Second-order (2+1) -dimensional anisotropic hydrodynamics

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

doi:10.1103/PhysRevC.90.054910

Title: Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics

Journal Article · Fri Nov 21 00:00:00 EST 2014 · Physical Review C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.90.054910· OSTI ID:1604545

Bazow, Dennis ^[1];

^[1]; Strickland, Michael ^[2]

The Ohio State Univ., Columbus, OH (United States)
Kent State Univ., Kent, OH (United States)

We present a complete formulation of second-order (2+1)-dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly.We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0004286; SC0004104

OSTI ID:: 1604545

Alternate ID(s):: OSTI ID: 1179929

Journal Information:: Physical Review C, Nuclear Physics, Vol. 90, Issue 5; ISSN 0556-2813

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 114 works

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References (57)

Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics Florkowski, Wojciech; Ryblewski, Radoslaw Physical Review C, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevC.85.044902	journal	April 2012
Relativistic Grad polynomials Anderson, James L. Journal of Mathematical Physics, Vol. 15, Issue 7 https://doi.org/10.1063/1.1666762	journal	July 1974
Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter Muronga, Azwinndini Physical Review C, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRevC.76.014910	journal	July 2007
Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions Florkowski, Wojciech; Ryblewski, Radoslaw Physical Review C, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevC.83.034907	journal	March 2011
Instabilities of an anisotropically expanding non-Abelian plasma: $1 D + 3 V$ discretized hard-loop simulations Rebhan, Anton; Strickland, Michael; Attems, Maximilian Physical Review D, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevD.78.045023	journal	August 2008
Relativistic third-order dissipative fluid dynamics from kinetic theory Jaiswal, Amaresh Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.021903	journal	August 2013
Transport rates and momentum isotropization of gluon matter in ultrarelativistic heavy-ion collisions Xu, Zhe; Greiner, Carsten Physical Review C, Vol. 76, Issue 2 https://doi.org/10.1103/PhysRevC.76.024911	journal	August 2007
Generalized Orthogonal Polynomial Solutions of the Boltzmann Equation Mintzer, David Physics of Fluids, Vol. 8, Issue 6 https://doi.org/10.1063/1.1761357	journal	January 1965
The Mathematical Theory of Non-Uniform Gases Chapman, Sydney; Cowling, T. G.; Park, David American Journal of Physics, Vol. 30, Issue 5 https://doi.org/10.1119/1.1942035	journal	May 1962
Event-by-Event Anisotropic Flow in Heavy-ion Collisions from Combined Yang-Mills and Viscous Fluid Dynamics Gale, Charles; Jeon, Sangyong; Schenke, Björn Physical Review Letters, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevLett.110.012302	journal	January 2013
Boost-invariant (2+1)-dimensional anisotropic hydrodynamics Martinez, Mauricio; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.064913	journal	June 2012
Collective modes of an anisotropic quark-gluon plasma Romatschke, Paul; Strickland, Michael Physical Review D, Vol. 68, Issue 3 https://doi.org/10.1103/PhysRevD.68.036004	journal	August 2003
Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions Song, Huichao; Heinz, Ulrich Physical Review C, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevC.77.064901	journal	June 2008
Matching pre-equilibrium dynamics and viscous hydrodynamics Martinez, Mauricio; Strickland, Michael Physical Review C, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevC.81.024906	journal	February 2010
Second order dissipative fluid dynamics from kinetic theory Betz, B.; Denicol, G. S.; Koide, T. EPJ Web of Conferences, Vol. 13 https://doi.org/10.1051/epjconf/20111307005	journal	January 2011
Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion Ryblewski, Radoslaw; Florkowski, Wojciech The European Physical Journal C, Vol. 71, Issue 11 https://doi.org/10.1140/epjc/s10052-011-1761-8	journal	November 2011
Mixture of Anisotropic Fluids Florkowski, W.; Maj, R. Acta Physica Polonica B, Vol. 44, Issue 10 https://doi.org/10.5506/APhysPolB.44.2003	journal	January 2013
Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma Rebhan, Anton; Steineder, Dominik Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.021601	journal	January 2012
Macroscopic approximation to relativistic kinetic theory from a nonlinear closure Peralta-Ramos, J.; Calzetta, E. Physical Review D, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevD.87.034003	journal	February 2013
Transient relativistic thermodynamics and kinetic theory Israel, W.; Stewart, J. M. Annals of Physics, Vol. 118, Issue 2 https://doi.org/10.1016/0003-4916(79)90130-1	journal	April 1979
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
Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade Xu, Zhe; Greiner, Carsten Physical Review C, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevC.71.064901	journal	June 2005
Dissipative dynamics of highly anisotropic systems Martinez, Mauricio; Strickland, Michael Nuclear Physics A, Vol. 848, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2010.08.011	journal	December 2010
Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory Denicol, G. S.; Koide, T.; Rischke, D. H. Physical Review Letters, Vol. 105, Issue 16 https://doi.org/10.1103/PhysRevLett.105.162501	journal	October 2010
Dissipative hydrodynamics and heavy-ion collisions Baier, Rudolf; Romatschke, Paul; Wiedemann, Urs Achim Physical Review C, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevC.73.064903	journal	June 2006
Causal theories of dissipative relativistic fluid dynamics for nuclear collisions Muronga, Azwinndini Physical Review C, Vol. 69, Issue 3 https://doi.org/10.1103/PhysRevC.69.034903	journal	March 2004
Higher flow harmonics from $(3 + 1)$ D event-by-event viscous hydrodynamics Schenke, Björn; Jeon, Sangyong; Gale, Charles Physical Review C, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevC.85.024901	journal	February 2012
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems Bhatnagar, P. L.; Gross, E. P.; Krook, M. Physical Review, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRev.94.511	journal	May 1954
Extension of relativistic dissipative hydrodynamics to third order El, Andrej; Xu, Zhe; Greiner, Carsten Physical Review C, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevC.81.041901	journal	April 2010
Non-boost-invariant motion of dissipative and highly anisotropic fluid Ryblewski, Radoslaw; Florkowski, Wojciech Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 1 https://doi.org/10.1088/0954-3899/38/1/015104	journal	December 2010
Multiplicity scaling in ideal and viscous hydrodynamics Song, Huichao; Heinz, Ulrich Physical Review C, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevC.78.024902	journal	August 2008
Hydrodynamic Gradient Expansion in Gauge Theory Plasmas Heller, Michal P.; Janik, Romuald A.; Witaszczyk, Przemysław Physical Review Letters, Vol. 110, Issue 21 https://doi.org/10.1103/PhysRevLett.110.211602	journal	May 2013
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
Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions Heinz, Ulrich; Snellings, Raimond Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170540	journal	October 2013
Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation Jaiswal, Amaresh Physical Review C, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevC.87.051901	journal	May 2013
Second-Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions Muronga, Azwinndini Physical Review Letters, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevLett.88.062302	journal	January 2002
On the kinetic theory of rarefied gases Grad, Harold Communications on Pure and Applied Mathematics, Vol. 2, Issue 4 https://doi.org/10.1002/cpa.3160020403	journal	December 1949
Dissipative hydrodynamics in $2 + 1$ dimensions Chaudhuri, A. K. Physical Review C, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevC.74.044904	journal	October 2006
Complete second-order dissipative fluid dynamics Betz, B.; Henkel, D.; Rischke, D. H. Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 6 https://doi.org/10.1088/0954-3899/36/6/064029	journal	May 2009
Parton equilibration in relativistic heavy ion collisions Biró, T. S.; van Doorn, E.; Müller, B. Physical Review C, Vol. 48, Issue 3 https://doi.org/10.1103/PhysRevC.48.1275	journal	September 1993
“Bottom-up” thermalization in heavy ion collisions Baier, R.; Mueller, A. H.; Schiff, D. Physics Letters B, Vol. 502, Issue 1-4 https://doi.org/10.1016/S0370-2693(01)00191-5	journal	March 2001
Constraining relativistic viscous hydrodynamical evolution Martinez, Mauricio; Strickland, Michael Physical Review C, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevC.79.044903	journal	April 2009
Non-boost-invariant anisotropic dynamics Martinez, Mauricio; Strickland, Michael Nuclear Physics A, Vol. 856, Issue 1 https://doi.org/10.1016/j.nuclphysa.2011.02.003	journal	April 2011
Derivation of fluid dynamics from kinetic theory with the 14-moment approximation Denicol, G. S.; Molnár, E.; Niemi, H. The European Physical Journal A, Vol. 48, Issue 11 https://doi.org/10.1140/epja/i2012-12170-x	journal	November 2012
New Developments in Relativistic Viscous Hydrodynamics Romatschke, Paul International Journal of Modern Physics E, Vol. 19, Issue 01 https://doi.org/10.1142/S0218301310014613	journal	January 2010
Elliptic and Triangular Flow in Event-by-Event $D = 3 + 1$ Viscous Hydrodynamics Schenke, Björn; Jeon, Sangyong; Gale, Charles Physical Review Letters, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevLett.106.042301	journal	January 2011
Derivation of transient relativistic fluid dynamics from the Boltzmann equation Denicol, G. S.; Niemi, H.; Molnár, E. Physical Review D, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevD.85.114047	journal	June 2012
Nonstationary irreversible thermodynamics: A causal relativistic theory Israel, Werner Annals of Physics, Vol. 100, Issue 1-2 https://doi.org/10.1016/0003-4916(76)90064-6	journal	September 1976
Hydrodynamics of anisotropic quark and gluon fluids Florkowski, Wojciech; Maj, Radoslaw; Ryblewski, Radoslaw Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.034914	journal	March 2013
Applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions Huovinen, Pasi; Molnar, Denes Physical Review C, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevC.79.014906	journal	January 2009
Dissipative hydrodynamics for viscous relativistic fluids Heinz, Ulrich; Song, Huichao; Chaudhuri, A. K. Physical Review C, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevC.73.034904	journal	March 2006
Conformal relativistic viscous hydrodynamics: Applications to RHIC results at $\sqrt{s_{NN}} = 200$ GeV Luzum, Matthew; Romatschke, Paul Physical Review C, Vol. 78, Issue 3 https://doi.org/10.1103/PhysRevC.78.034915	journal	September 2008
Anisotropic hydrodynamics for rapidly expanding systems Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Nuclear Physics A, Vol. 916 https://doi.org/10.1016/j.nuclphysa.2013.08.004	journal	October 2013
Testing viscous and anisotropic hydrodynamics in an exactly solvable case Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.024903	journal	August 2013
Thermal equilibration in ultra-relativistic heavy-ion collisions Baym, Gordon Physics Letters B, Vol. 138, Issue 1-3 https://doi.org/10.1016/0370-2693(84)91863-X	journal	April 1984
Hydrodynamic Modeling of Heavy-Ion Collisions Gale, Charles; Jeon, Sangyong; Schenke, BjÖRn International Journal of Modern Physics A, Vol. 28, Issue 11 https://doi.org/10.1142/S0217751X13400113	journal	April 2013
Highly anisotropic hydrodynamics in $3 + 1$ space-time dimensions Ryblewski, Radoslaw; Florkowski, Wojciech Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.064901	journal	June 2012

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