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Equations of State for Various Dimensional Hard Hyper-sphere Fluids

  • Sumit Kaur
  • Binay Prakash Akhouri
  • Praveen Singh
Conference paper

Abstract

We confirm the observations of Luban and Michel [Phys Rev A41:6796 (1990)] in five and Santos et al. [J Chem Phys 120:9113 (2004)] in seven dimensions that the equation of state fits the computer simulation data nearly as well as any other proposed form of equation of state for hard hyper-sphere fluids. We also confirm the observations of Song, Mason, and Stratt [J Phys Chem 93:6916 (1989)] that their theoretical predictions in terms of pair correlation functions in all the dimensions fits the computer simulation data very well.

References

  1. 1.
    Luban M, Bram A (1988) Third and fourth virial coefficients of hard hyperspheres of arbitrary dimensionality. J Chem Phys 6:1976Google Scholar
  2. 2.
    Baus M, Colot JL (1987) Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansion. Phys Rev A 36:3912CrossRefGoogle Scholar
  3. 3.
    Lyberg I (2008) The fourth virial coefficient of a fluid of hard spheres in odd dimensions. Cond Mat Stat Mech 2:11794–13840Google Scholar
  4. 4.
    Bishop M, Masters A, Vlasov AY (2004) Higher vial coefficients of four and five dimensional hard hyperspheres. J Chem Phys 121(14):6884–6886CrossRefGoogle Scholar
  5. 5.
    McCoy BM, Clisby N (2005) New results for virial coefficients of hard spheres in D dimensions. Pramana Ind Acad Sci 64(5):775–783Google Scholar
  6. 6.
    McCoy BM, Clisby N (2004) Analytical calculation of B4 for hard spheres in even dimensions. J Stat Phys 114:1343–1360CrossRefGoogle Scholar
  7. 7.
    Bishop M, Whitlock PA, Klein D (2005) The structure of hyperspherical fluids in various dimensions. J Chem Phys 122(7):074508CrossRefGoogle Scholar
  8. 8.
    Bishop M, Andrew MA, Vlasov Yu (2005) The eight virial coefficient of four and five dimensional hard hyperspheres. J Chem Phys 122(15):1882273CrossRefGoogle Scholar
  9. 9.
    Lue L, Bishop M, Whitlock PA (2010) The fluid to solid phase transition of hard hyperspheres in four and five dimensions. J Chem Phys 132(10):104509CrossRefGoogle Scholar
  10. 10.
    Bishop M, Clisby N, Whitlock PA (2008) The equation of state of hard hyperspheres in nine dimensions for low to moderate densities. J Chem Phys 128(3):034506CrossRefGoogle Scholar
  11. 11.
    Bishop M, Whitlock PA (2007) Monte Carlo simulation of hard hyperspheres in six, seven and eight dimensions for low to moderate densities. J Chem Phys 126(2):299–314MathSciNetCrossRefGoogle Scholar
  12. 12.
    Whitlock PA, Bishop M, Tiglias JL (2007) Structure factor for hard hyperspheres in higher dimensions. J Chem Phys 126(22):224505CrossRefGoogle Scholar
  13. 13.
    Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic press, LondonzbMATHGoogle Scholar
  14. 14.
    Sanchez IC (1994) Virial coefficients and close-packing of hard spheres and disks. J Chem Phys 101:7003CrossRefGoogle Scholar
  15. 15.
    Colot JL, Baus M (1986) The freezing of hard disks and hyperspheres. Phys Lett A 119(3):135–139CrossRefGoogle Scholar
  16. 16.
    Song Y, Mason EA, Stratt M (1989) Why does the Carnahan-Starling equation work so well? J Che Phys 93(19):6916–6919CrossRefGoogle Scholar
  17. 17.
    Luban M, Michels JPJ (1990) Equation of state of hard D-dimensional hypersphere. Phys Rev A 41(12):6796–6804CrossRefGoogle Scholar
  18. 18.
    Amros J, Solana JR, Villar E (1989) Equations of state for four and five dimensional hard hypersphere Fluids. Phys Chem Liq 19:119–124Google Scholar
  19. 19.
    Maeso MJ, Solana JR, Amros J, Villar E (1991) Equation of state for D-dimensional hard sphere fluids. Matt Chem Phys 30(11):39–42CrossRefGoogle Scholar
  20. 20.
    Carnahan NF, Starling NE (1969) Equation of state for non-attracting Rigid Spheres. J Chem Phys 51:635CrossRefGoogle Scholar
  21. 21.
    Rohrmann D, Robles M, de Haro L, Santos A (2008) Virial series for fluids of hard hyperspheres in odd dimensions. J Chem Phys 129:014510CrossRefGoogle Scholar
  22. 22.
    Santos A (2008) An equation of state Carnahan-Starling for a five-dimensional fluid of hard hyperspheres. J Stat Mech 8:1–3Google Scholar
  23. 23.
    Robles M, de Haro ML, Santos A (2008) Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations. Cond Mat Stat Mech 129:014510Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Sumit Kaur
    • 1
  • Binay Prakash Akhouri
    • 2
  • Praveen Singh
    • 3
  1. 1.Department of PhysicsNirmala CollegeRanchiIndia
  2. 2.Department of PhysicsBirsa CollegeKhuntiIndia
  3. 3.Department of Mechanical EngineeringAmity UniversityRanchiIndia

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