Advertisement

Mathematical Notes

, Volume 92, Issue 3–4, pp 402–411 | Cite as

Mathematical justification for the transition to negative pressures of the new ideal liquid

  • V. P. MaslovEmail author
Article

Abstract

Negative pressure also means negative energy and, therefore, “holes,” antiparticles. Continuation across infinity to negative energies is accomplished by using a parastatistical correction to the Bose-Einstein distribution.

Keywords

antiparticles holes negative pressure transition from the liquid phase to pumice binodal spinodal chemical potential temperature triple point law of corresponding states Van der Waals model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V.P. Maslov, “Degeneration on passing from a discrete spectrum to a continuous one and transition from quantum mechanics to classical mechanic,” Dokl.-Akad.-Nauk-SSSR (N.S.) 114, 957–960 (1957).MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. P. Maslov, Zeno-line, Binodal, T − ρ Diagram and Clusters as a new Bose-Condensate Bases on New Global Distributions in Number Theory, arXiv:1007.4182v3 [math-ph], 28 Dec 2010.Google Scholar
  3. 3.
    Yu. I. Manin, “Reflections on arithmetical physics,” in Conformal Invariance and String Theory, Poiana Brasov, 1987 (Academic Press, 1989), pp. 293–303; Mathematics as a Metaphor (MTsNMO, Moscow, 2008) [in Russian].Google Scholar
  4. 4.
    V.P. Maslov and T. V. Maslova, “An unbounded theory of probability and its applications,” Teor. Veroyatnost. Primenen. 57(3) (2012) (in press).Google Scholar
  5. 5.
    V. P. Maslov, “On the mathematical justification of experimental and computer physics,” Mat. Zametki, 92(4), 577–579 (2012).Google Scholar
  6. 6.
    I. A. Kvasnikov, Thermodynamics and Statistical Physics: Theory of Equilibrium Systems (URSS, Moscow, 2002), Vol. 2 [in Russian].Google Scholar
  7. 7.
    V. P. Maslov, Threshold Levels in Economics, arXiv:0903.4783v2 [q-fin. ST], 3 Apr 2009.Google Scholar
  8. 8.
    L. D. Landau and E.M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian].Google Scholar
  9. 9.
    V. P. Maslov, “Bose Condensate in the D-Dimensional Case, in particular, for D = 2,” Russ. J. Math. Phys. 19(3), 1–10 (2012).MathSciNetGoogle Scholar
  10. 10.
    V. P. Maslov “Taking parastatistical corrections to the Bose-Einstein distribution into account in the quantum and classical cases,” Teoret. Mat. Fiz. 172(3), 468–478 (2012) [Theoret. and Math. Phys. 172 (3), 1289–1299 (2012)].CrossRefGoogle Scholar
  11. 11.
    K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure”, The Journal of Chemical Physics 133, 174507, 1–8 (2010).Google Scholar
  12. 12.
    V. G. Baidakov and S. P. Protsenko, “Singular point of a system of Lennard-Jones particles at negative pressures,” Phys. Rev. Lett. 95(1) (2005).Google Scholar
  13. 13.
    F. Caupin, A. Arvengas, K. Davitt, M. M. Azouzi, K. I. Shmulovich et al., “Exploring Water and Other Liquids at Negative Pressure,” J. Phys.: Condens. Matter 24 1–7 (2012).CrossRefGoogle Scholar
  14. 14.
    E. M. Apfelbaum and V. S. Vorob’ev, “Correspondence between of the ideal Bose gas in a space of fractional dimension and a dense nonideal gas according to Maslov scheme”, Russian J. Math. Phys. 18(1), 19–25 (2011).MathSciNetGoogle Scholar
  15. 15.
    V. P. Maslov, “On Unbounded Probability Theory,” Math. Notes 92(1), 59–63, (2012).CrossRefGoogle Scholar
  16. 16.
    V. P. Maslov and T.V. Maslova, “Probability Theory for Random Variables with Unboundedly Growing Values and Its Applications,” Russian J. Math. Phys. 19(3), 324–339, (2012).MathSciNetCrossRefGoogle Scholar
  17. 17.
    V. P. Maslov and P. P. Mosolov, NonlinearWave Equations Perturbed by Viscous Terms (Walter de Gruyter, Berlin, 2000).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

Personalised recommendations