Analytical relativistic ideal hydrodynamical solutions in (1+3)D with longitudinal and transverse flows

Liao, Jinfeng; Koch, Volker

doi:10.1103/physrevc.80.034904

Title: Analytical relativistic ideal hydrodynamical solutions in ( $1 + 3$ )D with longitudinal and transverse flows

Journal Article · 15 September 2009 · Physical Review C, Nuclear Physics

DOI: https://doi.org/10.1103/physrevc.80.034904 · OSTI ID:1530200

Liao, Jinfeng ^[1]; Koch, Volker ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

A new method for solving relativistic ideal hydrodynamics in (1+3)D is developed. Longitudinal and transverse radial flows are explicitly embedded into the ansatz for the velocity field and the hydrodynamic equations are reduced to a single equation for the transverse velocity field only, which is analytically more tractable as compared to the full hydrodynamic equations. As an application we use the method to find analytically all possible solutions whose transverse velocity fields have power dependence on the proper time and transverse radius. Finally, the possible applications to relativistic heavy ion collisions and possible generalizations of the method are discussed.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1530200

Journal Information:: Physical Review C, Nuclear Physics, Journal Name: Physical Review C, Nuclear Physics Journal Issue: 3 Vol. 80; ISSN 0556-2813; ISSN PRVCAN

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (41)

Analytic solution for relativistic transverse flow at the softest point Biró, Tamás S. Physics Letters B, Vol. 474, Issue 1-2 https://doi.org/10.1016/S0370-2693(00)00018-6	journal	February 2000
Generating new solutions for relativistic transverse flow at the softest point Biró, Tamás S. Physics Letters B, Vol. 487, Issue 1-2 https://doi.org/10.1016/S0370-2693(00)00791-7	journal	August 2000
Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics Kolb, P. F.; Huovinen, P.; Heinz, U. Physics Letters B, Vol. 500, Issue 3-4 https://doi.org/10.1016/S0370-2693(01)00079-X	journal	February 2001
Hydrodynamical activity in thin accretion disks Regev, Oded New Astronomy Reviews, Vol. 51, Issue 10-12 https://doi.org/10.1016/j.newar.2008.03.011	journal	May 2008
What RHIC experiments and theory tell us about properties of quark–gluon plasma? Shuryak, Edward Nuclear Physics A, Vol. 750, Issue 1 https://doi.org/10.1016/j.nuclphysa.2004.10.022	journal	March 2005
New forms of QCD matter discovered at RHIC Gyulassy, Miklos; McLerran, Larry Nuclear Physics A, Vol. 750, Issue 1 https://doi.org/10.1016/j.nuclphysa.2004.10.034	journal	March 2005
Perfect fluidity of the quark–gluon plasma core as seen through its dissipative hadronic corona Hirano, Tetsufumi; Gyulassy, Miklos Nuclear Physics A, Vol. 769 https://doi.org/10.1016/j.nuclphysa.2006.02.005	journal	April 2006
Polymer chains and baryons in a strongly coupled quark–gluon plasma Liao, Jinfeng; Shuryak, Edward V. Nuclear Physics A, Vol. 775, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2006.06.169	journal	September 2006
Hot and dense matter: from RHIC to LHC – Theoretical overview Kharzeev, Dmitri E. Nuclear Physics A, Vol. 827, Issue 1-4 https://doi.org/10.1016/j.nuclphysa.2009.05.026	journal	August 2009
Magnetic monopoles in the high temperature phase of Yang–Mills theories D'Alessandro, A.; D'Elia, M. Nuclear Physics B, Vol. 799, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2008.03.002	journal	August 2008
Suppression of elliptic flow in a minimally viscous quark–gluon plasma Song, Huichao; Heinz, Ulrich Physics Letters B, Vol. 658, Issue 5 https://doi.org/10.1016/j.physletb.2007.11.019	journal	January 2008
Why does the quark–gluon plasma at RHIC behave as a nearly ideal fluid? Shuryak, Edward Progress in Particle and Nuclear Physics, Vol. 53, Issue 1 https://doi.org/10.1016/j.ppnp.2004.02.025	journal	July 2004
Physics of strongly coupled quark–gluon plasma Shuryak, Edward Progress in Particle and Nuclear Physics, Vol. 62, Issue 1 https://doi.org/10.1016/j.ppnp.2008.09.001	journal	January 2009
An introduction to relativistic hydrodynamics Gourgoulhon, E. EAS Publications Series, Vol. 21 https://doi.org/10.1051/eas:2006106	journal	January 2006
Fluid Mechanics Landau, L. D.; Lifshitz, E. M.; Sykes, J. B. Physics Today, Vol. 14, Issue 5 https://doi.org/10.1063/1.3057567	journal	May 1961
Relativistic hydrodynamics for heavy-ion collisions Ollitrault, Jean-Yves European Journal of Physics, Vol. 29, Issue 2 https://doi.org/10.1088/0143-0807/29/2/010	journal	January 2008
Anisotropic transverse flow and the quark-hadron phase transition Kolb, Peter F.; Sollfrank, Josef; Heinz, Ulrich Physical Review C, Vol. 62, Issue 5 https://doi.org/10.1103/PhysRevC.62.054909	journal	October 2000
Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze-out Hirano, Tetsufumi; Tsuda, Keiichi Physical Review C, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevC.66.054905	journal	November 2002
Comoving coordinate system for relativistic hydrodynamics Pratt, Scott Physical Review C, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevC.75.024907	journal	February 2007
Strongly coupled plasma with electric and magnetic charges Liao, Jinfeng; Shuryak, Edward Physical Review C, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevC.75.054907	journal	May 2007
Unified description of Bjorken and Landau 1+1 hydrodynamics Bialas, A.; Janik, R. A.; Peschanski, R. Physical Review C, Vol. 76, Issue 5 https://doi.org/10.1103/PhysRevC.76.054901	journal	November 2007
Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics Nagy, M. I.; Csörgő, T.; Csanád, M. Physical Review C, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevC.77.024908	journal	February 2008
Simulating elliptic flow with viscous hydrodynamics Dusling, K.; Teaney, D. Physical Review C, Vol. 77, Issue 3 https://doi.org/10.1103/PhysRevC.77.034905	journal	March 2008
Electric flux tube in a magnetic plasma Liao, Jinfeng; Shuryak, Edward Physical Review C, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevC.77.064905	journal	June 2008
Landau hydrodynamics reexamined Wong, Cheuk-Yin Physical Review C, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevC.78.054902	journal	November 2008
Statistical description of hadron constituents as a basis for the fluid model of high-energy collisions Hwa, Rudolph C. Physical Review D, Vol. 10, Issue 7 https://doi.org/10.1103/PhysRevD.10.2260	journal	October 1974
Highly relativistic nucleus-nucleus collisions: The central rapidity region Bjorken, J. D. Physical Review D, Vol. 27, Issue 1 https://doi.org/10.1103/PhysRevD.27.140	journal	January 1983
Anisotropy as a signature of transverse collective flow Ollitrault, Jean-Yves Physical Review D, Vol. 46, Issue 1 https://doi.org/10.1103/PhysRevD.46.229	journal	July 1992
What do lattice baryonic susceptibilities tell us about quarks, diquarks, and baryons at T > T c ? Liao, Jinfeng; Shuryak, Edward V. Physical Review D, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevD.73.014509	journal	January 2006
Microscopic formula for transport coefficients of causal hydrodynamics Koide, T. Physical Review E, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevE.75.060103	journal	June 2007
Transport coefficients of non-Newtonian fluid and causal dissipative hydrodynamics Koide, T.; Kodama, T. Physical Review E, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevE.78.051107	journal	November 2008
The Magnetic Component of Quark-Gluon Plasma is also a Liquid Liao, Jinfeng; Shuryak, Edward Physical Review Letters, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevLett.101.162302	journal	October 2008
Angular Dependence of Jet Quenching Indicates Its Strong Enhancement near the QCD Phase Transition Liao, Jinfeng; Shuryak, Edward Physical Review Letters, Vol. 102, Issue 20 https://doi.org/10.1103/PhysRevLett.102.202302	journal	May 2009
Exposing the Noncollectivity in Elliptic Flow Liao, Jinfeng; Koch, Volker Physical Review Letters, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevLett.103.042302	journal	July 2009
Flow at the SPS and RHIC as a Quark-Gluon Plasma Signature Teaney, D.; Lauret, J.; Shuryak, E. V. Physical Review Letters, Vol. 86, Issue 21 https://doi.org/10.1103/PhysRevLett.86.4783	journal	May 2001
Magnetic Component of Yang-Mills Plasma Chernodub, M. N.; Zakharov, V. I. Physical Review Letters, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevLett.98.082002	journal	February 2007
Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC? Romatschke, Paul; Romatschke, Ulrike Physical Review Letters, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevLett.99.172301	journal	October 2007
Similar final states from different initial states using new exact solutions of relativistic hydrodynamics Csanád, M.; Nagy, M. I.; Csörgő, T. The European Physical Journal Special Topics, Vol. 155, Issue 1 https://doi.org/10.1140/epjst/e2008-00585-2	journal	March 2008
Simple Solutions of Relativistic Hydrodynamics for Cylindrically Symmetric Systems Csörgő, T.; Grassi, F.; Hama, Y. Acta Physica Hungarica A) Heavy Ion Physics, Vol. 21, Issue 1 https://doi.org/10.1556/APH.21.2004.1.7	journal	July 2004
Expansion Rates at RHIC Kolb, Peter F. Acta Physica Hungarica A) Heavy Ion Physics, Vol. 21, Issue 2-4 https://doi.org/10.1556/APH.21.2004.2-4.22	journal	November 2004
Ellipsoidal Flows in Relativistic Hydrodynamics of Finite Systems Sinyukov, Yu. M.; Sinyukov, Yu. M.; Karpenko, Iu. A. Acta Physica Hungarica A) Heavy Ion Physics, Vol. 25, Issue 1 https://doi.org/10.1556/APH.25.2006.1.13	journal	March 2006

Similar Records

Analytical relativistic ideal hydrodynamical solutions in (1+3)D with longitudinal and transverse flows

Journal Article · 2009 · Physical Review. C, Nuclear Physics · OSTI ID:21293860

Jinfeng, Liao; Koch, Volker

Exact Relativistic Ideal Hydrodynamical Solutions in (1+3)D with Longitudinal and Transverse Flows

Journal Article · 2009 · Physical Review C · OSTI ID:971348

Liao, Jinfeng; Koch, Volker

Second-order

(2 + 1)

-dimensional anisotropic hydrodynamics

Journal Article · 2014 · Physical Review C, Nuclear Physics · OSTI ID:1604545

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Title: Analytical relativistic ideal hydrodynamical solutions in ( 1 + 3 )D with longitudinal and transverse flows

Citation Formats

References (41)

Similar Records

Related Subjects

Title: Analytical relativistic ideal hydrodynamical solutions in ( $1 + 3$ )D with longitudinal and transverse flows