Abstract

We utilize the Volume Integral Equation Formulation (VIEF) and the method of moments to calculate the electromagnetic scattering and absorption of aerosol particles with branched-chain structures. Two kinds of polarization of the incident electromagnetic wave were considered: the cross- and end-fire polarizations. The numerical results of internal electric field distribution, absorbed power, and extinction and scattering cross sections, obtained from the VIEF, show excellent agreement with the Mie theory for the special case of spherical particles. Comparison between the results of the VIEF and Iterative Extended Boundary Condition Method for very long oriented (elongated) chains of particles also showed good agreement. After validating the accuracy of the VIEF, the absorption characteristics of three branched-chain structures simulated from microscopic pictures of coagulated smoke aerosol particles were calculated. Results showed that the ratio of absorption in the two polarization cases, Pcross-fire/Pend-fire, for very long oriented chain structures is as high as a factor of 4 at lower frequencies (λ = 10 μm). While in the higher frequency (λ = 0.5-μm) case, the ratio of Pcross-fire/Pend-fire is reduced to 2.0. For branched-chain structures, the ratio of Pcross-fire/Pend-fire decreased with the increase in the number of the side branches. These observations show that the frequency, polarization, and structure factors play important roles in determining the optical characteristics of branched chains of aerosol particles.

© 1989 Optical Society of America

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References

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  1. B. L. Drolen, C. L. Tien, “Absorption and Scattering of Agglomerated Soot Particulate,” J. Quant. Spectrosc. Radiat. Transfer 37, 433–448 (1987).
    [Crossref]
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  3. J. V. Dave, “Coefficients of the Legendre and Fourier Series for the Scattering Functions of Spherical Particles,” Appl. Opt. 9, 1888–1896 (1970).
    [PubMed]
  4. R. D. Cess, “Nuclear War: Illustrative Effects of Atmospheric Smoke and Dust Upon Solar Radiation,” Clim. Change 7, (1985).
    [Crossref]
  5. J. E. Penner, “Uncertainties in the Smoke Source Term for ‘Nuclear Winter’ Studies,” Nature, London 324, 222–226 (1986).
    [Crossref]
  6. V. E. Cachorro, A. M. de Frutos, J. L. Casanova, “Absorption by Oxygen and Water Vapor in the Real Atmosphere,” Appl. Opt. 26, 501–505 (1987).
    [Crossref] [PubMed]
  7. J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
    [Crossref]
  8. M. V. Berry, I. C. Percival, “Optics of Fractal Custers Such as Smoke,” Opt. Acta 33, 577–591 (1986).
    [Crossref]
  9. C. L. Tien, S. C. Lee, “Flame Radiation,” Prog. Energy Combust. Sci. 8, 41–59 (1982).
    [Crossref]
  10. A. A. Broyles, “Smoke Generation in a Nuclear War,” Am. J. Phys. 53, 323–332 (1985).
    [Crossref]
  11. J. E. Penner, W. M. Porch, “Coagulation in Smoke Plumes after a Nuclear War,” Atmos. Environ. 21, 957–969 (1987).
    [Crossref]
  12. R. Jaenicke, “Natural Aerosols,” Ann. New York Acad. Sci. 338, 317–329 (1980).
    [Crossref]
  13. T. P. Ackerman, B. Toon, “Absorption of Visible Radiation in Atmosphere Containing Mixtures of Absorbing and Nonabsorbing Particles,” Appl. Opt. 20, 3661–3668 (1981).
    [Crossref] [PubMed]
  14. P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
    [Crossref]
  15. J. A. Morrison, M. J. Cross, “Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops,” Bell Syst. Tech. J. 53, 955–1019 (1974).
  16. G. Mie, “Beitrage zuγ Optik Truber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
    [Crossref]
  17. P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (speciale), 348–352 (1969).
  18. M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
    [Crossref]
  19. M. F. Iskander, S. C. Olson, R. E. Benner, D. Yoshida, “Optical Scattering by Metallic and Carbon Aerosols of High-Aspect Ratio,” Appl. Opt. 25, 2514–2520 (1986).
    [Crossref] [PubMed]
  20. M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
    [Crossref]
  21. M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
    [Crossref]
  22. J. Van Bladel, “Some Remarks on Green’s Dyadic for Infinite Space,” IRE Trans. Antennas Propag. AP-90, 563–566 (1961).
    [Crossref]
  23. D. E. Livesay, K. M. Chen, “Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
    [Crossref]
  24. K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1981), pp. 299–305.
  25. H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
    [Crossref]
  26. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  27. M. J. Hagmann, R. L. Levin, “Accuracy of Block Model for Evaluation of the Deposition of Energy by Electromagnetic Fields,” IEEE Trans. Microwave Theory Tech. MTT-34, 653–659 (1986).
    [Crossref]
  28. M. J. Hagmann, R. L. Levin, “Convergence of Local and Average Values in Three-Dimensional Moment-Method Solutions,” IEEE Trans. Microwave Theory Tech. MTT-33, 649–654 (1985).
    [Crossref]
  29. R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
    [Crossref]

1989 (2)

M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
[Crossref]

M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
[Crossref]

1987 (3)

B. L. Drolen, C. L. Tien, “Absorption and Scattering of Agglomerated Soot Particulate,” J. Quant. Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

J. E. Penner, W. M. Porch, “Coagulation in Smoke Plumes after a Nuclear War,” Atmos. Environ. 21, 957–969 (1987).
[Crossref]

V. E. Cachorro, A. M. de Frutos, J. L. Casanova, “Absorption by Oxygen and Water Vapor in the Real Atmosphere,” Appl. Opt. 26, 501–505 (1987).
[Crossref] [PubMed]

1986 (6)

M. J. Hagmann, R. L. Levin, “Accuracy of Block Model for Evaluation of the Deposition of Energy by Electromagnetic Fields,” IEEE Trans. Microwave Theory Tech. MTT-34, 653–659 (1986).
[Crossref]

M. F. Iskander, S. C. Olson, R. E. Benner, D. Yoshida, “Optical Scattering by Metallic and Carbon Aerosols of High-Aspect Ratio,” Appl. Opt. 25, 2514–2520 (1986).
[Crossref] [PubMed]

J. E. Penner, “Uncertainties in the Smoke Source Term for ‘Nuclear Winter’ Studies,” Nature, London 324, 222–226 (1986).
[Crossref]

J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
[Crossref]

M. V. Berry, I. C. Percival, “Optics of Fractal Custers Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[Crossref]

1985 (3)

A. A. Broyles, “Smoke Generation in a Nuclear War,” Am. J. Phys. 53, 323–332 (1985).
[Crossref]

R. D. Cess, “Nuclear War: Illustrative Effects of Atmospheric Smoke and Dust Upon Solar Radiation,” Clim. Change 7, (1985).
[Crossref]

M. J. Hagmann, R. L. Levin, “Convergence of Local and Average Values in Three-Dimensional Moment-Method Solutions,” IEEE Trans. Microwave Theory Tech. MTT-33, 649–654 (1985).
[Crossref]

1984 (1)

H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
[Crossref]

1983 (1)

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
[Crossref]

1982 (2)

C. L. Tien, S. C. Lee, “Flame Radiation,” Prog. Energy Combust. Sci. 8, 41–59 (1982).
[Crossref]

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[Crossref]

1981 (1)

1980 (1)

R. Jaenicke, “Natural Aerosols,” Ann. New York Acad. Sci. 338, 317–329 (1980).
[Crossref]

1974 (2)

J. A. Morrison, M. J. Cross, “Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops,” Bell Syst. Tech. J. 53, 955–1019 (1974).

D. E. Livesay, K. M. Chen, “Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[Crossref]

1970 (1)

1969 (1)

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (speciale), 348–352 (1969).

1961 (1)

J. Van Bladel, “Some Remarks on Green’s Dyadic for Infinite Space,” IRE Trans. Antennas Propag. AP-90, 563–566 (1961).
[Crossref]

1908 (1)

G. Mie, “Beitrage zuγ Optik Truber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Ackerman, T. P.

Barber, P. W.

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[Crossref]

Baum, H.

R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[Crossref]

Benner, R. E.

Berry, M. V.

M. V. Berry, I. C. Percival, “Optics of Fractal Custers Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Broyles, A. A.

A. A. Broyles, “Smoke Generation in a Nuclear War,” Am. J. Phys. 53, 323–332 (1985).
[Crossref]

Cachorro, V. E.

Casanova, J. L.

Cess, R. D.

R. D. Cess, “Nuclear War: Illustrative Effects of Atmospheric Smoke and Dust Upon Solar Radiation,” Clim. Change 7, (1985).
[Crossref]

Chen, H. Y.

M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
[Crossref]

M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
[Crossref]

Chen, K. M.

D. E. Livesay, K. M. Chen, “Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[Crossref]

K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1981), pp. 299–305.

Cross, M. J.

J. A. Morrison, M. J. Cross, “Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops,” Bell Syst. Tech. J. 53, 955–1019 (1974).

Dave, J. V.

de Frutos, A. M.

Drolen, B. L.

B. L. Drolen, C. L. Tien, “Absorption and Scattering of Agglomerated Soot Particulate,” J. Quant. Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

Duong, T. V.

M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
[Crossref]

Durney, C. H.

H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
[Crossref]

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
[Crossref]

Edwards, L. L.

J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
[Crossref]

Hagmann, M. J.

M. J. Hagmann, R. L. Levin, “Accuracy of Block Model for Evaluation of the Deposition of Energy by Electromagnetic Fields,” IEEE Trans. Microwave Theory Tech. MTT-34, 653–659 (1986).
[Crossref]

M. J. Hagmann, R. L. Levin, “Convergence of Local and Average Values in Three-Dimensional Moment-Method Solutions,” IEEE Trans. Microwave Theory Tech. MTT-33, 649–654 (1985).
[Crossref]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Haselman, L. C.

J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
[Crossref]

Iskander, M. F.

M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
[Crossref]

M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
[Crossref]

M. F. Iskander, S. C. Olson, R. E. Benner, D. Yoshida, “Optical Scattering by Metallic and Carbon Aerosols of High-Aspect Ratio,” Appl. Opt. 25, 2514–2520 (1986).
[Crossref] [PubMed]

H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
[Crossref]

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
[Crossref]

Jaenicke, R.

R. Jaenicke, “Natural Aerosols,” Ann. New York Acad. Sci. 338, 317–329 (1980).
[Crossref]

Lakhtakia, A.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
[Crossref]

Lee, S. C.

C. L. Tien, S. C. Lee, “Flame Radiation,” Prog. Energy Combust. Sci. 8, 41–59 (1982).
[Crossref]

Levin, R. L.

M. J. Hagmann, R. L. Levin, “Accuracy of Block Model for Evaluation of the Deposition of Energy by Electromagnetic Fields,” IEEE Trans. Microwave Theory Tech. MTT-34, 653–659 (1986).
[Crossref]

M. J. Hagmann, R. L. Levin, “Convergence of Local and Average Values in Three-Dimensional Moment-Method Solutions,” IEEE Trans. Microwave Theory Tech. MTT-33, 649–654 (1985).
[Crossref]

Livesay, D. E.

D. E. Livesay, K. M. Chen, “Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[Crossref]

Massoudi, H.

H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
[Crossref]

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[Crossref]

Mie, G.

G. Mie, “Beitrage zuγ Optik Truber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Morrison, J. A.

J. A. Morrison, M. J. Cross, “Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops,” Bell Syst. Tech. J. 53, 955–1019 (1974).

Mountain, R. D.

R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[Crossref]

Mulholland, G. W.

R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[Crossref]

Olson, S. C.

Penner, J. E.

M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
[Crossref]

J. E. Penner, W. M. Porch, “Coagulation in Smoke Plumes after a Nuclear War,” Atmos. Environ. 21, 957–969 (1987).
[Crossref]

J. E. Penner, “Uncertainties in the Smoke Source Term for ‘Nuclear Winter’ Studies,” Nature, London 324, 222–226 (1986).
[Crossref]

J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
[Crossref]

Percival, I. C.

M. V. Berry, I. C. Percival, “Optics of Fractal Custers Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Porch, W. M.

J. E. Penner, W. M. Porch, “Coagulation in Smoke Plumes after a Nuclear War,” Atmos. Environ. 21, 957–969 (1987).
[Crossref]

Tien, C. L.

B. L. Drolen, C. L. Tien, “Absorption and Scattering of Agglomerated Soot Particulate,” J. Quant. Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

C. L. Tien, S. C. Lee, “Flame Radiation,” Prog. Energy Combust. Sci. 8, 41–59 (1982).
[Crossref]

Toon, B.

Van Bladel, J.

J. Van Bladel, “Some Remarks on Green’s Dyadic for Infinite Space,” IRE Trans. Antennas Propag. AP-90, 563–566 (1961).
[Crossref]

Van De Hulst, H. C.

H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957.

Waterman, P. C.

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (speciale), 348–352 (1969).

Yoshida, D.

Aerosol Sci. Technol. (1)

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[Crossref]

Alta Freq. (1)

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (speciale), 348–352 (1969).

Am. J. Phys. (1)

A. A. Broyles, “Smoke Generation in a Nuclear War,” Am. J. Phys. 53, 323–332 (1985).
[Crossref]

Ann. New York Acad. Sci. (1)

R. Jaenicke, “Natural Aerosols,” Ann. New York Acad. Sci. 338, 317–329 (1980).
[Crossref]

Ann. Phys. (1)

G. Mie, “Beitrage zuγ Optik Truber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Appl. Opt. (4)

Atmos. Environ. (1)

J. E. Penner, W. M. Porch, “Coagulation in Smoke Plumes after a Nuclear War,” Atmos. Environ. 21, 957–969 (1987).
[Crossref]

Bell Syst. Tech. J. (1)

J. A. Morrison, M. J. Cross, “Scattering of a Plane Electromagnetic Wave by Axisymmetric Raindrops,” Bell Syst. Tech. J. 53, 955–1019 (1974).

Clim. Change (1)

R. D. Cess, “Nuclear War: Illustrative Effects of Atmospheric Smoke and Dust Upon Solar Radiation,” Clim. Change 7, (1985).
[Crossref]

IEEE Trans. Antennas Propag. (1)

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983).
[Crossref]

IEEE Trans. Electromag. Compat. (1)

M. F. Iskander, H. Y. Chen, T. V. Duong, “A New Sectioning Procedure for Calculating Scattering and Absorption by Elongated Dielectric Objects,” IEEE Trans. Electromag. Compat. EC-31, 157–163 (1989).
[Crossref]

IEEE Trans. Microwave Theory Tech. (4)

D. E. Livesay, K. M. Chen, “Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies,” IEEE Trans. Microwave Theory Tech. MTT-22, 1273–1280 (1974).
[Crossref]

H. Massoudi, C. H. Durney, M. F. Iskander, “Limitations of the Cubical Block Model of Man in Calculating SAR Distribution,” IEEE Trans. Microwave Theory Tech. MTT-32, 746–752 (1984).
[Crossref]

M. J. Hagmann, R. L. Levin, “Accuracy of Block Model for Evaluation of the Deposition of Energy by Electromagnetic Fields,” IEEE Trans. Microwave Theory Tech. MTT-34, 653–659 (1986).
[Crossref]

M. J. Hagmann, R. L. Levin, “Convergence of Local and Average Values in Three-Dimensional Moment-Method Solutions,” IEEE Trans. Microwave Theory Tech. MTT-33, 649–654 (1985).
[Crossref]

IRE Trans. Antennas Propag. (1)

J. Van Bladel, “Some Remarks on Green’s Dyadic for Infinite Space,” IRE Trans. Antennas Propag. AP-90, 563–566 (1961).
[Crossref]

J. Aerosol Sci. Technol. (1)

M. F. Iskander, H. Y. Chen, J. E. Penner, “Scattering and Absorption by Elongated Aerosol Particles,” J. Aerosol Sci. Technol. 10, 172–180 (1989).
[Crossref]

J. Climate Appl. Meteorol. (1)

J. E. Penner, L. C. Haselman, L. L. Edwards, “Smoke-Plume Distributions above Large-Scale Fires: Implications for Simulation of ‘Nuclear Winter’,” J. Climate Appl. Meteorol. 25, 1434–1444 (1986).
[Crossref]

J. Colloid Interface Sci. (1)

R. D. Mountain, G. W. Mulholland, H. Baum, “Simulation of Aerosol Agglomeration in the Free Molecular and Continuum Flow Regimes,” J. Colloid Interface Sci. 114, 67–81 (1986).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

B. L. Drolen, C. L. Tien, “Absorption and Scattering of Agglomerated Soot Particulate,” J. Quant. Spectrosc. Radiat. Transfer 37, 433–448 (1987).
[Crossref]

Nature, London (1)

J. E. Penner, “Uncertainties in the Smoke Source Term for ‘Nuclear Winter’ Studies,” Nature, London 324, 222–226 (1986).
[Crossref]

Opt. Acta (1)

M. V. Berry, I. C. Percival, “Optics of Fractal Custers Such as Smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Prog. Energy Combust. Sci. (1)

C. L. Tien, S. C. Lee, “Flame Radiation,” Prog. Energy Combust. Sci. 8, 41–59 (1982).
[Crossref]

Other (3)

H. C. Van De Hulst, Light Scattering by Small Particles (Wiley, New York, 1957.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

K. M. Chen, “Interaction of Electromagnetic Fields with Biological Bodies,” in Research Topics in Electromagnetic Wave Theory, J. A. Kong, Ed. (Wiley, New York, 1981), pp. 299–305.

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Figures (5)

Fig. 1
Fig. 1

Object and its mathematical cubical model: (a) spheroidal object; (b) N mathematical cells of the same volume as the object.

Fig. 2
Fig. 2

Geometrical location of the points ah along axis z of the spheroid for (a) cross-fire and (b) end-fire polarization.

Fig. 3
Fig. 3

Absorbed power vs aspect ratio of elongated aerosol particles with * = 1.75 + j0.3 and λ = 0.5 μm (visible) for two polarization. Calculations are obtained by the IEBCM and VIEF methods.

Fig. 4
Fig. 4

Absorbed power vs aspect ratio of elongated aerosol particles with * = 3.0 + j1.0 and λ = 10 μm (IR) for two polarizations. Calculations are obtained by the IEBCM and VIEF methods.

Fig. 5
Fig. 5

Three different diagrams of branched chains of aerosol particles that were used in the VIEF calculations. The total number of spheres in each diagram is assumed to be 125.

Tables (10)

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Table I Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r =0.02 μm, * = 1.75 + j0.3, and λ = 0.5 μm (Visible)

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Table II Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r = 0.02 μm, * = 3 + j1, and λ = 10 μm (IR)

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Table III Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, * = 1.75 + j0.3, λ = 0.5 μm (Visible) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20

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Table IV Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, * = 1.75 + j0.3, λ = 0.5 μm (Visible) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20

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Table V Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, * = 3 + j1, λ = 10 μm (IR) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20

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Table VI Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis 0.02 μm, * = 3 + j1, λ = 10 μm (IR) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20

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Table VII Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm, * = 3 + j1, at IR Frequency (λ = 10 μm): Comparison of IEBCM and VIEF Results

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Table VIII Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm,* = 1.75 + j0.3, at Visible Frequency (λ = 0.5 μm) Comparison of IEBCM and VIEF Results

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Table IX Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a

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Table X Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a

Equations (15)

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× E ¯ = j ω μ H ¯ ;
× H ¯ = ( σ + j ω ) E ¯ ;
· H ¯ = 0 ;
· E ¯ = ρ e ;
E ¯ = E ¯ i + E ¯ s ,
H ¯ = H ¯ i + H ¯ s .
E ¯ s = P V υ J ¯ eq ( r ¯ ) · G ( r ¯ , r ¯ ) d υ J ¯ eq ( r ¯ ) 3 j ω 0 ,
J ¯ eq ( r ¯ ) = { σ ( r ¯ ) + j ω [ ( r ¯ ) 0 ] } E ¯ ( r ¯ ) , G ( r ¯ , r ¯ ) = j ω μ 0 ( I + k 0 2 ) ψ ( r ¯ , r ¯ ) , ψ ( r ¯ , r ¯ ) = exp ( j k 0 | r ¯ r ¯ | ) 4 π | r ¯ r ¯ | , k 0 = ω ( μ 0 0 ) 1 / 2 , I = unit dyad .
[ 1 + τ ( r ¯ ) 3 j ω 0 ] E ¯ ( r ¯ ) P V V τ ( r ¯ ) E ¯ ( r ¯ ) · G ( r ¯ , r ¯ ) d V = E ¯ i ( r ¯ ) ,
J ¯ eq ( r ¯ ) 3 j ω 0 , J ¯ eq ( r ¯ ) = τ ( r ¯ ) E ¯ ( r ¯ ) ,
J ¯ eq ( r ¯ ) 3 j ω 0
[ [ G x x ] [ G x y ] [ G x z ] [ G y x ] [ G y y ] [ G y z ] [ G z x ] [ G z y ] [ G z z ] ] [ [ E x ] [ E y ] [ E z ] ] = [ [ E x i ] [ E y i ] [ E z i ] ] ,
G x p x q m n = j ω μ 0 k 0 τ ( r ¯ n ) Δ V n exp ( j α m n ) 4 π α m n 3 [ ( α m n 2 1 j α m n ) δ p q + ( x p m x p n ) ( x q m x q n ) R m n 2 ( 3 α m n 2 + 3 j α m n ) ] m n , G x p x q m n = δ p q { 2 j ω μ 0 τ ( r ¯ n ) 3 k 0 2 [ exp ( j k 0 a n ) ( 1 + j k 0 a n ) 1 ] [ 1 + τ ( r ¯ n ) 3 j ω 0 ] } m = n , δ p q = { 1 p = q , 0 p q , Δ V n = volume of the n th cell = V n d υ , α m n = k 0 R m n R m n = | r ¯ m r ¯ n | , a n = ( 3 Δ V n 4 π ) 1 / 3 , [ E x p ] = [ E x p ( r ¯ 1 ) E x p ( r ¯ 2 ) . . . E x p ( r ¯ n ) ] , [ E x p i ] = [ E x p i ( r ¯ 1 ) E x p i ( r ¯ 2 ) . . . E x p i ( r ¯ n ) ]
[ G ¯ ¯ ] [ E ¯ ] = [ E ¯ i ] .
P a b = υ 1 2 σ | E ¯ | 2 d υ ,

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