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Viscous anisotropic hydrodynamics for the Gubser flow
Nuclear Theory · Submitted 16 Apr 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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 $SO(3)_q\otimes SO(1,1)\otimes Z_2$ 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. 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.94 | 0.73 | 0.06 | asserted 0.95 |
| s1 | 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. | method 0.92 | 0.91 | 0.04 | asserted 1.00 |
| s2 | One requires an additional evolution equation in order to close the conservation laws. | method 0.54 | 0.20 | 0.02 | asserted 1.00 |
| s3 | This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. | method 0.98 | 0.84 | 0.03 | asserted 1.00 |
| s4 | As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the $SO(3)_q\otimes SO(1,1)\otimes Z_2$ symmetry of the Gubser flow in the deSitter space. | result 0.49 | 0.91 | 0.08 | asserted 1.00 |
| s5 | 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. | method 0.74 | 0.89 | 0.06 | asserted 0.94 |
| s6 | We also compare our numerical results with other fluid dynamical models. | method 0.75 | 0.88 | 0.03 | asserted 0.65 |
| s7 | 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. | result 0.94 | 0.89 | 0.84 | asserted 1.00 |
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The paper
Original 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 $SO(3)_q\otimes SO(1,1)\otimes Z_2$ 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. 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.
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Papers whose main result relates to this one's
States the same result 2 papers
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Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.
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We show that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.
What it cites · 12 sentences without a confident label
Builds on 3 papers
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[ref] for a rapidly expanding conformal fluid undergoing Gubser flow [ref] .
Symmetry constraints on generalizations of Bjorken flow · Introduction · 1.00
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[ref] for a rapidly expanding conformal fluid undergoing Gubser flow [ref] .
Conformal hydrodynamics in Minkowski and de Sitter spacetimes · Introduction · 1.00
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[ref] for a rapidly expanding conformal fluid undergoing Gubser flow [ref] .
Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation · Introduction · 1.00
Compares with 8 papers
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In our work [ref] we compare the predictions of the exact solution to the RTA Boltzmann equation for the Gubser flow [ref] with four different hydrodynamical models: anisotropic hydrodynamics with $𝒫̂_L$ matching [ref] , leading order anisotropic hydrodynamics in the NRS scheme [ref] , next-to-leading order anisotropic hydrodynamics in the NRS scheme [ref] amended by residual viscous corrections (NLO NRS) [ref] and standard second-order viscous hydrodynamics (DNMR) [ref] .
Derivation of transient relativistic fluid dynamics from the Boltzmann equation · Results · 0.93
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In our work [ref] we compare the predictions of the exact solution to the RTA Boltzmann equation for the Gubser flow [ref] with four different hydrodynamical models: anisotropic hydrodynamics with $𝒫̂_L$ matching [ref] , leading order anisotropic hydrodynamics in the NRS scheme [ref] , next-to-leading order anisotropic hydrodynamics in the NRS scheme [ref] amended by residual viscous corrections (NLO NRS) [ref] and standard second-order viscous hydrodynamics (DNMR) [ref] .
Second-order (2+1)-dimensional anisotropic hydrodynamics · Results · 0.93
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In our work [ref] we compare the predictions of the exact solution to the RTA Boltzmann equation for the Gubser flow [ref] with four different hydrodynamical models: anisotropic hydrodynamics with $𝒫̂_L$ matching [ref] , leading order anisotropic hydrodynamics in the NRS scheme [ref] , next-to-leading order anisotropic hydrodynamics in the NRS scheme [ref] amended by residual viscous corrections (NLO NRS) [ref] and standard second-order viscous hydrodynamics (DNMR) [ref] .
A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit · Results · 0.93
Cites as background 10 papers
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In these proceedings we report the most recent developments of anisotropic hydrodynamics presented in Ref. [ref] .
Anisotropic fluid dynamics for Gubser flow · Conclusions · 0.84
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The main aim of anisotropic hydrodynamics [ref] is to address these type of problems and to provide a consistent framework where pressure anisotropies are taken into account in a non-perturbatively controlled way.
Dissipative Dynamics of Highly Anisotropic Systems · Introduction · 0.89
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The main aim of anisotropic hydrodynamics [ref] is to address these type of problems and to provide a consistent framework where pressure anisotropies are taken into account in a non-perturbatively controlled way.
Non-boost-invariant motion of dissipative and highly anisotropic fluid · Introduction · 0.89
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