Viscous anisotropic hydrodynamics for the Gubser flow

Martinez, M.; McNelis, M.; Heinz, Ulrich

doi:10.1016/j.nuclphysa.2017.04.012

Title: Viscous anisotropic hydrodynamics for the Gubser flow

Abstract

In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Moln´ar et al. (MNR) [1, 2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the SO(3)q Ⓧ SO(1, 1) Ⓧ Z₂ symmetry of the Gubser flow in the deSitter space. These equations are solved numerically and compared with the predictions of the recently found exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We also compare our numerical results with other fluid dynamical models. As a result we observe that the MNR description of anisotropic fluid dynamics reproduces the space-time evolution of the system than all other currently known hydrodynamical approaches.

Authors:

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

^[2]

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

Publication Date:: 2017-09-25

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

OSTI Identifier:: 1502397

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

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Physics. A

Additional Journal Information:: Journal Volume: 967; Journal Issue: C; Journal ID: ISSN 0375-9474

Publisher:: Elsevier

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. Viscous anisotropic hydrodynamics for the Gubser flow.  United States: N. p., 2017. 
        Web.  doi:10.1016/j.nuclphysa.2017.04.012.

Copy to clipboard


                    Martinez, M., McNelis, M., & Heinz, Ulrich. Viscous anisotropic hydrodynamics for the Gubser flow.  United States.  doi:https://doi.org/10.1016/j.nuclphysa.2017.04.012

Copy to clipboard


                    Martinez, M., McNelis, M., and Heinz, Ulrich. Mon .  
        "Viscous anisotropic hydrodynamics for the Gubser flow".  United States.  doi:https://doi.org/10.1016/j.nuclphysa.2017.04.012.  https://www.osti.gov/servlets/purl/1502397.

Copy to clipboard


                    
@article{osti_1502397,

  title        = {Viscous anisotropic hydrodynamics for the Gubser flow},

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

  abstractNote = {In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Moln´ar et al. (MNR) [1, 2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the SO(3)q Ⓧ SO(1, 1) Ⓧ Z2 symmetry of the Gubser flow in the deSitter space. These equations are solved numerically and compared with the predictions of the recently found exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We also compare our numerical results with other fluid dynamical models. As a result we observe that the MNR description of anisotropic fluid dynamics reproduces the space-time evolution of the system than all other currently known hydrodynamical approaches.},

  doi          = {10.1016/j.nuclphysa.2017.04.012},

  journal      = {Nuclear Physics. A},

  number       = C,

  volume       = 967,

  place        = {United States},

  year         = {2017},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: https://doi.org/10.1016/j.nuclphysa.2017.04.012

Other availability

Search WorldCat to find libraries that may hold this journal

Figures / Tables:

Fig. 1. : de Sitter time evolution of the temperature T̂ and the normalized shear stress $\hat{\barπ}$ for the exact solution of the RTA Boltzmann equation [14, 15] (black solid lines) and four different hydrodynamic approximations: second-order viscous hydrodynamics (DNMR) [16] (short-dashed magenta lines), anisotropic hydrodynamics with $P̂$_$L$-matching [1, 2,more »

All figures and tables (1 total)

Save / Share:

Export Metadata

Save to My Library

Figures / Tables found in this record:

Fig. 1. (p. 3)

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

Similar Records in DOE PAGES and OSTI.GOV collections:

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 14
DOI: https://doi.org/10.1103/PhysRevD.97.044041
Anisotropic fluid dynamics for Gubser flow

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

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 amore »« less
Cited by 11
DOI: https://doi.org/10.1103/PhysRevC.95.054907

Full Text Available
Thermalization & hydrodynamics in Bjorken & Gubser flows

Journal Article Chattopadhyay, Chandrodoy ; Heinz, Ulrich ; Pal, Subrata ; ... - Nuclear Physics. A

The dynamical scaling behavior of hydrodynamic and non-hydrodynamic moments of the distribution function is studied using third-order Chapman-Enskog hydrodynamics and anisotropic hydrodynamics for systems undergoing Bjorken and Gubser expansions, where exact solutions of the Boltzmann equation in Relaxation Time Approximation (RTA) are available for comparison. While dimensionless quantities like normalized shear, pressure anisotropy and normalized entropy show at late times universal scaling relations with small (large) Knudsen number for Bjorken (Gubser) flows, dimensionful quantities like the entropy per unit rapidity do not. Although the two hydrodynamic approximation schemes describe the exact attractors for normalized shear with high accuracy, their descriptionmore »« less
Cited by 1
DOI: https://doi.org/10.1016/j.nuclphysa.2018.11.005
Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows

Journal Article Chattopadhyay, Chandrodoy ; Heinz, Ulrich ; Pal, Subrata ; ... - Physical Review C

We study the evolution of hydrodynamic and nonhydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e., of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from nonhydrodynamic modes couplingmore »« less
Cited by 4
DOI: https://doi.org/10.1103/PhysRevC.97.064909
Investigating the domain of validity of the Gubser solution to the Boltzmann equation

Journal Article Heinz, Ulrich ; Martinez, Mauricio - Nuclear Physics. A

Here, we study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric transverse and boost-invariant longitudinal expansion. We show, for arbitrary values of the shear viscosity to entropy density ratio, that the distribution function can become negative in certain kinematic regions of the available phase space depending on the boundary conditions. For thermal equilibrium initial conditions, we determine numerically the physical boundary in phase space where the distribution function is always positive definite. The requirement of positivity of this particular exactmore »« less
Cited by 7
DOI: https://doi.org/10.1016/j.nuclphysa.2015.08.009

Full Text Available

Similar Records