Skip to main content
Log in

On Mathematical Investigations Related to the Chernobyl Disaster

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

Together with the Darcy filtration model, another model of beta-radiation filtering is considered. This model is related to the heap paradox problem and to numeration theory. The phase transition from liquid to amorphous solid, which changes with temperature and preserves the numeration of particles, is described.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. P. Maslov, “My Dear Ludvig,” Mat. Zametki 101 (6), 803–806 (2017) [Math. Notes 101 (6), 925–927 (2017)].

    Article  MATH  Google Scholar 

  2. V. P. Maslov, V. P. Myasnikov, and V. G. Danilov, Mathematical Modeling of the Accident Block of Chernobyl Atomic Station (Nauka, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  3. V. P. Maslov and I. A. Molotkov, “High-Temperature Processes in a Porous Medium,” High Temperature 47 (2), 223–227 (2009).

    Article  Google Scholar 

  4. V. P. Maslov and I. A. Molotkov, “Steady Cooling and Global Overheating Process in a Hazardous Reactor,” Journal of Applied Mathematics and Mechanics 72, 689–693 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  5. Yu. L. Ershov, Numeration Theory (Nauka, Moscow, 1977).

    Google Scholar 

  6. G. L. Litvinov, “Maslov Dequantization, Idempotent and Tropical Mathematics: a Brief Introduction,” J. Math. Sci. 140 (3), 426–444 (2007).

    Article  MathSciNet  Google Scholar 

  7. E. M. Lifshits and L. P. Pitaevskii, Theoretical Physics, vol. X, Physical Kinetics (Fizmatlit, Moscow, 2007).

    Google Scholar 

  8. M. de Gosson, “On the Leray–Maslov Quantization of Lagrangian Submanifolds,” J. Geom. Phys. 13 (2), 158–168 (1994).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non- Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London–Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).

    Google Scholar 

  10. V. P. Maslov, “Mathematical Aspects of Weakly Nonideal Bose and Fermi Gases on a Crystal Base,” Funktsional. Anal. i Prilozhen. 37 (2), 16–27 (2003) [Functional Anal. Appl. 37 (2), (2003)].

    Article  MathSciNet  MATH  Google Scholar 

  11. V. P. Maslov, Quantum Economics (Nauka, Moscow, 2006) [in Russian].

    MATH  Google Scholar 

  12. N. Bohr and F. Kalckar “On the Transmution of Atomic Nuclei by Impact of Material Particles, I.” Kgl. Danske Vidensk Selskab Mat. Fys. Medd. 14 (10), 1–40 (1937) [Uspekhi Fiz. Nauk 20 (3), 317–340 (1938)].

    Google Scholar 

  13. F. C. Auluck and D. S. Kothari, “Statistical Mechanics and the Partitions of Numbers,” Math. Proc. Cambridge Philos. Soc. 42, 272–277 (1946).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. B. K. Agarwala and F. C. Auluck, “Statistical Mechanics and the Partitions Into Non-Integral Powers of Integers,” Math. Proc. Cambridge Philos. Soc. 47 (1), 207–216 (1951).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. A. Rovenchak, Statistical Mechanics Approach in the Counting of Integer Partitions arXiv:1603.01049v1 [math-ph] 3 Mar 2016.

    MATH  Google Scholar 

  16. A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971) [in Russian].

    MATH  Google Scholar 

  17. L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  18. W.-S. Dai and M. Xie, “Gentile Statistics with a Large Maximum Occupation Number,” Annals of Physics 309, 295–305 (2004).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. V. P. Maslov, “Analytical Number Theory and the Energy of Transition of the Bose Gas to the Fermi Gas. Critical Lines as Boundaries of the Noninteracting Gas (an Analog of the Bose Gas) in Classical Thermodynamics,” Russian J. Math. Phys., 25 (2), 220–232 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  20. V. P. Maslov, “New Insight into the Partition Theory of Integers Related to Problems of Thermodynamics and Mesoscopic Physics,” Math. Notes 102 (2), 234–251 (2017).

    MathSciNet  MATH  Google Scholar 

  21. A. Weinstein, “The Maslov cycle as a Legendre singularity and projection of a wavefront set,” Bulletin of the Brazilian Math. Society, New Series 44 (4), 593–610 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  22. V. Guillemin, S. Sternerg, Geometric asymptotics (Amer. Math. soc., Providence, Rhode Island, 1977).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. P. Maslov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maslov, V.P. On Mathematical Investigations Related to the Chernobyl Disaster. Russ. J. Math. Phys. 25, 309–318 (2018). https://doi.org/10.1134/S1061920818030044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920818030044

Navigation