Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 5, 2010, Pages

  Chavanis, P H ^a   Delfini, L ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BACTERIAL POPULATION; CANONICAL ENSEMBLE; KELLER-SEGEL MODEL; LONG RANGE; LONG RANGE INTERACTIONS; NEUTRALIZING BACKGROUND; NEWTONIANS; SCREENING LENGTHS; SELF-GRAVITATING SYSTEMS;

BACTERIOLOGY; BIOCHEMISTRY; COSMOLOGY;

PHASE TRANSITIONS;

EID: 77952045280     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.051103     Document Type: Article

References (78)

1. J. D. Murray, Mathematical Biology (Springer, Berlin, 1991).
2. A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. Di Talia, E. Giraudo, G. Serini, L. Preziosi, and F. Bussolino, Phys. Rev. Lett. 90, 118101 (2003). 10.1103/PhysRevLett.90.118101
3. E. Keller and L. A. Segel, J. Theor. Biol. 26, 399 (1970). 10.1016/0022-5193(70)90092-5
4. P. H. Chavanis, Eur. Phys. J. B 62, 179 (2008). 10.1140/epjb/e2008-00142- 9 (Pubitemid 351535293)
5. C. Sire and P. H. Chavanis, Phys. Rev. E 78, 061111 (2008). 10.1103/PhysRevE.78.061111
6. P. H. Chavanis, M. Ribot, C. Rosier, and C. Sire, Banach Cent Publ. 66, 103 (2004). 10.4064/bc66-0-7
7. B. Perthame, Appl. Math. (Germany) 49, 539 (2004). 10.1007/s10492-004- 6431-9 (Pubitemid 40041663)
8. T. Nagai, Adv. Math. Sci. Appl. 5, 581 (1995).
9. P. H. Chavanis, Physica A 361, 55 (2006). 10.1016/j.physa.2005.06.087 (Pubitemid 41627543)
10. D. R. Nicholson, Introduction to Plasma Theory (Krieger, Florida, 1992).
11. W. Jäger and S. Luckhaus, Trans. Am. Math. Soc. 329, 819 (1992). 10.2307/2153966
12. J. Peebles, Large-Scale Structures of the Universe (Princeton University Press, Princeton, 1980).
13. V. A. Antonov, Vest. Leningr. Gos. Univ. 7, 135 (1962).
14. D. Lynden-Bell and R. Wood, Mon. Not. R. Astron. Soc. 138, 495 (1968).
15. E. B. Aronson and C. J. Hansen, Astrophys. J. 177, 145 (1972). 10.1086/151693
16. G. Horwitz and J. Katz, Astrophys. J. 211, 226 (1977). 10.1086/154924
17. G. Horwitz and J. Katz, Astrophys. J. 222, 941 (1978). 10.1086/156213
18. J. Katz, Mon. Not. R. Astron. Soc. 183, 765 (1978).
19. J. Katz and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 184, 709 (1978).
20. J. Katz and M. Lecar, Astrophys. Space Sci. 68, 495 (1980). 10.1007/BF00639714
21. M. Kiessling, J. Stat. Phys. 55, 203 (1989). 10.1007/BF01042598
22. T. Padmanabhan, Phys. Rep. 188, 285 (1990). 10.1016/0370-1573(90)90051-3
23. B. Stahl, M. Kiessling, and K. Schindler, Planet. Space Sci. 43, 271 (1995). 10.1016/0032-0633(94)00188-W
24. J. J. Aly and J. Perez, Phys. Rev. E 60, 5185 (1999). 10.1103/PhysRevE.60.5185
25. H. J. de Vega and N. Sanchez, Nucl. Phys. B 625, 409 (2002). 10.1016/S0550-3213(02)00025-1
26. H. J. de Vega and N. Sanchez, Nucl. Phys. B 625, 460 (2002). 10.1016/S0550-3213(02)00026-3
27. P. H. Chavanis, Astron. Astrophys. 381, 340 (2002). 10.1051/0004-6361: 20011438
28. P. H. Chavanis, Phys. Rev. E 65, 056123 (2002). 10.1103/PhysRevE.65. 056123 (Pubitemid 40606859)
29. C. Sire and P. H. Chavanis, Phys. Rev. E 66, 046133 (2002). 10.1103/PhysRevE.66.046133 (Pubitemid 40606257)
30. J. Katz, Found. Phys. 33, 223 (2003). 10.1023/A:1023776921610
31. P. H. Chavanis, Astron. Astrophys. 401, 15 (2003). 10.1051/0004-6361: 20021779
32. P. H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006). 10.1142/S0217979206035400 (Pubitemid 44481503)
33. S. Inagaki, Prog. Theor. Phys. 90, 577 (1993). 10.1143/PTP.90.577
34. M. Antoni and S. Ruffo, Phys. Rev. E 52, 2361 (1995). 10.1103/PhysRevE.52.2361
35. P. H. Chavanis, J. Vatteville, and F. Bouchet, Eur. Phys. J. B 46, 61 (2005). 10.1140/epjb/e2005-00234-0 (Pubitemid 41144039)
36. A. Antoniazzi, D. Fanelli, S. Ruffo, and Y. Y. Yamaguchi, Phys. Rev. Lett. 99, 040601 (2007). 10.1103/PhysRevLett.99.040601 (Pubitemid 47171670)
37. F. Staniscia, P. H. Chavanis, G. De Ninno, and D. Fanelli, Phys. Rev. E 80, 021138 (2009). 10.1103/PhysRevE.80.021138
38. P. H. Chavanis and A. Campa, e-print arXiv:1001.2109.
39. B. N. Miller and P. Youngkins, Phys. Rev. Lett. 81, 4794 (1998). 10.1103/PhysRevLett.81.4794
40. J. Barré, D. Mukamel, and S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001). 10.1103/PhysRevLett.87.030601
41. M. Antoni, S. Ruffo, and A. Torcini, Phys. Rev. E 66, 025103 (R) (2002). 10.1103/PhysRevE.66.025103 (Pubitemid 40618690)
42. T. Tatekawa, F. Bouchet, T. Dauxois, and S. Ruffo, Phys. Rev. E 71, 056111 (2005). 10.1103/PhysRevE.71.056111 (Pubitemid 41480999)
43. P. Valageas, Astron. Astrophys. 450, 445 (2006). 10.1051/0004-6361: 20054472
44. A. Campa, T. Dauxois, and S. Ruffo, Phys. Rep. 480, 57 (2009). 10.1016/j.physrep.2009.07.001
45. J. Messer and H. Spohn, J. Stat. Phys. 29, 561 (1982). 10.1007/BF01342187
46. A. Campa and P. H. Chavanis, e-print arXiv:1003.2378.
47. D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967).
48. P. H. Chavanis, Astron. Astrophys. 451, 109 (2006). 10.1051/0004-6361: 20054008
49. R. Ellis, K. Haven, and B. Turkington, J. Stat. Phys. 101, 999 (2000). 10.1023/A:1026446225804 (Pubitemid 33214116)
50. F. Bouchet and J. Barré, J. Stat. Phys. 118, 1073 (2005). 10.1007/s10955-004-2059-0 (Pubitemid 40553410)
51. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1989).
52. M. A. Herrero, E. Medina, and J. J. L. Velazquez, J. Comput. Appl. Math. 97, 99 (1998). 10.1016/S0377-0427(98)00104-6
53. K. Huang, Statistical Mechanics (Wiley, New York, 1963).
54. D. H. E. Gross, Microcanonical Thermodynamics: Phase Transitions in "Small" Systems, Lecture Notes in Physics Vol. 66, (World Scientific, Singapore, 2001).
55. T. J. Newman and R. Grima, Phys. Rev. E 70, 051916 (2004). 10.1103/PhysRevE.70.051916 (Pubitemid 40086533)
56. P. H. Chavanis and C. Sire, Physica A 384, 199 (2007). 10.1016/j.physa.2007.05.069 (Pubitemid 47285637)
57. S. Chandrasekhar, Principles of Stellar Dynamics (University of Chicago Press, Chicago, 1942).
58. M. Antoni, S. Ruffo, and A. Torcini, Europhys. Lett. 66, 645 (2004). 10.1209/epl/i2004-10028-6
59. P. H. Chavanis, Astron. Astrophys. 432, 117 (2005). 10.1051/0004-6361: 20041114 (Pubitemid 40338898)
60. A. Einstein, Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. 1, 142 (1917).
61. G. E. Lemaître, in The Cosmological Constant, edited by, P. A. Schilpp, (Open Court, La Salle, Illinois, 1997).
62. A. S. Eddington, The Mathematical Theory of Relativity (Cambridge University, Cambridge, 1924).
63. E. A. Spiegel, in Gravitational Screening, edited by, A. Harvey, (Springer-Verlag, Heidelberg, 1998);
64. e-print arXiv:astro-ph/9801014.
65. M. Kiessling, Adv. Appl. Math. 31, 132 (2003); 10.1016/S0196-8858(02) 00556-0 (Pubitemid 36891311)
66. see also e-print arXiv:astro-ph/9910247.
67. S. Childress and J. K. Percus, Math. Biosci. 56, 217 (1981). 10.1016/0025-5564(81)90055-9 (Pubitemid 12238332)
68. P. H. Chavanis, Eur. Phys. J. B 52, 433 (2006). 10.1140/epjb/e2006-00310- y (Pubitemid 44198388)
69. P. H. Chavanis and C. Sire, Physica A 387, 4033 (2008). 10.1016/j.physa.2008.02.025
70. J. H. Jeans, Astronomy and Cosmogony (Cambridge University Press, Cambridge, 1929).
71. M. Joyce, in Dynamics and Thermodynamics of systems with long range interactions: Theory and experiments, edited by, A. Campa, A. Giansanti, G. Morigi and, F. Sylos Labini, (American Institute of Physics, New York, 2008), p. 970.
72. M. Joyce, B. Marcos, and F. Sylos Labini, J. Stat. Mech.: Theory Exp. 2009, 04019. 10.1088/1742-5468/2009/04/P04019
73. A. Gabrielli, M. Joyce, and F. Sicard, Phys. Rev. E 80, 041108 (2009). 10.1103/PhysRevE.80.041108
74. A. Gabrielli and M. Joyce, Phys. Rev. E 81, 021102 (2010). 10.1103/PhysRevE.81.021102
75. J. Binney and S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics (Princeton, New Jersey, 1987).
76. T. Padmanabhan, in Dynamics and Thermodynamics of Systems with Long Range Interactions, Lecture Notes in Physics Vol. 602, edited by, T. Dauxois, S. Ruffo, E. Arimondo, and, M. Wilkens, (Springer, Berlin, 2002), p. 165.
77. G. L. Camm, Mon. Not. R. Astron. Soc. 110, 305 (1950).
78. R. Schaaf, Trans. Am. Math. Soc. 292, 531 (1985). 10.2307/2000228