Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Heinz, U.; Bazow, D.; Denicol, G. S.; Martinez, M.; Nopoush, M.; Noronha, J.; Ryblewski, R.; Strickland, M.

doi:10.1016/j.nuclphysbps.2016.05.042

Title: Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Abstract

Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.

Authors:

^[1]; Bazow, D. ^[1]; Denicol, G. S. ^[2]; Martinez, M. ^[1]; Nopoush, M. ^[3]; Noronha, J. ^[4]; Ryblewski, R. ^[5]; Strickland, M. ^[3]

The Ohio State Univ., Columbus, OH (United States)
McGill Univ., Montreal, QC (Canada)
Kent State Univ., Kent, OH (United States)
Univ. de São Paulo, São Paulo, SP (Brazil). Inst. de Física
Polish Academy of Sciences (PAS), Krakow (Poland). H. Niewodniczański Inst. of Nuclear Physic

Publication Date:: Wed Jun 08 00:00:00 EDT 2016

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); Natural Sciences and Engineering Research Council of Canada (NSERC); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

OSTI Identifier:: 1604416

Alternate Identifier(s):: OSTI ID: 1466864

Grant/Contract Number:: SC0004286

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear and Particle Physics Proceedings

Additional Journal Information:: Journal Volume: 276-278; Journal Issue: C; Journal ID: ISSN 2405-6014

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

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

Citation Formats


                    Heinz, U., Bazow, D., Denicol, G. S., Martinez, M., Nopoush, M., Noronha, J., Ryblewski, R., and Strickland, M. Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions.  United States: N. p., 2016. 
Web.  doi:10.1016/j.nuclphysbps.2016.05.042.

Copy to clipboard


                    Heinz, U., Bazow, D., Denicol, G. S., Martinez, M., Nopoush, M., Noronha, J., Ryblewski, R., & Strickland, M. Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions.  United States.  https://doi.org/10.1016/j.nuclphysbps.2016.05.042

Copy to clipboard


                    Heinz, U., Bazow, D., Denicol, G. S., Martinez, M., Nopoush, M., Noronha, J., Ryblewski, R., and Strickland, M. Wed .  
"Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions".  United States.  https://doi.org/10.1016/j.nuclphysbps.2016.05.042.  https://www.osti.gov/servlets/purl/1604416.

Copy to clipboard


                    
@article{osti_1604416,

  title        = {Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions},

  author       = {Heinz, U. and Bazow, D. and Denicol, G. S. and Martinez, M. and Nopoush, M. and Noronha, J. and Ryblewski, R. and Strickland, M.},

  abstractNote = {Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.},

  doi          = {10.1016/j.nuclphysbps.2016.05.042},

  journal      = {Nuclear and Particle Physics Proceedings},

  number       = C,

  volume       = 276-278,

  place        = {United States},

  year         = {Wed Jun 08 00:00:00 EDT 2016},

  month        = {Wed Jun 08 00:00:00 EDT 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.nuclphysbps.2016.05.042

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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
DOI: 10.1103/PhysRevD.85.114047

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

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

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
DOI: 10.1103/PhysRevLett.113.202301

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

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

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

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

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

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

Dissipative dynamics of highly anisotropic systems
journal, December 2010

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

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

Nonconformal viscous anisotropic hydrodynamics
journal, June 2015

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

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics
journal, January 2015

Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.
Physical Review C, Vol. 91, Issue 1
DOI: 10.1103/PhysRevC.91.014903

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
DOI: 10.1016/j.nuclphysa.2015.08.009

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
DOI: 10.1103/PhysRevC.83.034907

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

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

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

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

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

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

Works referencing / citing this record:

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
text, January 2017

Denicol, Gabriel S.; Noronha, Jorge
arXiv
DOI: 10.48550/arxiv.1711.01657

Factors affecting user preference for mobile video quality
conference, July 2016

Molnar, Andreea
2016 IEEE International Conference on Multimedia and Expo (ICME)
DOI: 10.1109/icme.2016.7552872

Hydrodynamics from free-streaming to thermalization and back again
text, January 2019

Chattopadhyay, Chandrodoy; Heinz, Ulrich W.
arXiv
DOI: 10.48550/arxiv.1911.07765

Dissipative type theories for Bjorken and Gubser flows
preprint, January 2019

Calzetta, Esteban; Cantarutti, Lucas
arXiv
DOI: 10.48550/arxiv.1912.10562

Similar Records in DOE PAGES and OSTI.GOV collections:

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit

Journal Article Denicol, Gabriel S. ; Heinz, Ulrich ; Martinez, Mauricio ; ... - Physical Review Letters

We present an exact solution of the relativistic Boltzmann equation for a system undergoing boostinvariant longitudinal and azimuthally symmetric transverse flow (“Gubser flow”). The resulting exact nonequilibrium dynamics is compared to first and second order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. Finally, this novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.
Cited by 101
https://doi.org/10.1103/PhysRevLett.113.202301

Full Text Available
( $3 + 1$ )-dimensional anisotropic fluid dynamics with a lattice QCD equation of state

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

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections nonperturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for nonconformal fluids where both of these effects are treated nonperturbatively. The evolutionmore »« less
Cited by 16
https://doi.org/10.1103/PhysRevC.97.054912
Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach

Journal Article Huichao, Song ; Department of Physics, Ohio State University, Columbus, Ohio 43210 ; Bass, Steffen A ; ... - Physical Review. C, Nuclear Physics

A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics, while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the nonequilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles formore »« less
https://doi.org/10.1103/PHYSREVC.83.024912
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Journal Article Bazow, D. ; Denicol, G. S. ; Heinz, Ulrich ; ... - Physical Review D

The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is researched. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid whilemore »« less
Cited by 32
https://doi.org/10.1103/PhysRevD.94.125006

Full Text Available
Bayesian calibration of viscous anisotropic hydrodynamic simulations of heavy-ion collisions

Journal Article Liyanage, Dananjaya ; Sürer, Özge ; Plumlee, Matthew ; ... - Physical Review. C

Owing to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until O(1) fm/c after the collision. To address this one often introduces a prehydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the prehydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopically using the recently developed viscous anisotropic hydrodynamics (VAH). In high-energy heavy-ion collisions VAH is applicable already at very early times, and at later times transitions smoothly into conventional second-order viscous hydrodynamics. Here we present a Bayesian calibration of the VAH model with experimental data for Pb-Pb collisions at the LHC atmore »« less
https://doi.org/10.1103/physrevc.108.054905

Similar Records

Title: Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Abstract

Citation Formats

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

Anisotropic hydrodynamics for conformal Gubser flow journal, February 2015

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

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

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

Transient relativistic thermodynamics and kinetic theory journal, April 1979

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

Dissipative dynamics of highly anisotropic systems journal, December 2010

Anisotropic hydrodynamics for rapidly expanding systems journal, October 2013

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

Nonconformal viscous anisotropic hydrodynamics journal, June 2015

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics journal, January 2015

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

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

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

Symmetry constraints on generalizations of Bjorken flow journal, October 2010

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

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics text, January 2017

Factors affecting user preference for mobile video quality conference, July 2016

Hydrodynamics from free-streaming to thermalization and back again text, January 2019

Dissipative type theories for Bjorken and Gubser flows preprint, January 2019

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

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

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

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

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

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

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

Dissipative dynamics of highly anisotropic systems
journal, December 2010

Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013

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

Nonconformal viscous anisotropic hydrodynamics
journal, June 2015

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics
journal, January 2015

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

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

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

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

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

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
text, January 2017

Factors affecting user preference for mobile video quality
conference, July 2016

Hydrodynamics from free-streaming to thermalization and back again
text, January 2019

Dissipative type theories for Bjorken and Gubser flows
preprint, January 2019