Skip to main content
SpringerLink
Log in

Determination of radiation reflection and transmission operators in a slab

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

In the framework of a discrete radiative transfer model, a method is proposed for finding the reflection and transmission operators in the conservative case.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Bellman and G. Wing, An Introduction to Invariant Imbedding (Wiley, New York, 1975).

    MATH  Google Scholar 

  2. Alan Ping and I Wang, “Discrete radiative transfer in slabs,” J. Math. Anal. Appl. 24, 530–544 (1968).

    Article  MathSciNet  Google Scholar 

  3. M. G. Muradyan, “On the solution of a problem of transport theory,” Comput. Math. Math. Phys. 33(2), 241–250 (1993).

    MathSciNet  Google Scholar 

  4. M. G. Muradyan, “Analytical solution of the radiation-transfer problem in a periodic medium,” Comput. Math. Math. Phys. 37, 770–774 (1997).

    MathSciNet  Google Scholar 

  5. M. G. Muradyan, “Nonlinear equations and boundary value problems for linear ordinary differential equations,” in Differential and Integral Equations: Collection of Scientific Works (Yerevan, 1979), pp. 49–66 [in Russian].

    Google Scholar 

  6. R. Bellman, K. L. Cooke, R. Kolaba, and G. M. Wing, “Existence and Uniqueness Theorems in Invariant Imbedding I; Conservation Principles II,” J. Math. Anal. Appl. 10, 234–244 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. A. Ambartsumyan, Scientific Works (Akad. Nauk Arm. SSR, Yerevan, 1960), Vol. 1 [in Russian].

    Google Scholar 

  8. N. B. Engibaryan and E. A. Melkonyan, “Radiation transfer in a slab and Ambartsumyan’s equation,” in Invariance Principle and Its Applications (Akad. Nauk Arm. SSR, Yerevan, 1989), pp. 326–333 [in Russian].

    Google Scholar 

  9. M. G. Mouradian (Muradyan), “Analytical solution of the linear problem of radiation transfer in a plane homogeneous Layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 477–481 (1991).

    Article  Google Scholar 

  10. F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1959; Nauka, Moscow, 1988).

    MATH  Google Scholar 

  11. A. Shimizu and K. Aoki, Application of Invariant Imbedding to Reactor Physics (Academic, New York, 1972).

    Google Scholar 

  12. N. B. Engibaryan and M. A. Mnatsakanyan, “On linear transport problems,” Dokl. Akad. Nauk SSSR 217, 533–535 (1974).

    MathSciNet  Google Scholar 

  13. M. G. Muradyan, Doctoral Dissertation in Physics and Mathematics (Beloruss. Gos. Univ., Minsk, 1998).

    Google Scholar 

  14. M. G. Muradyan, “The Milne problem for a periodic medium,” Differ. Equations 40, 1113–1121 (2004).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Armenian State University of Economics, ul. Nalbandyan 128, Yerevan, 0025, Armenia

    M. G. Muradyan

Authors
  1. M. G. Muradyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. G. Muradyan.

Additional information

Original Russian Text © M.G. Muradyan, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 3, pp. 529–535.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muradyan, M.G. Determination of radiation reflection and transmission operators in a slab. Comput. Math. and Math. Phys. 54, 546–552 (2014). https://doi.org/10.1134/S0965542514030129

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542514030129

Keywords

Search

Navigation