coal workers’ pneumoconiosis,” Environ. Health Perspect. 108, 675–684 (2000).

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182, 273–279 (2000).
[Crossref]

1994 (1)

M. P. Menguc, S. Manickavasagam, and D. A. D’sa, “Determination of radiative properties of pulverized coal particles from experiments,” Fuel 73, 613–625 (1994).
[Crossref]

1984 (1)

M. Q. Brewster and T. Kunitomo, “The optical constants of coal, char and limestone,” J. Heat Transfer 106, 678–683 (1984).
[Crossref]

1977 (1)

S. Onari, T. Arai, and K. Kudo, “Infrared lattice vibrations and dielectric dispersion in α-Fe2O3,” Phys. Rev. B 16, 1717–1721 (1977).

1964 (1)

1961 (1)

W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands of quartz,” Phys. Rev. 121, 1324–1335 (1961).
[Crossref]

Allaire, S. E.

S. E. Allaire and L. E. Parent, “Size guide number and Rosin-Rammler approaches to describe particle size distribution of granular organic-based fertilisers,” Biosystems Eng. 86, 503–509 (2003).

An, W.

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

Arai, T.

S. Onari, T. Arai, and K. Kudo, “Infrared lattice vibrations and dielectric dispersion in α-Fe2O3,” Phys. Rev. B 16, 1717–1721 (1977).

Attfield, M. D.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Bell, J. F.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Bratveit, M.

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Brewster, M. Q.

M. Q. Brewster and T. Kunitomo, “The optical constants of coal, char and limestone,” J. Heat Transfer 106, 678–683 (1984).
[Crossref]

Candra, K. J.

K. J. Candra, S. A. Pulung, and M. A. Sadashiv, “Dust dispersion and management in underground mining faces,” Int. J. Min. Sci. Technol. 24, 39–44 (2014).

Cantor, B. A.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Castranova, V.

V. Castranova and V. Vallyathan, “Silicosis and coal workers’ pneumoconiosis,” Environ. Health Perspect. 108, 675–684 (2000).

Chen, B. T.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Chen, J. Q.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Chen, W.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Chutia, B.

P. Rai, B. Chutia, and S. Patil, “Monitoring of spatial variations of particulate matter (PM) pollution through bio-magnetic aspects of roadside plant leaves in an Indo-Burma hot spot region,” Urban Forestry Urban Greening 13, 761–770 (2014).

D’sa, D. A.

M. P. Menguc, S. Manickavasagam, and D. A. D’sa, “Determination of radiative properties of pulverized coal particles from experiments,” Fuel 73, 613–625 (1994).
[Crossref]

Dai, S.

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

Dech, S.

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

Deü, J.-F.

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Fu, C.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Fukutani, H.

H. Fukutani and O. Sueoka, Optical Properties and Electronic Structure of Metals and Alloys (North-Holland, 1966).

Gao, P.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Harrison, J. C.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Jia, Y.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

Kingman, S.

E. Petavratzi, S. Kingman, and I. Lowndes, “Particulates from mining operations: a review of sources, effects and regulations,” Miner. Eng. 18, 1183–1199 (2005).

Kleinman, D. A.

W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands of quartz,” Phys. Rev. 121, 1324–1335 (1961).
[Crossref]

Kudo, K.

S. Onari, T. Arai, and K. Kudo, “Infrared lattice vibrations and dielectric dispersion in α-Fe2O3,” Phys. Rev. B 16, 1717–1721 (1977).

Kuenzer, C.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

Kunitomo, T.

M. Q. Brewster and T. Kunitomo, “The optical constants of coal, char and limestone,” J. Heat Transfer 106, 678–683 (1984).
[Crossref]

Le Lay, F.

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Lee, J.

Legay, A.

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Lemmon, M. T.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Li, S.

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

Liang, H.

Y. Liang, H. Liang, and S. Zhu, “Mercury emission from coal seam fire at Wuda, Inner Mongolia, China,” Atmos. Environ. 83, 176–184 (2014).
[Crossref]

Liang, Y.

Y. Liang, H. Liang, and S. Zhu, “Mercury emission from coal seam fire at Wuda, Inner Mongolia, China,” Atmos. Environ. 83, 176–184 (2014).
[Crossref]

Liu, B.

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Liu, H.

H. Liu, Coal Mine Safety Regulation, Expert Interpretation (China University of Mining and Technology, 2006) (In Chinese).

Liu, L.

H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).

Liu, L. H.

L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
[Crossref]

Liu, Q.

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Lowndes, I.

E. Petavratzi, S. Kingman, and I. Lowndes, “Particulates from mining operations: a review of sources, effects and regulations,” Miner. Eng. 18, 1183–1199 (2005).

Luo, S.

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Ma, L. X.

Mamuya, S. D.

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Manickavasagam, S.

M. P. Menguc, S. Manickavasagam, and D. A. D’sa, “Determination of radiative properties of pulverized coal particles from experiments,” Fuel 73, 613–625 (1994).
[Crossref]

Mashalla, Y. S.

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Menguc, M. P.

M. P. Menguc, S. Manickavasagam, and D. A. D’sa, “Determination of radiative properties of pulverized coal particles from experiments,” Fuel 73, 613–625 (1994).
[Crossref]

Moen, B.

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Mwaiselage, J.

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Onari, S.

S. Onari, T. Arai, and K. Kudo, “Infrared lattice vibrations and dielectric dispersion in α-Fe2O3,” Phys. Rev. B 16, 1717–1721 (1977).

Onder, M.

M. Onder and S. Onder, “Evaluation of occupational exposures to respirable dust in underground coal mines,” Ind. Health. 47, 43–49 (2009).

Onder, S.

M. Onder and S. Onder, “Evaluation of occupational exposures to respirable dust in underground coal mines,” Ind. Health. 47, 43–49 (2009).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

Parent, L. E.

S. E. Allaire and L. E. Parent, “Size guide number and Rosin-Rammler approaches to describe particle size distribution of granular organic-based fertilisers,” Biosystems Eng. 86, 503–509 (2003).

Patil, S.

P. Rai, B. Chutia, and S. Patil, “Monitoring of spatial variations of particulate matter (PM) pollution through bio-magnetic aspects of roadside plant leaves in an Indo-Burma hot spot region,” Urban Forestry Urban Greening 13, 761–770 (2014).

Petavratzi, E.

E. Petavratzi, S. Kingman, and I. Lowndes, “Particulates from mining operations: a review of sources, effects and regulations,” Miner. Eng. 18, 1183–1199 (2005).

Pfefferkorn, H. W.

H. W. Pfefferkorn and J. Wang, “Early Permian coal-forming floras preserved as compressions from the Wuda District (Inner Mongolia, China),” Int. J. Coal Geol. 69, 90–102 (2007).
[Crossref]

Plass, G. N.

Pulung, S. A.

K. J. Candra, S. A. Pulung, and M. A. Sadashiv, “Dust dispersion and management in underground mining faces,” Int. J. Min. Sci. Technol. 24, 39–44 (2014).

Qi, H.

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

Rai, P.

P. Rai, B. Chutia, and S. Patil, “Monitoring of spatial variations of particulate matter (PM) pollution through bio-magnetic aspects of roadside plant leaves in an Indo-Burma hot spot region,” Urban Forestry Urban Greening 13, 761–770 (2014).

Ren, D.

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

Rouleau, L.

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Ruan, L.

H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).

Ruan, L. M.

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
[Crossref]

Ruppin, R.

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182, 273–279 (2000).
[Crossref]

Sadashiv, M. A.

K. J. Candra, S. A. Pulung, and M. A. Sadashiv, “Dust dispersion and management in underground mining faces,” Int. J. Min. Sci. Technol. 24, 39–44 (2014).

Schatzel, S. J.

S. J. Schatzel and B. W. Stewart, “A provenance study of mineral matter in coal from Appalachian Basin coal mining regions and implications regarding the respirable health of underground coal workers: a geochemical and Nd isotope investigation,” Int. J. Coal Geol. 94, 123–136 (2012).
[Crossref]

S. J. Schatzel, “Identifying sources of respirable quartz and silica dust in underground coal mines in southern West Virginia, western Virginia, and eastern Kentucky,” Int. J. Coal Geol. 78, 110–118 (2009).
[Crossref]

Shao, L.

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

Shi, G. Q.

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

W. Z. Wang, Y. M. Wang, and G. Q. Shi, “Forward research on transmission characteristics of near-surface particulate-matter-polluted atmosphere in mining area combined with CFD method,” Opt. Express 23, A1010–A1023 (2015).
[Crossref]

Shuai, Y.

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

Smith, M. D.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Smith, P. H.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Song, Z.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

Spitzer, W. G.

W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands of quartz,” Phys. Rev. 121, 1324–1335 (1961).
[Crossref]

Stewart, B. W.

S. J. Schatzel and B. W. Stewart, “A provenance study of mineral matter in coal from Appalachian Basin coal mining regions and implications regarding the respirable health of underground coal workers: a geochemical and Nd isotope investigation,” Int. J. Coal Geol. 94, 123–136 (2012).
[Crossref]

Sueoka, O.

H. Fukutani and O. Sueoka, Optical Properties and Electronic Structure of Metals and Alloys (North-Holland, 1966).

Sun, Y.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

Tan, H.

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).

Tan, H. P.

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
[Crossref]

Tan, J. Y.

Tang, Y.

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

Vallyathan, V.

V. Castranova and V. Vallyathan, “Silicosis and coal workers’ pneumoconiosis,” Environ. Health Perspect. 108, 675–684 (2000).

Wallace, W. E.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Wang, C. A.

Wang, C. C.

Wang, D. M.

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

Wang, F.

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

Wang, F. Q.

Wang, J.

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

H. W. Pfefferkorn and J. Wang, “Early Permian coal-forming floras preserved as compressions from the Wuda District (Inner Mongolia, China),” Int. J. Coal Geol. 69, 90–102 (2007).
[Crossref]

Wang, W. Z.

W. Z. Wang, Y. M. Wang, and G. Q. Shi, “Forward research on transmission characteristics of near-surface particulate-matter-polluted atmosphere in mining area combined with CFD method,” Opt. Express 23, A1010–A1023 (2015).
[Crossref]

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

Wang, Y. M.

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

W. Z. Wang, Y. M. Wang, and G. Q. Shi, “Forward research on transmission characteristics of near-surface particulate-matter-polluted atmosphere in mining area combined with CFD method,” Opt. Express 23, A1010–A1023 (2015).
[Crossref]

Wolff, M. J.

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Xia, X.

H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).

Yang, L.

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Yi, H.

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

Yuan, Y.

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

Zhang, J.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

Zhang, Z.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

Zhu, H.

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

Zhu, S.

Y. Liang, H. Liang, and S. Zhu, “Mercury emission from coal seam fire at Wuda, Inner Mongolia, China,” Atmos. Environ. 83, 176–184 (2014).
[Crossref]

Zhuang, Z.

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Zuo, H.

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Ann. Occup. Hyg. (1)

S. D. Mamuya, M. Bratveit, J. Mwaiselage, Y. S. Mashalla, and B. Moen, “High exposure to respirable dust and quartz in a labour-intensive coal mine in Tanzania,” Ann. Occup. Hyg. 50, 197–204 (2006).

Appl. Opt. (2)

Atmos. Environ. (2)

Y. Liang, H. Liang, and S. Zhu, “Mercury emission from coal seam fire at Wuda, Inner Mongolia, China,” Atmos. Environ. 83, 176–184 (2014).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, B. Liu, and H. Tan, “Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model,” Atmos. Environ. 45, 4892–4897 (2011).
[Crossref]

Biosystems Eng. (1)

S. E. Allaire and L. E. Parent, “Size guide number and Rosin-Rammler approaches to describe particle size distribution of granular organic-based fertilisers,” Biosystems Eng. 86, 503–509 (2003).

Environ. Health Perspect. (1)

V. Castranova and V. Vallyathan, “Silicosis and coal workers’ pneumoconiosis,” Environ. Health Perspect. 108, 675–684 (2000).

Fuel (1)

M. P. Menguc, S. Manickavasagam, and D. A. D’sa, “Determination of radiative properties of pulverized coal particles from experiments,” Fuel 73, 613–625 (1994).
[Crossref]

Icarus (1)

M. T. Lemmon, M. J. Wolff, J. F. Bell, M. D. Smith, B. A. Cantor, and P. H. Smith, “Dust aerosol, clouds, and the atmospheric optical depth record over 5 Mars years of the Mars Exploration Rover mission,” Icarus 251, 96–111 (2015).
[Crossref]

Ind. Health. (1)

M. Onder and S. Onder, “Evaluation of occupational exposures to respirable dust in underground coal mines,” Ind. Health. 47, 43–49 (2009).

Int. J. Coal Geol. (6)

S. J. Schatzel, “Identifying sources of respirable quartz and silica dust in underground coal mines in southern West Virginia, western Virginia, and eastern Kentucky,” Int. J. Coal Geol. 78, 110–118 (2009).
[Crossref]

S. J. Schatzel and B. W. Stewart, “A provenance study of mineral matter in coal from Appalachian Basin coal mining regions and implications regarding the respirable health of underground coal workers: a geochemical and Nd isotope investigation,” Int. J. Coal Geol. 94, 123–136 (2012).
[Crossref]

C. Kuenzer, J. Zhang, Y. Sun, Y. Jia, and S. Dech, “Coal fires revisited: the Wuda coal field in the aftermath of extensive coal fire research and accelerating extinguishing activities,” Int. J. Coal Geol. 102, 75–86 (2012).
[Crossref]

S. Dai, D. Ren, Y. Tang, L. Shao, and S. Li, “Distribution, isotopic variation and origin of sulfur in coals in the Wuda coalfield, Inner Mongolia, China,” Int. J. Coal Geol. 51, 237–250 (2002).
[Crossref]

H. W. Pfefferkorn and J. Wang, “Early Permian coal-forming floras preserved as compressions from the Wuda District (Inner Mongolia, China),” Int. J. Coal Geol. 69, 90–102 (2007).
[Crossref]

Z. Song, C. Kuenzer, H. Zhu, Z. Zhang, Y. Jia, Y. Sun, and J. Zhang, “Analysis of coal fire dynamics in the Wuda syncline impacted by fire-fighting activities based on in-situ observations and Landsat-8 remote sensing data,” Int. J. Coal Geol. 141–142, 91–102 (2015).
[Crossref]

Int. J. Heat Mass Transfer (1)

L. H. Liu, L. M. Ruan, and H. P. Tan, “On the discrete ordinates method for radiative heat transfer in anisotropically scattering media,” Int. J. Heat Mass Transfer 45, 3259–3262 (2002).
[Crossref]

Int. J. Min. Sci. Technol. (1)

K. J. Candra, S. A. Pulung, and M. A. Sadashiv, “Dust dispersion and management in underground mining faces,” Int. J. Min. Sci. Technol. 24, 39–44 (2014).

Int. J. Thermophys. (1)

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28, 1322–1341 (2007).
[Crossref]

J. Heat Transfer (1)

M. Q. Brewster and T. Kunitomo, “The optical constants of coal, char and limestone,” J. Heat Transfer 106, 678–683 (1984).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (2)

H. Zuo, Q. Liu, J. Wang, L. Yang, and S. Luo, “Selecting appropriate wavelengths to improve the precision of retrieving the aerosol size-distribution,” J. Quant. Spectrosc. Radiat. Transfer 111, 205–213 (2010).
[Crossref]

Y. Yuan, H. Yi, Y. Shuai, F. Wang, and H. Tan, “Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization,” J. Quant. Spectrosc. Radiat. Transfer 111, 2106–2114 (2010).
[Crossref]

Math. Probl. Eng. (1)

W. Z. Wang, Y. M. Wang, G. Q. Shi, and D. M. Wang, “Numerical study on infrared optical property of diffuse coal particles in mine fully mechanized working combined with CFD method,” Math. Probl. Eng. 2015, 501401 (2015).

Mech. Mater. (1)

L. Rouleau, J.-F. Deü, A. Legay, and F. Le Lay, “Application of Kramers–Kronig relations to time-temperature superposition for viscoelastic materials,” Mech. Mater. 65, 66–75 (2013).
[Crossref]

Miner. Eng. (1)

E. Petavratzi, S. Kingman, and I. Lowndes, “Particulates from mining operations: a review of sources, effects and regulations,” Miner. Eng. 18, 1183–1199 (2005).

Occup. Environ. Med. (1)

W. Chen, Z. Zhuang, M. D. Attfield, B. T. Chen, P. Gao, J. C. Harrison, C. Fu, J. Q. Chen, and W. E. Wallace, “Exposure to silica and silicosis among tin miners in China: exposure-response analyses and risk assessment,” Occup. Environ. Med. 58, 31–37 (2001).
[Crossref]

Opt. Commun. (1)

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182, 273–279 (2000).
[Crossref]

Opt. Express (2)

Phys. Rev. (1)

W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands of quartz,” Phys. Rev. 121, 1324–1335 (1961).
[Crossref]

Phys. Rev. B (1)

S. Onari, T. Arai, and K. Kudo, “Infrared lattice vibrations and dielectric dispersion in α-Fe2O3,” Phys. Rev. B 16, 1717–1721 (1977).

Urban Forestry Urban Greening (1)

P. Rai, B. Chutia, and S. Patil, “Monitoring of spatial variations of particulate matter (PM) pollution through bio-magnetic aspects of roadside plant leaves in an Indo-Burma hot spot region,” Urban Forestry Urban Greening 13, 761–770 (2014).

Other (5)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

H. Fukutani and O. Sueoka, Optical Properties and Electronic Structure of Metals and Alloys (North-Holland, 1966).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).

H. Tan, X. Xia, L. Liu, and L. Ruan, Numerical Calculation of Infrared Radiation Properties and Transfer (Harbin Institute of Technology, 2006) (In Chinese).

H. Liu, Coal Mine Safety Regulation, Expert Interpretation (China University of Mining and Technology, 2006) (In Chinese).

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the technical route of this study.
Fig. 2.
Fig. 2. Schematic of the geometric model and sampling points.
Fig. 3.
Fig. 3. Concentration distribution of rock dust along tunneling roadway.
Fig. 4.
Fig. 4. SEM image of rock dust sampled 20 m from the dust source: (a)  scale = 20 μm and (b)  scale = 50 μm .
Fig. 5.
Fig. 5. Size distribution of rock dust by Rosin–Rammler function and histogram at different sampling points: (a) 0 m, (b) 10 m, (c) 20 m, and (d) 30 m from the dust source.
Fig. 6.
Fig. 6. Spectral transmittance of rock dust in KBr matrix within 400 4000 cm 1 .
Fig. 7.
Fig. 7. Validation of the complex refractive index of rock dust: (a) the n value of complex refractive index and (b) the k value of complex refractive index.
Fig. 8.
Fig. 8. Transmission properties of rock dust: (a) in the vertical direction and (b) in the horizontal direction.

Tables (3)

Tables Icon

Table 1. X-Ray Fluorescence (XRF) Results of Rock Dust a

Tables Icon

Table 2. Complex Refractive Index of Rock Dust

Tables Icon

Table 3. Comparison of the Peaking Wavelength

Equations (9)

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

τ λ = exp ( κ λ L ) ,
Q e , λ = 4 π D 2 N L ln τ λ ,
Q e , λ ( m , χ ) = 4 Re ( S 0 ( m , χ ) ) χ 2 ,
n ( λ ) = 1 + 2 λ 2 π P 0 k ( λ 0 ) λ 0 ( λ 2 λ 0 2 ) d λ 0 ,
lim λ 0 k ( λ ) = C p λ 3 / c 0 3 ,
lim λ k ( λ ) = C h c 0 / λ ,
ε mix = ε e + 3 ε e k = 1 K f k ε k ε e ε k + 2 ε e 1 k = 1 K f k ε k ε e ε k + 2 ε e ,
n mix = ε mix 2 + ε mix 2 + ε mix 2 ,
k mix = ε mix 2 + ε mix 2 ε mix 2 .

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