Iterative fluid dynamics

Regular Article - Theoretical Physics
Part of the following topical collections:
  1. Topical Issue on Relativistic Hydro- and Thermodynamics

Abstract

An iterative scheme is presented to solve analytically the relativistic fluid dynamics equations. The scheme is applied to the longitudinal expansion, the transversal symmetric and the transversal asymmetric (triaxial) expansion as well. Within this scheme it is possible to describe the dynamics of a strongly coupled (i.e. conformal) medium for parameters referring to heavy-ion collisions at LHC.

Keywords

Energy Density Iterative Scheme Transversal Expansion Iterative Result Longitudinal Expansion 

References

  1. 1.
    P.F. Kolb, U.W. Heinz, P. Huovinen, K.J. Eskola, K. Tuominen, Nucl. Phys. A 696, 197 (2001) arXiv:hep-ph/0103234 ADSCrossRefGoogle Scholar
  2. 2.
    C. Shen, U. Heinz, P. Huovinen, H. Song, Phys. Rev. C 84, 044903 (2011) arXiv:nucl-th/1105.3226ADSCrossRefGoogle Scholar
  3. 3.
    C.E. Aguiar, Y. Hama, T. Kodama, T. Osada, Nucl. Phys. A 698, 639 (2002) arXiv:hep-ph/0106266 ADSCrossRefGoogle Scholar
  4. 4.
    Z. Qiu, U.W. Heinz, Phys. Rev. C 84, 024911 (2011) arXiv:nucl-th/1104.0650ADSCrossRefGoogle Scholar
  5. 5.
    B. Schenke, P. Tribedy, R. Venugopalan, arXiv:nucl-th/1202.6646Google Scholar
  6. 6.
    B. Schenke, S. Jeon, C. Gale, J. Phys. G 38, 124169 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    M. Dion, C. Gale, S. Jeon, J.-F. Paquet, B. Schenke, C. Young, J. Phys. G 38, 124138 (2011) arXiv:hep-ph/1107.0889ADSCrossRefGoogle Scholar
  8. 8.
    F.G. Gardim, Y. Hama, F. Grassi, arXiv:nucl-th/1110.5658Google Scholar
  9. 9.
    R.P.G. Andrade, F. Grassi, Y. Hama, W.-L. Qian, Nucl. Phys. A 854, 81 (2011) arXiv:hep-ph/1008.0139ADSCrossRefGoogle Scholar
  10. 10.
    K. Werner, I. Karpenko, T. Pierog, M. Bleicher, K. Mikhailov, Phys. Rev. C 82, 044904 (2010) arXiv:nucl-th/1004.0805ADSCrossRefGoogle Scholar
  11. 11.
    R. Derradi de Souza, J. Takahashi, T. Kodama, P. Sorensen, Phys. Rev. C 85, 054909 (2012) arXiv:hep-ph/1110.5698ADSCrossRefGoogle Scholar
  12. 12.
    R. Chatterjee, H. Holopainen, T. Renk, K.J. Eskola, J. Phys. G 38, 124136 (2011) arXiv:hep-ph/1106.3884ADSCrossRefGoogle Scholar
  13. 13.
    S. Borsanyi, G. Endrodi, Z. Fodor, C. Hoelbling, S. Katz, S. Krieg, C. Ratti, K. Szabo, J. Phys. Conf. Ser. 316, 012020 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo, JHEP 01, 089 (2006) arXiv:hep-lat/0510084 ADSCrossRefGoogle Scholar
  15. 15.
    P. Huovinen, P. Petreczky, J. Phys. G 38, 124103 (2011) arXiv:nucl-th/1106.6227ADSCrossRefGoogle Scholar
  16. 16.
    WHOT-QCD Collaboration (S. Ejiri et al.), Phys. Rev. D 82, 014508 (2010) arXiv:hep-lat/0909.2121ADSCrossRefGoogle Scholar
  17. 17.
    F. Karsch, H.W. Wyld, Phys. Rev. D 35, 2518 (1987)ADSCrossRefGoogle Scholar
  18. 18.
    G. Aarts, J.M. Martinez Resco, Nucl. Phys. Proc. Suppl. 119, 505 (2003) arXiv:hep-lat/0209033 ADSCrossRefMATHGoogle Scholar
  19. 19.
    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, U.A. Wiedemann, arXiv:hep-th/1101.0618Google Scholar
  20. 20.
    P. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005) arXiv:hep-th/0405231 ADSCrossRefGoogle Scholar
  21. 21.
    A. Buchel, Phys. Lett. B 663, 286 (2008) arXiv:hep-th/0708.3459ADSCrossRefGoogle Scholar
  22. 22.
    B. Friman, C. Höhne, J. Knoll, S. Leupold, J. Randrup, R. Rapp, P. Senger (Editors), Lect. Notes Phys. 814, 1 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    L.D. Landau, Izv. Akad. Nauk Ser. Fiz. 17, 51 (1953)Google Scholar
  24. 24.
    S.Z. Belenkij, L.D. Landau, Nuovo Cimento Suppl. 3S10, 15 (1956)CrossRefGoogle Scholar
  25. 25.
    W. Israel, J.M. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    G.S. Denicol, H. Niemi, E. Molnar, D.H. Rischke, arXiv:nucl-th/1202.4551Google Scholar
  27. 27.
    P. Van, T.S. Biro, Eur. Phys. J. ST 155, 201 (2008) arXiv:nucl-th/0704.2039CrossRefGoogle Scholar
  28. 28.
    P. Van, T.S. Biro, Phys. Lett. B 709, 106 (2012) arXiv:nucl-th/1109.0985MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    J.D. Bjorken, Phys. Rev. D 27, 140 (1983)ADSCrossRefGoogle Scholar
  30. 30.
    S.S. Gubser, Phys. Rev. D 82, 085027 (2010) arXiv:hep-th/1006.0006MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    T. Csörgő, F. Grassi, Y. Hama, T. Kodama, Phys. Lett. B 565, 107 (2003) arXiv:nucl-th/0305059 ADSCrossRefGoogle Scholar
  32. 32.
    T. Csörgő, L.P. Csernai, Y. Hama, T. Kodama, Heavy Ion Phys. A 21, 73 (2004) arXiv:nucl-th/0306004 CrossRefGoogle Scholar
  33. 33.
    T. Csörgő, M.I. Nagy, M. Csanad, Phys. Lett. B 663, 306 (2008) arXiv:nucl-th/0605070 ADSCrossRefGoogle Scholar
  34. 34.
    L.P. Csernai, Introduction to Relativistic Heavy-Ion Collisions (Wiley Chichester, UK, 1994)Google Scholar
  35. 35.
    S. de Haro, S.N. Solodukhin, K. Skenderis, Commun. Math. Phys. 217, 595 (2001) arXiv:hep-th/0002230 MathSciNetADSCrossRefMATHGoogle Scholar
  36. 36.
    R.A. Janik, Lect. Notes Phys. 828, 147 (2011) arXiv:hep-th/1003.3291ADSCrossRefGoogle Scholar
  37. 37.
    K. Tsumura, T. Kunihiro, arXiv:physics.flu-dyn/1206.3913.Google Scholar
  38. 38.
    K.J. Eskola, K. Kajantie, P.V. Ruuskanen, Eur. Phys. J. C 1, 627 (1998) arXiv:nucl-th/9705015 ADSCrossRefGoogle Scholar
  39. 39.
    C. Shen, U. Heinz, P. Huovinen, H. Song, Phys. Rev. C 82, 054904 (2010) arXiv:nucl-th/1010.1856ADSCrossRefGoogle Scholar
  40. 40.
    S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S.D. Katz, S. Krieg, C. Ratti, K.K. Szabo, JHEP 11, 077 (2010) arXiv:hep-lat/1007.2580ADSCrossRefGoogle Scholar
  41. 41.
    S.A. Bass, C. Gale, A. Majumder, C. Nonaka, G.-Y. Qin, T. Renk, J. Ruppert, Phys. Rev. C 79, 024901 (2009) arXiv:nucl-th/0808.0908ADSCrossRefGoogle Scholar
  42. 42.
    R. Rapp, Acta Phys. Polon. B 42, 2823 (2011) arXiv:nucl-th/1110.4345CrossRefGoogle Scholar
  43. 43.
    D.E. Knuth, The Art of Computer Programming: Fundamental Algorithms, Vol. 1 (Addison-Wesley Publishing Company, Reading, Massachusetts, 1973) p. 50Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Helmholtz-Zentrum Dresden-RossendorfDresdenGermany

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