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Equations of State for Various Dimensional Hard Hyper-sphere Fluids

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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.

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References

  1. Luban M, Bram A (1988) Third and fourth virial coefficients of hard hyperspheres of arbitrary dimensionality. J Chem Phys 6:1976

    Google Scholar 

  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 36:3912

    Article  Google Scholar 

  3. Lyberg I (2008) The fourth virial coefficient of a fluid of hard spheres in odd dimensions. Cond Mat Stat Mech 2:11794–13840

    Google Scholar 

  4. Bishop M, Masters A, Vlasov AY (2004) Higher vial coefficients of four and five dimensional hard hyperspheres. J Chem Phys 121(14):6884–6886

    Article  Google Scholar 

  5. McCoy BM, Clisby N (2005) New results for virial coefficients of hard spheres in D dimensions. Pramana Ind Acad Sci 64(5):775–783

    Google Scholar 

  6. McCoy BM, Clisby N (2004) Analytical calculation of B4 for hard spheres in even dimensions. J Stat Phys 114:1343–1360

    Article  Google Scholar 

  7. Bishop M, Whitlock PA, Klein D (2005) The structure of hyperspherical fluids in various dimensions. J Chem Phys 122(7):074508

    Article  Google Scholar 

  8. Bishop M, Andrew MA, Vlasov Yu (2005) The eight virial coefficient of four and five dimensional hard hyperspheres. J Chem Phys 122(15):1882273

    Article  Google Scholar 

  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):104509

    Article  Google Scholar 

  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):034506

    Article  Google Scholar 

  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):299–314

    Article  MathSciNet  Google Scholar 

  12. Whitlock PA, Bishop M, Tiglias JL (2007) Structure factor for hard hyperspheres in higher dimensions. J Chem Phys 126(22):224505

    Article  Google Scholar 

  13. Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic press, London

    MATH  Google Scholar 

  14. Sanchez IC (1994) Virial coefficients and close-packing of hard spheres and disks. J Chem Phys 101:7003

    Article  Google Scholar 

  15. Colot JL, Baus M (1986) The freezing of hard disks and hyperspheres. Phys Lett A 119(3):135–139

    Article  Google Scholar 

  16. Song Y, Mason EA, Stratt M (1989) Why does the Carnahan-Starling equation work so well? J Che Phys 93(19):6916–6919

    Article  Google Scholar 

  17. Luban M, Michels JPJ (1990) Equation of state of hard D-dimensional hypersphere. Phys Rev A 41(12):6796–6804

    Article  Google Scholar 

  18. Amros J, Solana JR, Villar E (1989) Equations of state for four and five dimensional hard hypersphere Fluids. Phys Chem Liq 19:119–124

    Google Scholar 

  19. Maeso MJ, Solana JR, Amros J, Villar E (1991) Equation of state for D-dimensional hard sphere fluids. Matt Chem Phys 30(11):39–42

    Article  Google Scholar 

  20. Carnahan NF, Starling NE (1969) Equation of state for non-attracting Rigid Spheres. J Chem Phys 51:635

    Article  Google Scholar 

  21. Rohrmann D, Robles M, de Haro L, Santos A (2008) Virial series for fluids of hard hyperspheres in odd dimensions. J Chem Phys 129:014510

    Article  Google Scholar 

  22. Santos A (2008) An equation of state Carnahan-Starling for a five-dimensional fluid of hard hyperspheres. J Stat Mech 8:1–3

    Google Scholar 

  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 129:014510

    Google Scholar 

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Correspondence to Sumit Kaur .

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Kaur, S., Akhouri, B.P., Singh, P. (2019). Equations of State for Various Dimensional Hard Hyper-sphere Fluids. In: Chattopadhyay, J., Singh, R., Prakash, O. (eds) Renewable Energy and its Innovative Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-13-2116-0_11

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  • DOI: https://doi.org/10.1007/978-981-13-2116-0_11

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  • Online ISBN: 978-981-13-2116-0

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