Skip to main content
SpringerLink
Log in

Large Index Asymptotics of Collision Integral Kernels of the Linear Boltzmann Equation in the Case of Hard-Sphere Potential

  • Published:
Technical Physics Letters Aims and scope Submit manuscript

Abstract

We have identified the asymptotic behavior of the kernels with large indices of integral operators representing the coefficients of expansion in Legendre polynomials of the collision integral of the linear Boltzmann equation for hard-sphere potential. In the case of interacting particles with nonequal absolute values of velocities, the kernels exhibit exponential decay, where the base of the exponent contains the ratio of the lower to higher velocity. In the case of interacting particles with equal absolute values of velocities, the kernels decay according to the power law.

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. White, R. Robson, S. Dujko, P. Nicoletopoulos, and B. Li, J. Phys. D: Appl. Phys. 42, 194001 (2009).

    Article  ADS  Google Scholar 

  2. D. A. Konovalov, D. G. Cocks, and R. D. White, Eur. Phys. J. D 71, 258 (2017).

    Article  ADS  Google Scholar 

  3. A. Mustafaev, A. Grabovskiy, O. Murillo, and V. Soukhomlinov, J. Phys.: Conf. Ser. 958, 012005 (2018).

    Google Scholar 

  4. A. Ya. Ender, I. A. Ender, L. A. Bakaleinikov, and E. Yu. Flegontova, Tech. Phys. 57, 735 (2012).

    Article  Google Scholar 

  5. J. Ferziger and H. Kaper, Mathematical Theory of Transfer Processes in Gases (North-Holland, Amsterdam, 1972).

    Google Scholar 

  6. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1980; Fizmatgiz, Moscow, 1962).

    Google Scholar 

  7. E. Ya. Riekstyn’sh, Asymptotic Expansions of Integrals (Zinatne, Riga, 1981), Vol. 3 [in Russian].

  8. N. N. Lebedev, Special Functions and Their Applications (Fizmatgiz, Moscow, Leningrad, 1963) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, 194201, Russia

    L. A. Bakaleinikov, E. A. Tropp & E. Yu. Flegontova

Authors
  1. L. A. Bakaleinikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Tropp
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Yu. Flegontova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Yu. Flegontova.

Additional information

Original Russian Text © L.A. Bakaleinikov, E.A. Tropp, E.Yu. Flegontova, 2018, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2018, Vol. 44, No. 16, pp. 33–40.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bakaleinikov, L.A., Tropp, E.A. & Flegontova, E.Y. Large Index Asymptotics of Collision Integral Kernels of the Linear Boltzmann Equation in the Case of Hard-Sphere Potential. Tech. Phys. Lett. 44, 719–722 (2018). https://doi.org/10.1134/S1063785018080187

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063785018080187

Search

Navigation