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Asymptotics of activity series at the divergence point

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Abstract

For statistical models of imperfect gases, a new method is proposed to evaluate the reducible cluster integrals of very high (actually unlimited) orders on the basis of information on the irreducible integrals (virial coefficients) or information on the corresponding radius of convergence for the virial series in powers of activity. This method is used to transform conventional expansions for pressure and density in powers of activity to a functional form that allows the analytical study of those series at the vicinity of their divergence point. In particular, the results of this study confirm the adequacy of the cluster-based approach at the condensation region and agree with the results of the previous studies of partition function in terms of irreducible integrals.

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References

  1. M V Ushcats, Phys. Rev. Lett. 109, 040601 (2012)

    Article  ADS  Google Scholar 

  2. J E Mayer and M Goeppert Mayer, Statistical mechanics (John Wiley, New York, 1977)

    MATH  Google Scholar 

  3. M V Ushcats, J. Chem. Phys. 138, 094309 (2013)

    Article  ADS  Google Scholar 

  4. M V Ushcats, Phys. Rev. E 87, 042111 (2013)

    Article  ADS  Google Scholar 

  5. Vishnu M Bannur, Physica A 419, 675 (2015)

    Article  ADS  Google Scholar 

  6. M V Ushcats, L A Bulavin, V M Sysoev, V Yu Bardik and A N Alekseev, J. Mol. Liq. 224, 694 (2016)

  7. J F Cariñena, A G Choudhury and P Guha, Pramana – J. Phys. 84 (3), 373 (2015)

    Article  ADS  Google Scholar 

  8. R K Pathria, Statistical mechanics (Butterworth-Heinemann, Oxford, 1996)

    MATH  Google Scholar 

  9. R Sarath and P C Vinodkumar, Pramana – J. Phys. 85(1), 77 (2015)

    Article  ADS  Google Scholar 

  10. M V Ushcats, L A Bulavin, V M Sysoev and S Yu Ushcats, Ukr. J. Phys. 62, 533 (2017)

    Article  Google Scholar 

  11. M V Ushcats, L A Bulavin, V M Sysoev and S Yu Ushcats, Phys. Rev. E 96, 062115 (2017)

    Article  ADS  Google Scholar 

  12. A J Schultz and D A Kofke, Mol. Phys. 107, 2309 (2009)

    Article  ADS  Google Scholar 

  13. M V Ushcats, Ukr. J. Phys. 59, 737 (2014)

    Article  Google Scholar 

  14. M V Ushcats, Ukr. J. Phys. 59, 172 (2014)

    Article  Google Scholar 

  15. M V Ushcats, J. Chem. Phys. 140, 234309 (2014)

    Article  ADS  Google Scholar 

  16. M V Ushcats, S Yu Ushcats and A A Mochalov, Ukr. J. Phys. 61, 160 (2016)

    Article  Google Scholar 

  17. M V Ushcats, J. Chem. Phys. 141, 101103 (2014)

    Article  ADS  Google Scholar 

  18. C Feng, A J Schultz, V Chaudhary and D A Kofke, J. Chem. Phys. 143, 044504 (2015)

    Article  ADS  Google Scholar 

  19. E Donoghue and J H Gibbs, J. Chem. Phys. 74, 2975 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  20. J H Gibbs, B Bagchi and U Mohanty, Phys. Rev. B 24, 2893 (1981)

    Article  ADS  Google Scholar 

  21. R J Wheatley, Phys. Rev. Lett. 110, 200601 (2013)

    Article  ADS  Google Scholar 

  22. M V Ushcats, L A Bulavin, V M Sysoev and S Yu Ushcats, Phys. Rev. E 94, 012143 (2016)

    Article  ADS  Google Scholar 

  23. J Hadamard, Journal de Mathématiques Pures et Appliquées 8, 101 (1892)

    Google Scholar 

  24. T D Lee and C N Yang, Phys. Rev. 87, 410 (1952)

    Article  ADS  Google Scholar 

  25. M V Ushcats, Phys. Rev. E 91, 052144 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  26. J E Lennard-Jones, Proc. R. Soc. London A 106, 441 (1924)

    Article  ADS  Google Scholar 

  27. J E Lennard-Jones, Proc. R. Soc. London A 106, 463 (1924)

    Article  ADS  Google Scholar 

  28. J Groeneveld, Phys. Lett. 3, 50 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  29. O Penrose, J. Math. Phys. 4, 1312 (1963)

    Article  ADS  Google Scholar 

  30. J L Lebowitz and O Penrose, J. Math. Phys. 5, 841 (1964)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Physics Department, Admiral Makarov National University of Shipbuilding, Mykolayiv , 54025, Ukraine

    Svetlana Ushcats & Mykhailo Ushcats

  2. Department of Molecular Physics, Taras Shevchenko University of Kiev, Kiev , 03680, Ukraine

    Mykhailo Ushcats, Leonid Bulavin & Oksana Svechnikova

  3. Department of Information Management Systems and Technologies, Admiral Makarov National University of Shipbuilding, Mykolayiv , 54025, Ukraine

    Ihor Mykheliev

Authors
  1. Svetlana Ushcats
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  2. Mykhailo Ushcats
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  3. Leonid Bulavin
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  4. Oksana Svechnikova
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  5. Ihor Mykheliev
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Corresponding author

Correspondence to Mykhailo Ushcats.

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Ushcats, S., Ushcats, M., Bulavin, L. et al. Asymptotics of activity series at the divergence point. Pramana - J Phys 91, 31 (2018). https://doi.org/10.1007/s12043-018-1604-3

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  • DOI: https://doi.org/10.1007/s12043-018-1604-3

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