Monte Carlo simulation of hard hyperspheres in six, seven and eight dimensions for low to moderate densities

Journal of Statistical Physics

Volumn 126, Issue 2, 2007, Pages 299-314

  Bishop, Marvin ^a   Whitlock, Paula A ^b  

^a MANHATTAN COLLEGE   (United States)

^b CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Equation of state; Hyperspheres; Monte carlo; Pair correlation function

Indexed keywords

EID: 33846656942     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9266-9     Document Type: Article

References (47)

1. H. L. Frisch, N. Rivier, and D. Wyler, Classical Hard-Sphere Fluid in Infinitely Many Dimensions. Phys. Rev. Lett. 54:2061-2063 (1985).
2. H. L. Frisch and J. K. Percus, Nonuniform classical fluid at high dimensionality. Phys. Rev. A 35:4696-4702 (1987).
3. H. L. Frisch and T. K. Percus, High dimensionality as an organizing device for classical fluids. Phys. Rev. E 60:2942-2948 (1999).
4. Y. Song, E. A. Mason, and R. M. Stratt, Why does the Carnahan-Starling equation work so well? J. Phys. Chem. 93:6916-6919 (1989).
5. M. Bishop, P. A. Whitlock, and D. Klein, The structure of hyperspherical fluids in various dimensions. J. Chem. Phys. 122:074508-1-7 (2005).
6. M. Bishop and P. A. Whitlock, The equation of state of hard hyperspheres in four and five dimensions. J. Chem. Phys. 123:014507-1-3 (2005).
7. M. Luban and A. Baram, Third and fourth virial coefficients of hard hyperspheres of arbitrary dimensionality. J. Chem. Phys. 76:3233-3241 (1982).
8. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
9. D. A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976).
10. 4 for Hard Spheres in Even Dimensions. J. Stat. Phys. 114:1343-1361 (2004).
11. I. Lyberg, The fourth virial coefficent of a fluid of hard spheres in odd dimensions. J. Stat. Phys. 119:747-764 (2005).
12. N. Clisby and B. M. McCoy, Negative virial coefficients and the dominance of loose packed diagrams for D-dimensional hard spheres. J. Stat. Phys. 114:1361-1392 (2004).
13. M. Bishop, A. Masters, and J. H. R. Clarke, Equation of state of hard and Weeks-Chandler-Anderson hyperspheres in four and five dimensions. J. Chem. Phys. 110:11449-11453 (1999).
14. N. Clisby and B. M. McCoy, New results for virial coefficients of hard spheres in D-dimensions. Pramana-J. Phys. 64:775-783 (2005).
15. N. Clisby, Negative virial coefficients for hard spheres. Ph.D. Thesis, Department of Physics, SUNY at Stony Brook (2004).
16. M. Bishop, A. Masters, and A. Yu. Vlasov, Higher virial coefficients of four and five dimensional hard hyperspheres. J. Chem. Phys. 121:6884-6886 (2004).
17. M. Bishop, A. Masters, and A. Yu. Vlasov, The eighth virial coefficient of four- and five-dimensional hard hyperspheres. J. Chem. Phys. 122:154502-1-2 (2005).
18. N. Clisby and B. M. McCoy, Ninth and tenth order virial coefficients for hard spheres in D-dimensions. J. Stat. Phys. 122:15-57 (2006).
19. G. A. Baker and P. Graves-Morris, Padé Approximants (Cambridge University Press, Cambridge, 1996).
20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University Press, Cambridge, 1992).
21. M. Baus and J. L. Colot, Thermodynamics and structure of a fluid of hard rods, disks, spheres or hyperspheres from rescaled virial expansions. Phys. Rev. A 36:3912-3925 (1987).
22. M. Luban and J. P. J. Michels, Equation of state of hard D-dimensional hyperspheres. Phys. Rev A 41:6796-6804 (1990).
23. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087-1092 (1953).
24. B. L. Holian, O. E. Percus, T. T. Warnock, and P. A. Whitlock, Pseudorandom number generator for massively parallel molecular dynamics simulations. Phys. Rev. E 50:1607-1615 (1994).
25. T. Gurov and P. A. Whitlock, Investigation of the sensitivity of the Monte Carlo solution for the Barker-Ferry equation using different sequential and parallel pseudorandom number generators. In Lecture Notes in Computer Science, Number 3039, M. Bubak, G.D. van Albada, and P.M.A. Sloot (eds.) (Springer Verlag, Heidelberg, 2004).
26. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1993).
27. B. Quentrec and C. Brot, New method for searching for neighbors in molecular dynamics computations. J. Comp. Phys. 13:430-432 (1973).
28. K. Ying, D. Arnow, and D. Clark, Evaluating Communication Protocols for WebComputing. In Proceedings of the 1999 International Conference on Parallel and Distributed Processing Techniques and Applications, CSREA Press, Las Vegas, June, 1999.
29. D. Arnow, G. Weiss, K. Ying, and D. Clark, SWC: A Small Framework for WebComputing. In Proceedings of the International Conference on Parallel Computing, Delft, Netherlands, August, 1999.
30. P. A. Whitlock, M. Bishop, and D. Klein, Small Web Computing Applied to Distributed Monte Carlo Calculations. In Lecture Notes in Computer Science, Number 3993, V.N. Alexandrov, G.D. van Albada, P.M.A. Sloot, and J. Dongarra (eds.) (Springer Verlag, Heidelberg, 2006).
31. J. M. Haile, Molecular Dynamics Simulation (John-Wiley and Sons, New York, 1992).
32. R. Kubo, Statistical Mechanics (North-Holland, Amsterdam, 1965).
33. M. Robles, M. L. de Haro, and A. Santos, Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations. J. Chem. Phys. 120:9113-9122 (2004).
34. L. Lue and M. Bishop, Molecular Dynamics Study of the Thermodynamics and Transport Coefficients of Hard Hyperspheres in Six and Seven Dimensions. Phys. Rev. E 74:021201-1-6 (2006).
35. N. F. Carnahan and K. E. Starling, Equation of state of nonattracting rigid spheres. J. Chem. Phys. 51:635-636 (1969).
36. A. Santos, An equation of state á la Carnahan-Starling for a five-dimensional fluid of hard hyperspheres. J. Chem. Phys. 112:10680-10681 (2000).
37. L. Lue and M. Bishop, Private Communication.
38. L. Tonks, The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres. Phys. Rev. 50:955-963 (1936).
39. B. J. Alder and T. E. Wainwright, Phase Transition in Elastic Disks. Phys. Rev. 127:359-361 (1962).
40. W. W. Wood, Physics of Simple Liquids. H.N.V. Temperley, J.S. Rowlinson, and G.S. Rushbrooke (eds.) (North-Holland, Amsterdam, 1968).
41. B. J. Alder and T. E. Wainwright, Phase transition for a hard sphere system. J. Chem. Phys. 27:1208-1211 (1957).
42. W. W. Wood and J. D. Jacobson, Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres. J. Chem. Phys. 27:1207 (1957).
43. J. P. J. Michels and N. J. Trappeniers, Dynamical Computer Simulations on Hard Hyperspheres in Four- and Five-Dimensional Space. Phys. Lett. 104:425-429 (1984).
44. J. L. Colot and M. Baus, The Freeezing of Hard Disks and Hyperspheres. Phys. Lett. A 119:135-139 (1986).
45. B. Bagchi and S. A. Rice, On the stability of the infinite dimensional fluid of hard hyperspheres: a statistical mechanical estimate of the density of closest packing of simple hypercubic lattices in spaces of large dimensionality. J. Chem. Phys. 88:1177-1184 (1988).
46. R. Finken, M. Schmidt, and H. Lowen, Freeezing transition of hard hyperspheres. Phys. Rev. E 65:016108-1-9 (2001).
47. M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, Packing Hyperspheres in high-dimensional Euclidean spaces. Phys. Rev. E74: 041127-1-11 (2006).