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Volumn 83, Issue 3, 2011, Pages

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature

Author keywords

[No Author keywords available]

Indexed keywords

BACTERIAL POPULATION; BROWNIAN PARTICLES; CENTRAL DENSITY; COLD SYSTEMS; COLLAPSE TIME; EXACT ANALYTICAL SOLUTIONS; FINITE TIME; FINITE TIME SINGULARITY; GRAVITATIONAL COLLAPSE; INITIAL TIME; KELLER-SEGEL MODEL; PARABOLIC DENSITY PROFILE; POST-COLLAPSE; SELF-SIMILAR; SMOLUCHOWSKI-POISSON SYSTEM; ZERO TEMPERATURES;

EID: 79961065202     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.031131     Document Type: Article
Times cited : (27)

References (62)
  • 2
    • 79961082779 scopus 로고    scopus 로고
    • e-print arXiv: 1003.1118
    • e-print arXiv: 1003.1118.
  • 3
    • 0242411895 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.68.036108
    • P. H. Chavanis, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.036108 68, 036108 (2003).
    • (2003) Phys. Rev. e , vol.68 , pp. 036108
    • Chavanis, P.H.1
  • 4
    • 42149190237 scopus 로고    scopus 로고
    • Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
    • DOI 10.1140/epjb/e2008-00142-9
    • P. H. Chavanis, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2008- 00142-9 62, 179 (2008). (Pubitemid 351535293)
    • (2008) European Physical Journal B , vol.62 , Issue.2 , pp. 179-208
    • Chavanis, P.H.1
  • 7
    • 68949187762 scopus 로고    scopus 로고
    • PRPLCM 0370-1573 10.1016/j.physrep.2009.07.001
    • A. Campa, T. Dauxois, and S. Ruffo, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.07.001 480, 57 (2009).
    • (2009) Phys. Rep. , vol.480 , pp. 57
    • Campa, A.1    Dauxois, T.2    Ruffo, S.3
  • 8
    • 27744550311 scopus 로고    scopus 로고
    • Hamiltonian and Brownian systems with long-range interactions: II. Kinetic equations and stability analysis
    • DOI 10.1016/j.physa.2005.06.088, PII S0378437105007168
    • P. H. Chavanis, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.06.088 361, 81 (2006). (Pubitemid 41627544)
    • (2006) Physica A: Statistical Mechanics and its Applications , vol.361 , Issue.1 , pp. 81-123
    • Chavanis, P.-H.1
  • 9
    • 0001110865 scopus 로고    scopus 로고
    • PHYADX 1539-3755 10.1103/PhysRevE.57.6634
    • L. Borland, Phys. Rev. E PHYADX 1539-3755 10.1103/PhysRevE.57.6634 57, 6634 (1998).
    • (1998) Phys. Rev. e , vol.57 , pp. 6634
    • Borland, L.1
  • 10
    • 0035879433 scopus 로고    scopus 로고
    • Non-linear kinetics underlying generalized statistics
    • DOI 10.1016/S0378-4371(01)00184-4, PII S0378437101001844
    • G. Kaniadakis, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00184-4 296, 405 (2001). (Pubitemid 32594505)
    • (2001) Physica A: Statistical Mechanics and its Applications , vol.296 , Issue.3-4 , pp. 405-425
    • Kaniadakis, G.1
  • 11
    • 3342946092 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2004.04.102
    • P. H. Chavanis, P. Laurençot, and M. Lemou, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.04.102 341, 145 (2004).
    • (2004) Physica A , vol.341 , pp. 145
    • Chavanis, P.H.1    Laurençot, P.2    Lemou, M.3
  • 12
    • 33646516485 scopus 로고
    • JSTPBS 0022-4715 10.1007/BF01016429
    • C. Tsallis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016429 52, 479 (1988).
    • (1988) J. Stat. Phys. , vol.52 , pp. 479
    • Tsallis, C.1
  • 13
    • 33846814921 scopus 로고    scopus 로고
    • Phase separation of bacterial colonies in a limit of high degradation : AAnalogy with Jupiter's great red spot
    • DOI 10.1140/epjb/e2007-00021-y
    • P. H. Chavanis, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007- 00021-y 54, 525 (2006). (Pubitemid 46208989)
    • (2006) European Physical Journal B , vol.54 , Issue.4 , pp. 525-549
    • Chavanis, P.H.1
  • 14
    • 79952105141 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2010.12.018
    • P. H. Chavanis, Physica A PHYADX 0378-4371 10.1016/j.physa.2010.12.018 390, 1546 (2011).
    • (2011) Physica A , vol.390 , pp. 1546
    • Chavanis, P.H.1
  • 15
    • 0001965304 scopus 로고
    • 10.1051/jp2:1993112
    • H. Spohn, J. Phys. 10.1051/jp2:1993112 3, 69 (1993).
    • (1993) J. Phys. , vol.3 , pp. 69
    • Spohn, H.1
  • 16
    • 33747367865 scopus 로고
    • PHYADX 0378-4371 10.1016/0378-4371(95)00211-1
    • A. R. Plastino and A. Plastino, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00211-1 222, 347 (1995).
    • (1995) Physica A , vol.222 , pp. 347
    • Plastino, A.R.1    Plastino, A.2
  • 18
    • 0034370899 scopus 로고    scopus 로고
    • PHYADX 1424-0637 10.1007/s000230050003
    • P. Biler and J. Dolbeault, Ann. Henri Poincaré PHYADX 1424-0637 10.1007/s000230050003 1, 461 (2000).
    • (2000) Ann. Henri Poincaré , vol.1 , pp. 461
    • Biler, P.1    Dolbeault, J.2
  • 20
    • 0000244470 scopus 로고
    • JPCHAX 0022-3654 10.1021/j100031a036
    • A. Syganow and E. von Kitzing, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100031a036 99, 12030 (1995).
    • (1995) J. Phys. Chem. , vol.99 , pp. 12030
    • Syganow, A.1    Von Kitzing, E.2
  • 21
    • 0034450587 scopus 로고    scopus 로고
    • Extended hydrodynamical model of carrier transport in semiconductors
    • DOI 10.1137/S003613999833294X, PII S003613999833294X
    • A. M. Anile, V. Romano, and G. Russo, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S003613999833294X 61, 74 (2000). (Pubitemid 32300845)
    • (2000) SIAM Journal on Applied Mathematics , vol.61 , Issue.1 , pp. 74-101
    • Anile, A.M.1    Romano, V.2    Russo, G.3
  • 23
    • 0003410218 scopus 로고
    • Princeton University Press, Princeton, NJ
    • J. Binney and S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics (Princeton University Press, Princeton, NJ, 1987).
    • (1987) Galactic Dynamics
    • Binney, J.1    Tremaine, S.2
  • 26
    • 0000034685 scopus 로고
    • PRPLCM 0370-1573 10.1016/0370-1573(90)90051-3
    • T. Padmanabhan, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(90)90051-3 188, 285 (1990).
    • (1990) Phys. Rep. , vol.188 , pp. 285
    • Padmanabhan, T.1
  • 27
    • 33749256260 scopus 로고    scopus 로고
    • Phase transitions in self-gravitating systems
    • DOI 10.1142/S0217979206035400, PII S0217979206035400
    • P. H. Chavanis, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979206035400 20, 3113 (2006). (Pubitemid 44481503)
    • (2006) International Journal of Modern Physics B , vol.20 , Issue.22 , pp. 3113-3198
    • Chavanis, P.H.1
  • 30
    • 0015011285 scopus 로고
    • JTBIAP 0022-5193 10.1016/0022-5193(71)90050-6
    • E. F. Keller and L. A. Segel, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(71)90050-6 30, 225 (1971).
    • (1971) J. Theor. Biol. , vol.30 , pp. 225
    • Keller, E.F.1    Segel, L.A.2
  • 31
    • 77954828190 scopus 로고    scopus 로고
    • JTBIAP 1539-3755 10.1103/PhysRevE.82.011402
    • A. Dominguez, M. Oettel, and S. Dietrich, Phys. Rev. E JTBIAP 1539-3755 10.1103/PhysRevE.82.011402 82, 011402 (2010).
    • (2010) Phys. Rev. e , vol.82 , pp. 011402
    • Dominguez, A.1    Oettel, M.2    Dietrich, S.3
  • 32
    • 0001448604 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.76.1094
    • G. Giacomin and J. L. Lebowitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1094 76, 1094 (1996).
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 1094
    • Giacomin, G.1    Lebowitz, J.L.2
  • 33
    • 28844432303 scopus 로고    scopus 로고
    • Aggregation of finite-Size particles with variable mobility
    • DOI 10.1103/PhysRevLett.95.226106, 226106
    • D. D. Holm and V. Putkaradze, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226106 95, 226106 (2005). (Pubitemid 41776992)
    • (2005) Physical Review Letters , vol.95 , Issue.22 , pp. 1-4
    • Holm, D.D.1    Putkaradze, V.2
  • 34
    • 0001363055 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.69.2776
    • R. Robert and J. Sommeria, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2776 69, 2776 (1992).
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2776
    • Robert, R.1    Sommeria, J.2
  • 35
    • 21444442314 scopus 로고    scopus 로고
    • Statistical Mechanics of Two-dimensional Vortices and Collisionless Stellar Systems
    • DOI 10.1086/177977
    • P. H. Chavanis, J. Sommeria, and R. Robert, Astrophys. J. AJLEEY 0004-637X 10.1086/177977 471, 385 (1996). (Pubitemid 126143762)
    • (1996) Astrophysical Journal , vol.471 , Issue.1 , pp. 385-399
    • Chavanis, P.H.1    Sommeria, J.2    Robert, R.3
  • 36
    • 0242270400 scopus 로고    scopus 로고
    • in edited by T. Dauxois, S. Ruffo, E. Arimondo, and M. Wilkens, Lecture Notes in Physics Vol. 602 (Springer, Berlin
    • P. H. Chavanis, in Dynamics and Thermodynamics of Systems with Long Range Interactions, edited by, T. Dauxois, S. Ruffo, E. Arimondo, and, M. Wilkens, Lecture Notes in Physics Vol. 602 (Springer, Berlin, 2002).
    • (2002) Dynamics and Thermodynamics of Systems with Long Range Interactions
    • Chavanis, P.H.1
  • 39
    • 42749098103 scopus 로고    scopus 로고
    • AJLEEY 1539-3755 10.1103/PhysRevE.69.066109
    • C. Sire and P. H. Chavanis, Phys. Rev. E AJLEEY 1539-3755 10.1103/PhysRevE.69.066109 69, 066109 (2004).
    • (2004) Phys. Rev. e , vol.69 , pp. 066109
    • Sire, C.1    Chavanis, P.H.2
  • 40
    • 77949277172 scopus 로고    scopus 로고
    • PYLAAG 0375-9601 10.1016/j.physleta.2010.01.068
    • P. Lushnikov, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2010.01. 068 374, 1678 (2010).
    • (2010) Phys. Lett. A , vol.374 , pp. 1678
    • Lushnikov, P.1
  • 41
    • 0001278734 scopus 로고
    • AJLEEY 0004-637X 10.1086/147410
    • C. Hunter, Astrophys. J. AJLEEY 0004-637X 10.1086/147410 136, 594 (1962).
    • (1962) Astrophys. J. , vol.136 , pp. 594
    • Hunter, C.1
  • 45
    • 0000276869 scopus 로고
    • JSTPBS 0022-4715 10.1007/BF01042598
    • M. Kiessling, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01042598 55, 203 (1989).
    • (1989) J. Stat. Phys. , vol.55 , pp. 203
    • Kiessling, M.1
  • 46
    • 0036190825 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20011438
    • P. H. Chavanis, Astron. Astrophys. AAEJAF 0004-6361 10.1051/0004-6361: 20011438 381, 340 (2002).
    • (2002) Astron. Astrophys. , vol.381 , pp. 340
    • Chavanis, P.H.1
  • 49
    • 0000006668 scopus 로고
    • AJLEEY 0004-637X 10.1086/158511
    • H. Cohn, Astrophys. J. AJLEEY 0004-637X 10.1086/158511 242, 765 (1980).
    • (1980) Astrophys. J. , vol.242 , pp. 765
    • Cohn, H.1
  • 50
  • 54
    • 3042773339 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2004.03.077
    • P. H. Chavanis, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.03.077 340, 57 (2004);
    • (2004) Physica A , vol.340 , pp. 57
    • Chavanis, P.H.1
  • 55
    • 48649088473 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2008.06.016
    • P. H. Chavanis, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.06.016 387, 5716 (2008).
    • (2008) Physica A , vol.387 , pp. 5716
    • Chavanis, P.H.1
  • 56
    • 78650859160 scopus 로고    scopus 로고
    • EPJBFY 1434-6028 10.1140/epjb/e2010-90839-3
    • P. H. Chavanis and R. Mannella, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-90839-3 78, 139 (2010).
    • (2010) Eur. Phys. J. B , vol.78 , pp. 139
    • Chavanis, P.H.1    Mannella, R.2
  • 58
    • 0000551787 scopus 로고    scopus 로고
    • JCPSA6 0021-9606 10.1063/1.478705
    • U. M. B. Marconi and P. Tarazona, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.478705 110, 8032 (1999).
    • (1999) J. Chem. Phys. , vol.110 , pp. 8032
    • Marconi, U.M.B.1    Tarazona, P.2
  • 59
    • 0000559394 scopus 로고
    • JSTPBS 0022-4715 10.1007/BF01342187
    • J. Messer and H. Spohn, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01342187 29, 561 (1982).
    • (1982) J. Stat. Phys. , vol.29 , pp. 561
    • Messer, J.1    Spohn, H.2
  • 60
    • 0018446914 scopus 로고
    • ADPHAH 0001-8732 10.1080/00018737900101365
    • R. Evans, Adv. Phys. ADPHAH 0001-8732 10.1080/00018737900101365 28, 143 (1979).
    • (1979) Adv. Phys. , vol.28 , pp. 143
    • Evans, R.1
  • 62
    • 14844303779 scopus 로고    scopus 로고
    • On the lifetime of metastable states in self-gravitating systems
    • DOI 10.1051/0004-6361:20041114
    • P. H. Chavanis, Astron. Astrophys. AAEJAF 0004-6361 10.1051/0004-6361: 20041114 432, 117 (2005). (Pubitemid 40338898)
    • (2005) Astronomy and Astrophysics , vol.432 , Issue.1 , pp. 117-138
    • Chavanis, P.H.1


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