Anisotropic fluid dynamics for Gubser flow

doi:https://doi.org/10.1103/PhysRevC.95.054907

Title: Anisotropic fluid dynamics for Gubser flow

Abstract

Investigating a variety of closing schemes to the infinite hierarchy of momentum moments of the exactly solvable Boltzmann equation for systems undergoing Gubser flow, we study the precision with which the resulting hydrodynamic equations reproduce the exact evolution of hydrodynamic moments of the distribution function. We find that anisotropic hydrodynamics, obtained by expanding the distribution function around a dynamically evolving locally anisotropic background whose evolution is matched to exactly reproduce the macroscopic pressure anisotropy caused by the different longitudinal and transverse expansion rates in Gubser ow, provides the most accurate macroscopic description of the microscopic kinetic evolution. This confirms a similar earlier finding for Bjorken ow [Molnar, Niemi and Rischke, Phys. Rev. D 94, 125003 (2016)]. Also, we explain the physics behind this optimal matching procedure and show that one can efficiently correct for a nonoptimized matching choice by adding a residual shear stress to the energy-momentum tensor whose evolution is again determined by the Boltzmann equation. Further insights to guide the optimal choice of a macroscopic anisotropic hydrodynamic framework for strongly-coupled systems that do not admit a microscopic kinetic description are reported.

Authors:

Martinez, M. ^[1]; McNelis, M. ^[2];

^[2]

The Ohio State Univ., Columbus, OH (United States); North Carolina State Univ., Raleigh, NC (United States)
The Ohio State Univ., Columbus, OH (United States)

Publication Date:: 2017-05-18

Research Org.:: The Ohio State Univ., Columbus, OH (United States); North Carolina State Univ., Raleigh, NC (United States)

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

Contributing Org.:: University of Sao Paulo

OSTI Identifier:: 1604333

Alternate Identifier(s):: OSTI ID: 1357851

Grant/Contract Number:: SC0004286; FG02-03ER41260

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 95; Journal Issue: 5; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; relativistic heavy-ion collisions; quark-gluon plasma; anisotropic hydrodynamics; Boltzmann equation; viscous fluid dynamics

Citation Formats


                    Martinez, M., McNelis, M., and Heinz, Ulrich. Anisotropic fluid dynamics for Gubser flow.  United States: N. p., 2017. 
        Web.  doi:10.1103/PhysRevC.95.054907.

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                    Martinez, M., McNelis, M., & Heinz, Ulrich. Anisotropic fluid dynamics for Gubser flow.  United States.  https://doi.org/10.1103/PhysRevC.95.054907

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                    Martinez, M., McNelis, M., and Heinz, Ulrich. Thu .  
        "Anisotropic fluid dynamics for Gubser flow".  United States.  https://doi.org/10.1103/PhysRevC.95.054907.  https://www.osti.gov/servlets/purl/1604333.

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@article{osti_1604333,

  title        = {Anisotropic fluid dynamics for Gubser flow},

  author       = {Martinez, M. and McNelis, M. and Heinz, Ulrich},

  abstractNote = {Investigating a variety of closing schemes to the infinite hierarchy of momentum moments of the exactly solvable Boltzmann equation for systems undergoing Gubser flow, we study the precision with which the resulting hydrodynamic equations reproduce the exact evolution of hydrodynamic moments of the distribution function. We find that anisotropic hydrodynamics, obtained by expanding the distribution function around a dynamically evolving locally anisotropic background whose evolution is matched to exactly reproduce the macroscopic pressure anisotropy caused by the different longitudinal and transverse expansion rates in Gubser ow, provides the most accurate macroscopic description of the microscopic kinetic evolution. This confirms a similar earlier finding for Bjorken ow [Molnar, Niemi and Rischke, Phys. Rev. D 94, 125003 (2016)]. Also, we explain the physics behind this optimal matching procedure and show that one can efficiently correct for a nonoptimized matching choice by adding a residual shear stress to the energy-momentum tensor whose evolution is again determined by the Boltzmann equation. Further insights to guide the optimal choice of a macroscopic anisotropic hydrodynamic framework for strongly-coupled systems that do not admit a microscopic kinetic description are reported.},

  doi          = {10.1103/PhysRevC.95.054907},

  url          = {https://www.osti.gov/biblio/1604333},
  journal      = {Physical Review C},

  issn         = {2469-9985},

  number       = 5,

  volume       = 95,

  place        = {United States},

  year         = {2017},

  month        = {5}

}

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Works referenced in this record:

Dissipative dynamics of highly anisotropic systems
journal, December 2010

Martinez, Mauricio; Strickland, Michael
Nuclear Physics A, Vol. 848, Issue 1-2
https://doi.org/10.1016/j.nuclphysa.2010.08.011

Non-boost-invariant anisotropic dynamics
journal, April 2011

Martinez, Mauricio; Strickland, Michael
Nuclear Physics A, Vol. 856, Issue 1
https://doi.org/10.1016/j.nuclphysa.2011.02.003

Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
journal, March 2011

Florkowski, Wojciech; Ryblewski, Radoslaw
Physical Review C, Vol. 83, Issue 3
https://doi.org/10.1103/PhysRevC.83.034907

Non-boost-invariant motion of dissipative and highly anisotropic fluid
journal, December 2010

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

Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics
journal, April 2012

Florkowski, Wojciech; Ryblewski, Radoslaw
Physical Review C, Vol. 85, Issue 4
https://doi.org/10.1103/PhysRevC.85.044902

Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion
journal, November 2011

Ryblewski, Radoslaw; Florkowski, Wojciech
The European Physical Journal C, Vol. 71, Issue 11
https://doi.org/10.1140/epjc/s10052-011-1761-8

Boost-invariant (2+1)-dimensional anisotropic hydrodynamics
journal, June 2012

Martinez, Mauricio; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 85, Issue 6
https://doi.org/10.1103/PhysRevC.85.064913

Highly anisotropic hydrodynamics in $3 + 1$ space-time dimensions
journal, June 2012

Ryblewski, Radoslaw; Florkowski, Wojciech
Physical Review C, Vol. 85, Issue 6
https://doi.org/10.1103/PhysRevC.85.064901

Hydrodynamics of anisotropic quark and gluon fluids
journal, March 2013

Florkowski, Wojciech; Maj, Radoslaw; Ryblewski, Radoslaw
Physical Review C, Vol. 87, Issue 3
https://doi.org/10.1103/PhysRevC.87.034914

Mixture of Anisotropic Fluids
journal, January 2013

Florkowski, W.; Maj, R.
Acta Physica Polonica B, Vol. 44, Issue 10
https://doi.org/10.5506/APhysPolB.44.2003

Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics
journal, November 2014

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
Physical Review C, Vol. 90, Issue 5
https://doi.org/10.1103/PhysRevC.90.054910

Projection method and new formulation of leading-order anisotropic hydrodynamics
journal, March 2014

Tinti, Leonardo; Florkowski, Wojciech
Physical Review C, Vol. 89, Issue 3
https://doi.org/10.1103/PhysRevC.89.034907

Leading-order anisotropic hydrodynamics for systems with massive particles
journal, May 2014

Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 89, Issue 5
https://doi.org/10.1103/PhysRevC.89.054909

Kinetic Description of Mixtures of Anisotropic Fluids
journal, January 2014

Florkowski, W.; Madetko, O.
Acta Physica Polonica B, Vol. 45, Issue 5
https://doi.org/10.5506/APhysPolB.45.1103

Bulk viscous evolution within anisotropic hydrodynamics
journal, July 2014

Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 90, Issue 1
https://doi.org/10.1103/PhysRevC.90.014908

Shear-bulk coupling in nonconformal hydrodynamics
journal, October 2014

Denicol, Gabriel S.; Florkowski, Wojciech; Ryblewski, Radoslaw
Physical Review C, Vol. 90, Issue 4
https://doi.org/10.1103/PhysRevC.90.044905

Nonconformal viscous anisotropic hydrodynamics
journal, June 2015

Bazow, Dennis; Heinz, Ulrich; Martinez, Mauricio
Physical Review C, Vol. 91, Issue 6
https://doi.org/10.1103/PhysRevC.91.064903

Leading-order anisotropic hydrodynamics for central collisions
journal, October 2015

Nopoush, Mohammad; Strickland, Michael; Ryblewski, Radoslaw
Physical Review C, Vol. 92, Issue 4
https://doi.org/10.1103/PhysRevC.92.044912

Anisotropic hydrodynamics for a mixture of quark and gluon fluids
journal, November 2015

Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw
Physical Review C, Vol. 92, Issue 5
https://doi.org/10.1103/PhysRevC.92.054912

Quasiparticle equation of state for anisotropic hydrodynamics
journal, November 2015

Alqahtani, Mubarak; Nopoush, Mohammad; Strickland, Michael
Physical Review C, Vol. 92, Issue 5
https://doi.org/10.1103/PhysRevC.92.054910

Transient oscillations in a macroscopic effective theory of the Boltzmann equation
journal, February 2016

Bazow, Dennis; Martinez, Mauricio; Heinz, Ulrich
Physical Review D, Vol. 93, Issue 3
https://doi.org/10.1103/PhysRevD.93.034002

Testing different formulations of leading-order anisotropic hydrodynamics
journal, February 2016

Tinti, Leonardo; Ryblewski, Radoslaw; Florkowski, Wojciech
Nuclear Physics A, Vol. 946
https://doi.org/10.1016/j.nuclphysa.2015.11.006

Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
journal, October 2015

Bluhm, M.; Schäfer, T.
Physical Review A, Vol. 92, Issue 4
https://doi.org/10.1103/PhysRevA.92.043602

Model-Independent Determination of the Shear Viscosity of a Trapped Unitary Fermi gas: Application to High-Temperature Data
journal, March 2016

Bluhm, M.; Schäfer, T.
Physical Review Letters, Vol. 116, Issue 11
https://doi.org/10.1103/PhysRevLett.116.115301

Quasiparticle anisotropic hydrodynamics for central collisions
journal, March 2017

Alqahtani, Mubarak; Nopoush, Mohammad; Strickland, Michael
Physical Review C, Vol. 95, Issue 3
https://doi.org/10.1103/PhysRevC.95.034906

Non-boost-invariant dissipative hydrodynamics
journal, December 2016

Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 94, Issue 6
https://doi.org/10.1103/PhysRevC.94.064903

Phenomenological predictions of 3+1d anisotropic hydrodynamics
journal, April 2017

Nopoush, Mohammad; Strickland, Michael; Ryblewski, Radoslaw
Journal of Physics: Conference Series, Vol. 832
https://doi.org/10.1088/1742-6596/832/1/012054

Gradient expansion for anisotropic hydrodynamics
journal, December 2016

Florkowski, Wojciech; Ryblewski, Radoslaw; Spaliński, Michał
Physical Review D, Vol. 94, Issue 11
https://doi.org/10.1103/PhysRevD.94.114025

Generalized theory of diffusion based on kinetic theory
journal, October 2016

Schäfer, T.
Physical Review A, Vol. 94, Issue 4
https://doi.org/10.1103/PhysRevA.94.043644

Derivation of transient relativistic fluid dynamics from the Boltzmann equation
journal, June 2012

Denicol, G. S.; Niemi, H.; Molnár, E.
Physical Review D, Vol. 85, Issue 11
https://doi.org/10.1103/PhysRevD.85.114047

Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)]
journal, February 2015

Denicol, G. S.; Niemi, H.; Molnár, E.
Physical Review D, Vol. 91, Issue 3
https://doi.org/10.1103/PhysRevD.91.039902

Dissipative hydrodynamics and heavy-ion collisions
journal, June 2006

Baier, Rudolf; Romatschke, Paul; Wiedemann, Urs Achim
Physical Review C, Vol. 73, Issue 6
https://doi.org/10.1103/PhysRevC.73.064903

Suppression of elliptic flow in a minimally viscous quark–gluon plasma
journal, January 2008

Song, Huichao; Heinz, Ulrich
Physics Letters B, Vol. 658, Issue 5
https://doi.org/10.1016/j.physletb.2007.11.019

Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions
journal, June 2008

Song, Huichao; Heinz, Ulrich
Physical Review C, Vol. 77, Issue 6
https://doi.org/10.1103/PhysRevC.77.064901

Second-Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions
journal, January 2002

Muronga, Azwinndini
Physical Review Letters, Vol. 88, Issue 6
https://doi.org/10.1103/PhysRevLett.88.062302

Erratum: Second Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions [Phys. Rev. Lett. 88 , 062302 (2002)]
journal, September 2002

Muronga, Azwinndini
Physical Review Letters, Vol. 89, Issue 15
https://doi.org/10.1103/PhysRevLett.89.159901

Causal theories of dissipative relativistic fluid dynamics for nuclear collisions
journal, March 2004

Muronga, Azwinndini
Physical Review C, Vol. 69, Issue 3
https://doi.org/10.1103/PhysRevC.69.034903

Dissipative hydrodynamics for viscous relativistic fluids
journal, March 2006

Heinz, Ulrich; Song, Huichao; Chaudhuri, A. K.
Physical Review C, Vol. 73, Issue 3
https://doi.org/10.1103/PhysRevC.73.034904

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter
journal, July 2007

Muronga, Azwinndini
Physical Review C, Vol. 76, Issue 1
https://doi.org/10.1103/PhysRevC.76.014910

Relativistic dynamics of nonideal fluids: Viscous and heat-conducting fluids. I. General aspects and $3 + 1$ formulation for nuclear collisions
journal, July 2007

Muronga, Azwinndini
Physical Review C, Vol. 76, Issue 1
https://doi.org/10.1103/PhysRevC.76.014909

Energy loss of a heavy fermion in an anisotropic QED plasma
journal, March 2004

Romatschke, Paul; Strickland, Michael
Physical Review D, Vol. 69, Issue 6
https://doi.org/10.1103/PhysRevD.69.065005

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
journal, June 2016

Molnár, Etele; Niemi, Harri; Rischke, Dirk H.
Physical Review D, Vol. 93, Issue 11
https://doi.org/10.1103/PhysRevD.93.114025

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation
journal, December 2016

Molnár, E.; Niemi, H.; Rischke, D. H.
Physical Review D, Vol. 94, Issue 12
https://doi.org/10.1103/PhysRevD.94.125003

Anisotropic matching principle for the hydrodynamic expansion
journal, October 2016

Tinti, Leonardo
Physical Review C, Vol. 94, Issue 4
https://doi.org/10.1103/PhysRevC.94.044902

Thermal equilibration in ultra-relativistic heavy-ion collisions
journal, April 1984

Baym, Gordon
Physics Letters B, Vol. 138, Issue 1-3
https://doi.org/10.1016/0370-2693(84)91863-X

Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013

Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
Nuclear Physics A, Vol. 916
https://doi.org/10.1016/j.nuclphysa.2013.08.004

Testing viscous and anisotropic hydrodynamics in an exactly solvable case
journal, August 2013

Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 88, Issue 2
https://doi.org/10.1103/PhysRevC.88.024903

Exact solution of the ( $0 + 1$ )-dimensional Boltzmann equation for a massive gas
journal, May 2014

Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw
Physical Review C, Vol. 89, Issue 5
https://doi.org/10.1103/PhysRevC.89.054908

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
journal, December 2014

Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio
Physical Review D, Vol. 90, Issue 12
https://doi.org/10.1103/PhysRevD.90.125026

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit
journal, November 2014

Denicol, Gabriel S.; Heinz, Ulrich; Martinez, Mauricio
Physical Review Letters, Vol. 113, Issue 20
https://doi.org/10.1103/PhysRevLett.113.202301

Investigating the domain of validity of the Gubser solution to the Boltzmann equation
journal, November 2015

Heinz, Ulrich; Martinez, Mauricio
Nuclear Physics A, Vol. 943
https://doi.org/10.1016/j.nuclphysa.2015.08.009

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

Gubser, Steven S.
Physical Review D, Vol. 82, Issue 8
https://doi.org/10.1103/PhysRevD.82.085027

Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011

Gubser, Steven S.; Yarom, Amos
Nuclear Physics B, Vol. 846, Issue 3
https://doi.org/10.1016/j.nuclphysb.2011.01.012

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
Physical Review D, Vol. 91, Issue 4
https://doi.org/10.1103/PhysRevD.91.045007

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
journal, December 2016

Bazow, D.; Denicol, G. S.; Heinz, U.
Physical Review D, Vol. 94, Issue 12
https://doi.org/10.1103/PhysRevD.94.125006

Kinetic foundations of relativistic dissipative fluid dynamics
journal, November 2014

Denicol, G. S.
Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 12
https://doi.org/10.1088/0954-3899/41/12/124004

Anisotropic hydrodynamics, bulk viscosities, and $r$ -modes of strange quark stars with strong magnetic fields
journal, February 2010

Huang, Xu-Guang; Huang, Mei; Rischke, Dirk H.
Physical Review D, Vol. 81, Issue 4
https://doi.org/10.1103/PhysRevD.81.045015

Kubo formulas for relativistic fluids in strong magnetic fields
journal, December 2011

Huang, Xu-Guang; Sedrakian, Armen; Rischke, Dirk H.
Annals of Physics, Vol. 326, Issue 12
https://doi.org/10.1016/j.aop.2011.08.001

Relativistic hydrodynamics and thermodynamics of anisotropic plasmas
journal, August 1991

Gedalin, M.
Physics of Fluids B: Plasma Physics, Vol. 3, Issue 8
https://doi.org/10.1063/1.859656

Generally covariant relativistic anisotropic magnetohydrodynamics
journal, May 1995

Gedalin, M.; Oiberman, I.
Physical Review E, Vol. 51, Issue 5
https://doi.org/10.1103/PhysRevE.51.4901

Collective modes of an anisotropic quark-gluon plasma
journal, August 2003

Romatschke, Paul; Strickland, Michael
Physical Review D, Vol. 68, Issue 3
https://doi.org/10.1103/PhysRevD.68.036004

Equilibration of the quark-gluon plasma produced in relativistic heavy ion collisions
journal, June 1989

Banerjee, B.; Bhalerao, R. S.; Ravishankar, V.
Physics Letters B, Vol. 224, Issue 1-2
https://doi.org/10.1016/0370-2693(89)91041-1

Shear Viscosity of Strongly Coupled $N = 4$ Supersymmetric Yang-Mills Plasma
journal, August 2001

Policastro, G.; Son, D. T.; Starinets, A. O.
Physical Review Letters, Vol. 87, Issue 8
https://doi.org/10.1103/PhysRevLett.87.081601

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005

Kovtun, P. K.; Son, D. T.; Starinets, A. O.
Physical Review Letters, Vol. 94, Issue 11
https://doi.org/10.1103/PhysRevLett.94.111601

Do nuclear collisions create a locally equilibrated quark–gluon plasma?
journal, January 2017

Romatschke, P.
The European Physical Journal C, Vol. 77, Issue 1
https://doi.org/10.1140/epjc/s10052-016-4567-x

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

Israel, W.; Stewart, J. M.
Annals of Physics, Vol. 118, Issue 2
https://doi.org/10.1016/0003-4916(79)90130-1

Relativistic viscous hydrodynamics, conformal invariance, and holography
journal, April 2008

Baier, Rudolf; Romatschke, Paul; Son, Dam Thanh
Journal of High Energy Physics, Vol. 2008, Issue 04
https://doi.org/10.1088/1126-6708/2008/04/100

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Title: Anisotropic fluid dynamics for Gubser flow

Abstract

Citation Formats

Dissipative dynamics of highly anisotropic systems journal, December 2010

Non-boost-invariant anisotropic dynamics journal, April 2011

Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions journal, March 2011

Non-boost-invariant motion of dissipative and highly anisotropic fluid journal, December 2010

Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics journal, April 2012

Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion journal, November 2011

Boost-invariant (2+1)-dimensional anisotropic hydrodynamics journal, June 2012

Highly anisotropic hydrodynamics in 3 + 1 space-time dimensions journal, June 2012

Hydrodynamics of anisotropic quark and gluon fluids journal, March 2013

Mixture of Anisotropic Fluids journal, January 2013

Second-order ( 2 + 1 ) -dimensional anisotropic hydrodynamics journal, November 2014

Projection method and new formulation of leading-order anisotropic hydrodynamics journal, March 2014

Leading-order anisotropic hydrodynamics for systems with massive particles journal, May 2014

Kinetic Description of Mixtures of Anisotropic Fluids journal, January 2014

Bulk viscous evolution within anisotropic hydrodynamics journal, July 2014

Shear-bulk coupling in nonconformal hydrodynamics journal, October 2014

Nonconformal viscous anisotropic hydrodynamics journal, June 2015

Leading-order anisotropic hydrodynamics for central collisions journal, October 2015

Anisotropic hydrodynamics for a mixture of quark and gluon fluids journal, November 2015

Quasiparticle equation of state for anisotropic hydrodynamics journal, November 2015

Transient oscillations in a macroscopic effective theory of the Boltzmann equation journal, February 2016

Testing different formulations of leading-order anisotropic hydrodynamics journal, February 2016

Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics journal, October 2015

Model-Independent Determination of the Shear Viscosity of a Trapped Unitary Fermi gas: Application to High-Temperature Data journal, March 2016

Quasiparticle anisotropic hydrodynamics for central collisions journal, March 2017

Non-boost-invariant dissipative hydrodynamics journal, December 2016

Phenomenological predictions of 3+1d anisotropic hydrodynamics journal, April 2017

Gradient expansion for anisotropic hydrodynamics journal, December 2016

Generalized theory of diffusion based on kinetic theory journal, October 2016

Derivation of transient relativistic fluid dynamics from the Boltzmann equation journal, June 2012

Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)] journal, February 2015

Dissipative hydrodynamics and heavy-ion collisions journal, June 2006

Suppression of elliptic flow in a minimally viscous quark–gluon plasma journal, January 2008

Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions journal, June 2008

Second-Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions journal, January 2002

Erratum: Second Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions [Phys. Rev. Lett. 88 , 062302 (2002)] journal, September 2002

Causal theories of dissipative relativistic fluid dynamics for nuclear collisions journal, March 2004

Dissipative hydrodynamics for viscous relativistic fluids journal, March 2006

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter journal, July 2007

Relativistic dynamics of nonideal fluids: Viscous and heat-conducting fluids. I. General aspects and 3 + 1 formulation for nuclear collisions journal, July 2007

Energy loss of a heavy fermion in an anisotropic QED plasma journal, March 2004

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation journal, June 2016

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation journal, December 2016

Anisotropic matching principle for the hydrodynamic expansion journal, October 2016

Thermal equilibration in ultra-relativistic heavy-ion collisions journal, April 1984

Anisotropic hydrodynamics for rapidly expanding systems journal, October 2013

Testing viscous and anisotropic hydrodynamics in an exactly solvable case journal, August 2013

Exact solution of the ( 0 + 1 )-dimensional Boltzmann equation for a massive gas journal, May 2014

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation journal, December 2014

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit journal, November 2014

Investigating the domain of validity of the Gubser solution to the Boltzmann equation journal, November 2015

Symmetry constraints on generalizations of Bjorken flow journal, October 2010

Conformal hydrodynamics in Minkowski and de Sitter spacetimes journal, May 2011

Anisotropic hydrodynamics for conformal Gubser flow journal, February 2015

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime journal, December 2016

Kinetic foundations of relativistic dissipative fluid dynamics journal, November 2014

Anisotropic hydrodynamics, bulk viscosities, and r -modes of strange quark stars with strong magnetic fields journal, February 2010

Kubo formulas for relativistic fluids in strong magnetic fields journal, December 2011

Relativistic hydrodynamics and thermodynamics of anisotropic plasmas journal, August 1991

Generally covariant relativistic anisotropic magnetohydrodynamics journal, May 1995

Collective modes of an anisotropic quark-gluon plasma journal, August 2003

Equilibration of the quark-gluon plasma produced in relativistic heavy ion collisions journal, June 1989

Shear Viscosity of Strongly Coupled N = 4 Supersymmetric Yang-Mills Plasma journal, August 2001

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics journal, March 2005

Do nuclear collisions create a locally equilibrated quark–gluon plasma? journal, January 2017

Transient relativistic thermodynamics and kinetic theory journal, April 1979

Relativistic viscous hydrodynamics, conformal invariance, and holography journal, April 2008

Including off-diagonal anisotropies in anisotropic hydrodynamics journal, July 2019

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow journal, September 2019

Bottomonium suppression using a lattice QCD vetted potential journal, January 2018

Hyperbolic theory of relativistic conformal dissipative fluids journal, January 2018

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow journal, February 2018

Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow journal, June 2019

Dissipative dynamics of highly anisotropic systems
journal, December 2010

Non-boost-invariant anisotropic dynamics
journal, April 2011

Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
journal, March 2011

Non-boost-invariant motion of dissipative and highly anisotropic fluid
journal, December 2010

Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics
journal, April 2012

Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion
journal, November 2011

Boost-invariant (2+1)-dimensional anisotropic hydrodynamics
journal, June 2012

Highly anisotropic hydrodynamics in $3 + 1$ space-time dimensions
journal, June 2012

Hydrodynamics of anisotropic quark and gluon fluids
journal, March 2013

Mixture of Anisotropic Fluids
journal, January 2013

Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics
journal, November 2014

Projection method and new formulation of leading-order anisotropic hydrodynamics
journal, March 2014

Leading-order anisotropic hydrodynamics for systems with massive particles
journal, May 2014

Kinetic Description of Mixtures of Anisotropic Fluids
journal, January 2014

Bulk viscous evolution within anisotropic hydrodynamics
journal, July 2014

Shear-bulk coupling in nonconformal hydrodynamics
journal, October 2014

Nonconformal viscous anisotropic hydrodynamics
journal, June 2015

Leading-order anisotropic hydrodynamics for central collisions
journal, October 2015

Anisotropic hydrodynamics for a mixture of quark and gluon fluids
journal, November 2015

Quasiparticle equation of state for anisotropic hydrodynamics
journal, November 2015

Transient oscillations in a macroscopic effective theory of the Boltzmann equation
journal, February 2016

Testing different formulations of leading-order anisotropic hydrodynamics
journal, February 2016

Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
journal, October 2015

Model-Independent Determination of the Shear Viscosity of a Trapped Unitary Fermi gas: Application to High-Temperature Data
journal, March 2016

Quasiparticle anisotropic hydrodynamics for central collisions
journal, March 2017

Non-boost-invariant dissipative hydrodynamics
journal, December 2016

Phenomenological predictions of 3+1d anisotropic hydrodynamics
journal, April 2017

Gradient expansion for anisotropic hydrodynamics
journal, December 2016

Generalized theory of diffusion based on kinetic theory
journal, October 2016

Derivation of transient relativistic fluid dynamics from the Boltzmann equation
journal, June 2012

Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)]
journal, February 2015

Dissipative hydrodynamics and heavy-ion collisions
journal, June 2006

Suppression of elliptic flow in a minimally viscous quark–gluon plasma
journal, January 2008

Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions
journal, June 2008

Second-Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions
journal, January 2002

Erratum: Second Order Dissipative Fluid Dynamics for Ultrarelativistic Nuclear Collisions [Phys. Rev. Lett. 88 , 062302 (2002)]
journal, September 2002

Causal theories of dissipative relativistic fluid dynamics for nuclear collisions
journal, March 2004

Dissipative hydrodynamics for viscous relativistic fluids
journal, March 2006

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter
journal, July 2007

Relativistic dynamics of nonideal fluids: Viscous and heat-conducting fluids. I. General aspects and $3 + 1$ formulation for nuclear collisions
journal, July 2007

Energy loss of a heavy fermion in an anisotropic QED plasma
journal, March 2004

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
journal, June 2016

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation
journal, December 2016

Anisotropic matching principle for the hydrodynamic expansion
journal, October 2016

Thermal equilibration in ultra-relativistic heavy-ion collisions
journal, April 1984

Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013

Testing viscous and anisotropic hydrodynamics in an exactly solvable case
journal, August 2013

Exact solution of the ( $0 + 1$ )-dimensional Boltzmann equation for a massive gas
journal, May 2014

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
journal, December 2014

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit
journal, November 2014

Investigating the domain of validity of the Gubser solution to the Boltzmann equation
journal, November 2015

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
journal, December 2016

Kinetic foundations of relativistic dissipative fluid dynamics
journal, November 2014

Anisotropic hydrodynamics, bulk viscosities, and $r$ -modes of strange quark stars with strong magnetic fields
journal, February 2010

Kubo formulas for relativistic fluids in strong magnetic fields
journal, December 2011

Relativistic hydrodynamics and thermodynamics of anisotropic plasmas
journal, August 1991

Generally covariant relativistic anisotropic magnetohydrodynamics
journal, May 1995

Collective modes of an anisotropic quark-gluon plasma
journal, August 2003

Equilibration of the quark-gluon plasma produced in relativistic heavy ion collisions
journal, June 1989

Shear Viscosity of Strongly Coupled $N = 4$ Supersymmetric Yang-Mills Plasma
journal, August 2001

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005

Do nuclear collisions create a locally equilibrated quark–gluon plasma?
journal, January 2017

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

Relativistic viscous hydrodynamics, conformal invariance, and holography
journal, April 2008

Including off-diagonal anisotropies in anisotropic hydrodynamics
journal, July 2019

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
journal, September 2019

Bottomonium suppression using a lattice QCD vetted potential
journal, January 2018

Hyperbolic theory of relativistic conformal dissipative fluids
journal, January 2018

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
journal, February 2018

Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
journal, June 2019