Relativistic Fluid Dynamics Far From Local Equilibrium

Romatschke, Paul

doi:10.1103/PhysRevLett.120.012301

Title: Relativistic Fluid Dynamics Far From Local Equilibrium

Abstract

Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. As a result, arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N = 4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.

Authors:: Romatschke, Paul

Publication Date:: Fri Jan 05 00:00:00 EST 2018

Research Org.:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1415876

Alternate Identifier(s):: OSTI ID: 1498985

Grant/Contract Number:: SC0008132

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 120 Journal Issue: 1; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Romatschke, Paul. Relativistic Fluid Dynamics Far From Local Equilibrium.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevLett.120.012301.

Copy to clipboard


                    Romatschke, Paul. Relativistic Fluid Dynamics Far From Local Equilibrium.  United States.  https://doi.org/10.1103/PhysRevLett.120.012301

Copy to clipboard


                    Romatschke, Paul. Fri .  
"Relativistic Fluid Dynamics Far From Local Equilibrium".  United States.  https://doi.org/10.1103/PhysRevLett.120.012301.

Copy to clipboard


                    
@article{osti_1415876,

  title        = {Relativistic Fluid Dynamics Far From Local Equilibrium},

  author       = {Romatschke, Paul},

  abstractNote = {Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. As a result, arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N = 4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.},

  doi          = {10.1103/PhysRevLett.120.012301},

  journal      = {Physical Review Letters},

  number       = 1,

  volume       = 120,

  place        = {United States},

  year         = {Fri Jan 05 00:00:00 EST 2018},

  month        = {Fri Jan 05 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevLett.120.012301

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 126 works

Citation information provided by
Web of Science

Figures / Tables:

Figure 1: Numerical results for energy density evolution as a function of inverse gradient strength τT for conformal Bjorken flow in three different microscopic theories. Note that for Boltzmann and AdS=CFT, the numerical solutions shown are low-dimensional projections from an infinite dimensional space of initial conditions. See text for details.

All figures and tables (2 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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
DOI: 10.1088/1126-6708/2008/04/100

Resurgence in extended hydrodynamics
journal, April 2016

Aniceto, Inês; Spaliński, Michał
Physical Review D, Vol. 93, Issue 8
DOI: 10.1103/PhysRevD.93.085008

Characteristics of Thermalization of Boost-Invariant Plasma from Holography
journal, May 2012

Heller, Michal P.; Janik, Romuald A.; Witaszczyk, Przemysław
Physical Review Letters, Vol. 108, Issue 20
DOI: 10.1103/PhysRevLett.108.201602

Hydrodynamic Gradient Expansion in Gauge Theory Plasmas
journal, May 2013

Heller, Michal P.; Janik, Romuald A.; Witaszczyk, Przemysław
Physical Review Letters, Vol. 110, Issue 21
DOI: 10.1103/PhysRevLett.110.211602

Transport coefficients for bulk viscous evolution in the relaxation-time approximation
journal, October 2014

Jaiswal, Amaresh; Ryblewski, Radoslaw; Strickland, Michael
Physical Review C, Vol. 90, Issue 4
DOI: 10.1103/PhysRevC.90.044908

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
DOI: 10.1103/PhysRevLett.89.159901

Formalizing the slow-roll approximation in inflation
journal, December 1994

Liddle, Andrew R.; Parsons, Paul; Barrow, John D.
Physical Review D, Vol. 50, Issue 12
DOI: 10.1103/PhysRevD.50.7222

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
journal, November 2014

Bu, Yanyan; Lublinsky, Michael
Journal of High Energy Physics, Vol. 2014, Issue 11
DOI: 10.1007/JHEP11(2014)064

Nonhydrodynamic Transport in Trapped Unitary Fermi Gases
journal, November 2015

Brewer, Jasmine; Romatschke, Paul
Physical Review Letters, Vol. 115, Issue 19
DOI: 10.1103/PhysRevLett.115.190404

Highly relativistic nucleus-nucleus collisions: The central rapidity region
journal, January 1983

Bjorken, J. D.
Physical Review D, Vol. 27, Issue 1
DOI: 10.1103/PhysRevD.27.140

One fluid to rule them all: Viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at $\sqrt{s} = 5.02$ TeV
journal, November 2017

Weller, Ryan D.; Romatschke, Paul
Physics Letters B, Vol. 774
DOI: 10.1016/j.physletb.2017.09.077

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015

Kurkela, Aleksi; Zhu, Yan
Physical Review Letters, Vol. 115, Issue 18
DOI: 10.1103/PhysRevLett.115.182301

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

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

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

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

Boost-invariant early time dynamics from AdS/CFT
journal, October 2009

Beuf, Guillaume; Heller, Michal P.; Janik, Romuald A.
Journal of High Energy Physics, Vol. 2009, Issue 10
DOI: 10.1088/1126-6708/2009/10/043

Relativistic (lattice) Boltzmann equation with nonideal equation of state
journal, March 2012

Romatschke, Paul
Physical Review D, Vol. 85, Issue 6
DOI: 10.1103/PhysRevD.85.065012

Horizon Formation and Far-from-Equilibrium Isotropization in a Supersymmetric Yang-Mills Plasma
journal, May 2009

Chesler, Paul M.; Yaffe, Laurence G.
Physical Review Letters, Vol. 102, Issue 21
DOI: 10.1103/PhysRevLett.102.211601

Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in $N = 4$ supersymmetric Yang-Mills theory
journal, July 2010

Chesler, Paul M.; Yaffe, Laurence G.
Physical Review D, Vol. 82, Issue 2
DOI: 10.1103/PhysRevD.82.026006

Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions
journal, June 2016

Romatschke, Paul
The European Physical Journal C, Vol. 76, Issue 6
DOI: 10.1140/epjc/s10052-016-4169-7

How much entropy is produced in strongly coupled quark-gluon plasma (sQGP) by dissipative effects?
journal, August 2007

Lublinsky, M.; Shuryak, E.
Physical Review C, Vol. 76, Issue 2
DOI: 10.1103/PhysRevC.76.021901

Holographic thermalization with radial flow
journal, March 2013

van der Schee, Wilke
Physical Review D, Vol. 87, Issue 6
DOI: 10.1103/PhysRevD.87.061901

“Ridge” in Proton-Proton Scattering at 7 TeV
journal, March 2011

Werner, K.; Karpenko, Iu.; Pierog, T.
Physical Review Letters, Vol. 106, Issue 12
DOI: 10.1103/PhysRevLett.106.122004

Gradient expansion for anisotropic hydrodynamics
journal, December 2016

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

Zum Paradoxon der W�rmeleitungstheorie
journal, August 1967

M�ller, Ingo
Zeitschrift f�r Physik, Vol. 198, Issue 4
DOI: 10.1007/BF01326412

Nonlinear fluid dynamics from gravity
journal, February 2008

Bhattacharyya, Sayantani; Minwalla, Shiraz; Hubeny, Veronika E.
Journal of High Energy Physics, Vol. 2008, Issue 02
DOI: 10.1088/1126-6708/2008/02/045

Quasinormal modes of black holes and black branes
journal, July 2009

Berti, Emanuele; Cardoso, Vitor; Starinets, Andrei O.
Classical and Quantum Gravity, Vol. 26, Issue 16
DOI: 10.1088/0264-9381/26/16/163001

On the apparent convergence of perturbative QCD at high temperature
journal, July 2003

Blaizot, J. -P.; Iancu, E.; Rebhan, A.
Physical Review D, Vol. 68, Issue 2
DOI: 10.1103/PhysRevD.68.025011

Absence of a local rest frame in far from equilibrium quantum matter
journal, October 2014

Arnold, Peter; Romatschke, Paul; van der Schee, Wilke
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)110

Observation of Long-Range Elliptic Azimuthal Anisotropies in $\sqrt{s} = 13$ and 2.76 TeV $p p$ Collisions with the ATLAS Detector
journal, April 2016

Aad, G.; Abbott, B.; Abdallah, J.
Physical Review Letters, Vol. 116, Issue 17
DOI: 10.1103/PhysRevLett.116.172301

Elliptic flow in proton–proton collisions at $\sqrt{s}=7$ TeV
journal, January 2011

Bożek, Piotr
The European Physical Journal C, Vol. 71, Issue 1
DOI: 10.1140/epjc/s10052-010-1530-0

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

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

Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013

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

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

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

Hydrodynamics, resurgence, and transasymptotics
journal, December 2015

Başar, Gökçe; Dunne, Gerald V.
Physical Review D, Vol. 92, Issue 12
DOI: 10.1103/PhysRevD.92.125011

Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography
journal, November 2016

Buchel, Alex; Heller, Michal P.; Noronha, Jorge
Physical Review D, Vol. 94, Issue 10
DOI: 10.1103/PhysRevD.94.106011

SHOCK WAVE COLLISIONS IN AdS ₅ : APPROXIMATE NUMERICAL SOLUTIONS
journal, December 2011

Wu, Bin; Romatschke, Paul
International Journal of Modern Physics C, Vol. 22, Issue 12
DOI: 10.1142/S0129183111016920

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
journal, August 2015

Heller, Michal P.; Spaliński, Michał
Physical Review Letters, Vol. 115, Issue 7
DOI: 10.1103/PhysRevLett.115.072501

From strong to weak coupling in holographic models of thermalization
journal, July 2016

Grozdanov, Sašo; Kaplis, Nikolaos; Starinets, Andrei O.
Journal of High Energy Physics, Vol. 2016, Issue 7
DOI: 10.1007/JHEP07(2016)151

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions
journal, October 2013

Casalderrey-Solana, Jorge; Heller, Michal P.; Mateos, David
Physical Review Letters, Vol. 111, Issue 18
DOI: 10.1103/PhysRevLett.111.181601

Constructing higher-order hydrodynamics: The third order
journal, March 2016

Grozdanov, Sašo; Kaplis, Nikolaos
Physical Review D, Vol. 93, Issue 6
DOI: 10.1103/PhysRevD.93.066012

Figures / Tables found in this record:

Figure 1 (p. 3)

Figure 2 (p. 4)

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Hydrodynamic generators in relativistic kinetic theory

Journal Article McNelis, M. ; Heinz, U. - Physical Review. C

We resum the nonequilibrium gradient corrections to a single-particle distribution function evolved by the Boltzmann equation in the relaxation time approximation (RTA). We first study a system undergoing Bjorken expansion and show that, for a constant relaxation time, the exact solution of the RTA Boltzmann equation at late times (i.e., after the decay of nonhydrodynamic modes) generates the Borel resummed Chapman-Enskog series. Extending this correspondence to systems without Bjorken symmetry, we construct a (3+1)-dimensional hydrodynamic generator for RTA kinetic theory, which is an integral representation of the Chapman-Enskog series in the limit of vanishing nonhydrodynamic modes. Relaxing this limit, wemore »« less
Cited by 6
https://doi.org/10.1103/PhysRevC.101.054901

Full Text Available
Hydrodynamization times of a holographic fluid far from equilibrium

Journal Article Rougemont, Romulo ; Barreto, Willians ; Noronha, Jorge - Physical Review. D.

We investigate several hydrodynamization times for an ensemble of different far-from-equilibrium solutions of the strongly coupled N = 4 supersymmetric Yang-Mills plasma undergoing Bjorken flow. For the ensemble of initial data analyzed in the present work, we find that, with typical tolerances between 3% to 5%, the average hydrodynamization time associated with the late time convergence of the pressure anisotropy to the corresponding Borel resummed hydrodynamic attractor is approximately equal to the average hydrodynamization time associated with the Navier-Stokes result, while both are shorter than the average hydrodynamization time associated with second-order hydrodynamics. On the other hand, we find thatmore »« less
https://doi.org/10.1103/physrevd.105.046009

Full Text Available
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

Journal Article Behtash, Alireza ; Cruz-Camacho, C. N. ; Martinez, M. - Physical Review. D.

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtainedmore »« less
Cited by 65
https://doi.org/10.1103/PhysRevD.97.044041
Divergence-type 2+1 dissipative hydrodynamics applied to heavy-ion collisions

Journal Article Peralta-Ramos, J ; Calzetta, E - Physical Review. C, Nuclear Physics

We apply divergence-type theory (DTT) dissipative hydrodynamics to study the 2+1 space-time evolution of the fireball created in Au+Au relativistic heavy-ion collisions at {radical}(s{sub NN})=200 GeV. DTTs are exact hydrodynamic theories that do not rely on velocity gradient expansions and therefore go beyond second-order theories. We numerically solve the equations of motion of the DTT for Glauber initial conditions and compare the results with those of second-order theory based on conformal invariance (Baier-Romatschke-Son-Starinets model) and with data. We find that the charged-hadron minimum-bias elliptic flow reaches its maximum value at lower p{sub T} in the DTT, and that the DTTmore »« less
https://doi.org/10.1103/PHYSREVC.82.054905
Resummed hydrodynamic expansion for a plasma of particles interacting with fields

Journal Article Tinti, L. ; Vujanovic, G. ; Noronha, J. ; ... - Physical Review D

A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and nonhydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in a consistent and numerically efficient way; at lowest order it reduces to an Israel-Stewart-like theory. This formalism is especially suited to investigate the general problem of particles interacting with fields. We tested the accuracy of this approach against the exact solution of the coupled Boltzmann-Vlasov-Maxwell equations for a plasma in an electromagnetic field undergoing Bjorken-like expansion, including extreme cases characterized by large deviations frommore »« less
Cited by 9
https://doi.org/10.1103/PhysRevD.99.016009

Similar Records

Title: Relativistic Fluid Dynamics Far From Local Equilibrium

Abstract

Citation Formats

Figures / Tables:

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

Resurgence in extended hydrodynamics journal, April 2016

Characteristics of Thermalization of Boost-Invariant Plasma from Holography journal, May 2012

Hydrodynamic Gradient Expansion in Gauge Theory Plasmas journal, May 2013

Transport coefficients for bulk viscous evolution in the relaxation-time approximation journal, October 2014

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

Formalizing the slow-roll approximation in inflation journal, December 1994

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics journal, November 2014

Nonhydrodynamic Transport in Trapped Unitary Fermi Gases journal, November 2015

Highly relativistic nucleus-nucleus collisions: The central rapidity region journal, January 1983

One fluid to rule them all: Viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at s = 5.02 TeV journal, November 2017

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions journal, October 2015

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

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

Boost-invariant early time dynamics from AdS/CFT journal, October 2009

Relativistic (lattice) Boltzmann equation with nonideal equation of state journal, March 2012

Horizon Formation and Far-from-Equilibrium Isotropization in a Supersymmetric Yang-Mills Plasma journal, May 2009

Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory journal, July 2010

Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions journal, June 2016

How much entropy is produced in strongly coupled quark-gluon plasma (sQGP) by dissipative effects? journal, August 2007

Holographic thermalization with radial flow journal, March 2013

“Ridge” in Proton-Proton Scattering at 7 TeV journal, March 2011

Gradient expansion for anisotropic hydrodynamics journal, December 2016

Zum Paradoxon der W�rmeleitungstheorie journal, August 1967

Nonlinear fluid dynamics from gravity journal, February 2008

Quasinormal modes of black holes and black branes journal, July 2009

On the apparent convergence of perturbative QCD at high temperature journal, July 2003

Absence of a local rest frame in far from equilibrium quantum matter journal, October 2014

Observation of Long-Range Elliptic Azimuthal Anisotropies in s = 13 and 2.76 TeV p p Collisions with the ATLAS Detector journal, April 2016

Elliptic flow in proton–proton collisions at $\sqrt{s}=7$ TeV journal, January 2011

Transient relativistic thermodynamics and kinetic theory journal, April 1979

Anisotropic hydrodynamics for rapidly expanding systems journal, October 2013

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

Hydrodynamics, resurgence, and transasymptotics journal, December 2015

Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography journal, November 2016

SHOCK WAVE COLLISIONS IN AdS 5 : APPROXIMATE NUMERICAL SOLUTIONS journal, December 2011

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation journal, August 2015

From strong to weak coupling in holographic models of thermalization journal, July 2016

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions journal, October 2013

Constructing higher-order hydrodynamics: The third order journal, March 2016

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

Resurgence in extended hydrodynamics
journal, April 2016

Characteristics of Thermalization of Boost-Invariant Plasma from Holography
journal, May 2012

Hydrodynamic Gradient Expansion in Gauge Theory Plasmas
journal, May 2013

Transport coefficients for bulk viscous evolution in the relaxation-time approximation
journal, October 2014

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

Formalizing the slow-roll approximation in inflation
journal, December 1994

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
journal, November 2014

Nonhydrodynamic Transport in Trapped Unitary Fermi Gases
journal, November 2015

Highly relativistic nucleus-nucleus collisions: The central rapidity region
journal, January 1983

One fluid to rule them all: Viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at $\sqrt{s} = 5.02$ TeV
journal, November 2017

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015

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

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

Boost-invariant early time dynamics from AdS/CFT
journal, October 2009

Relativistic (lattice) Boltzmann equation with nonideal equation of state
journal, March 2012

Horizon Formation and Far-from-Equilibrium Isotropization in a Supersymmetric Yang-Mills Plasma
journal, May 2009

Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in $N = 4$ supersymmetric Yang-Mills theory
journal, July 2010

Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions
journal, June 2016

How much entropy is produced in strongly coupled quark-gluon plasma (sQGP) by dissipative effects?
journal, August 2007

Holographic thermalization with radial flow
journal, March 2013

“Ridge” in Proton-Proton Scattering at 7 TeV
journal, March 2011

Gradient expansion for anisotropic hydrodynamics
journal, December 2016

Zum Paradoxon der W�rmeleitungstheorie
journal, August 1967

Nonlinear fluid dynamics from gravity
journal, February 2008

Quasinormal modes of black holes and black branes
journal, July 2009

On the apparent convergence of perturbative QCD at high temperature
journal, July 2003

Absence of a local rest frame in far from equilibrium quantum matter
journal, October 2014

Observation of Long-Range Elliptic Azimuthal Anisotropies in $\sqrt{s} = 13$ and 2.76 TeV $p p$ Collisions with the ATLAS Detector
journal, April 2016

Elliptic flow in proton–proton collisions at $\sqrt{s}=7$ TeV
journal, January 2011

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013

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

Hydrodynamics, resurgence, and transasymptotics
journal, December 2015

Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography
journal, November 2016

SHOCK WAVE COLLISIONS IN AdS ₅ : APPROXIMATE NUMERICAL SOLUTIONS
journal, December 2011

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
journal, August 2015

From strong to weak coupling in holographic models of thermalization
journal, July 2016

From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions
journal, October 2013

Constructing higher-order hydrodynamics: The third order
journal, March 2016