Simple Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Systems

Csörgő, T.; Grassi, F.; Hama, Yogiro; Kodama, T.

doi:10.1556/aph.21.2004.1.6

Cited by 15 publications

(35 citation statements)

References 22 publications

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“…Let us notice that if the induced current vanishes, the electric conductivity of the QGP becomes almost irrelevant for the magnetic field evolution. This is also in agreement with our previous results from [10], where we showed that in 23 This is the essence of the 1 + 1 self-similar flow [15]. nonideal transverse MHD the magnetic field is not significantly modified by the finite electric conductivity, and that a finite electric conductivity does not necessarily lead to a deviation from the ideal MHD.…”

Section: Discussionsupporting

confidence: 92%

“…Here, Q 0 ≡ Q(τ 0 , r 0 ), ̺ 0 ≡ τ 2 0 − r 2 0 and Q is an arbitrary differentiable function of ϑ, referred to as the scaling function of Q [14,15]. Plugging, at this stage, (II.18), (IV.5) and (IV.6) into the energy equation (II.15) gives rise to…”

Section: The 3 + 1 Dimensional Self-similar Flow In Relativistic Mhdmentioning

confidence: 99%

“…This leads to the same velocity profile (VI.7), but physical quantities, in particular, the electromagnetic field strength tensor may acquire θ dependence. Following the arguments presented in [10,15], it turns out that the θ dependence of the energy density and pressure are eliminated. However, certain scaling function for the temperature remains (see Appendix B for some more details).…”

Section: Conformal Mhdmentioning

confidence: 99%

“…This fact motivated several attempts on the generalization of the Bjorken flow to solutions including an appropriate transverse expansion. It is the main purpose of the present paper to focus on the 3 + 1 dimensional self-similar flow from [14,15] and the Gubser flow from [16,17], and to determine the magnetic field evolution arising from these flows. To do this, we present a realization of these flows in an ideal MHD using, in particular, similar symmetry arguments as in [18].…”

Section: Introductionmentioning

confidence: 99%

“…A 3+1 dimensional self-similar flow can be regarded as a combination of three Bjorken flows in three spatial directions. Although this flow is a simple spherical Hubble expansion, more symmetries can be introduced by similarity variables [14,15,19]. Other attempts are made, e.g., in [20] to introduce more realistic elliptically-shaped solutions of hydrodynamic equations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Shokri

Sadooghi

2018

J. High Energ. Phys.

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Motivated by the recently found realization of the 1 + 1 dimensional Bjorken flow in ideal and nonideal relativistic magnetohydrodynamics (MHD), we use appropriate symmetry arguments, and determine the evolution of magnetic fields arising from the 3 + 1 dimensional self-similar and Gubser flows in an infinitely conductive relativistic fluid (ideal MHD). In the case of the 3 + 1 dimensional self-similar flow, we arrive at a family of solutions, that are related through a differential equation arising from the corresponding Euler equation. To find the magnetic field evolution from the Gubser flow, we solve the MHD equations of a stationary fluid in a conformally flat dS 3 ×E 1 spacetime. The results are then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the resulting magnetic field is shown to exhibit a transition between an early time 1/t decay to a 1/t 3 decay at a late time. Here, t is the time coordinate. Transverse and longitudinal components of the magnetic fields arising from these flows are also found. The latter turns out to be sensitive to the transverse size of the fluid. In contrast to the result arising from the Gubser flow, the radial domain of validity of the magnetic field arising from the self-similar flow is highly restricted. A comparison of the results suggests that the (conformal) Gubser MHD may give a more appropriate qualitative picture of the magnetic field decay in the plasma of quarks and gluons created in heavy ion collisions. PACS numbers: 12.38.Mh, 47.75.+f, 52.27.Ny, 52.30.Cv * m shokri@physics.sharif.ir † sadooghi@physics.sharif.ir 1 Here, e is the electric charge and mπ ∼ 140 MeV the pion mass.

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Section: Discussionsupporting

confidence: 92%

Section: The 3 + 1 Dimensional Self-similar Flow In Relativistic Mhdmentioning

confidence: 99%

Section: Conformal Mhdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Shokri

Sadooghi

2018

J. High Energ. Phys.

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Exact -dimensional flows of a perfect fluid

Peschanski¹,

Saridakis²

2011

Nuclear Physics A

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We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a linear combination of two generating functions with polynomial coefficients of 2 variables. The polynomials, whose algebraic equations are solved, define an infinite-dimensional basis of solutions. The kinematics of the (1 + 1)-dimensional flow are reconstructed from the potential.

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Formation of Hubble-like flow in little bangs

2005

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A dynamical appearance of scaling solutions in the relativistic hydrodynamics applied to describe ultra-relativistic heavy-ion collisions is studied. We consider the boost-invariant cylindrically symmetric systems and the effects of the phase transition are taken into account by using a temperature dependent sound velocity inferred from the lattice simulations of QCD. We find that the transverse flow acquires the scaling form r/t within the short evolution times, 10-15 fm, only if the initial transverse flow originating from the pre-equilibrium collective behavior is present at the initial stage of the hydrodynamic evolution. The amount of such pre-equilibrium flow is correlated with the initial pressure gradient; larger initial gradients require smaller initial flow. The results of the numerical calculations support the phenomenological parameterizations used in the Blast-Wave, Buda-Lund, and Cracow models of the freeze-out process.

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Simple Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Systems

Abstract: Simple, self-similar, analytic solutions of 1 + 1 dimensional relativistic hydrodynamics are presented, generalizing Bjorken's solution to inhomogeneous rapidity distribution.

Cited by 15 publications

References 22 publications

Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Exact -dimensional flows of a perfect fluid

Formation of Hubble-like flow in little bangs

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