[Show abstract][Hide abstract] ABSTRACT: In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of
relativistic dissipative fluid dynamics were derived from the relativistic
Boltzmann equation. These equations contain a multitude of terms of second
order in Knudsen number, in inverse Reynolds number, or their product. Terms of
second order in Knudsen number give rise to non-hyperbolic (and thus acausal)
behavior and must be neglected in (numerical) solutions of relativistic
dissipative fluid dynamics. The coefficients of the terms which are of the
order of the product of Knudsen and inverse Reynolds numbers have been
explicitly computed in the above reference, in the limit of a massless
Boltzmann gas. Terms of second order in inverse Reynolds number arise from the
collision term in the Boltzmann equation, upon expansion to second order in
deviations from the single-particle distribution function in local
thermodynamical equilibrium. In this work, we compute these second-order terms
for a massless Boltzmann gas with constant scattering cross section.
Consequently, we assess their relative importance in comparison to the terms
which are of the order of the product of Knudsen and inverse Reynolds numbers.
[Show abstract][Hide abstract] ABSTRACT: Israel-Stewart theory is a causal, stable formulation of relativistic
dissipative fluid dynamics. This theory has been shown to give a decent
description of the dynamical behavior of a relativistic fluid in cases where
shear stress becomes important. In principle, it should also be applicable to
situations where heat flow becomes important. However, it has been shown that
there are cases where Israel-Stewart theory cannot reproduce phenomena
associated with heat flow. In this paper, we derive a relativistic dissipative
fluid-dynamical theory from kinetic theory which provides a good description of
all dissipative phenomena, including heat flow. We explicitly demonstrate this
by comparing this theory with numerical solutions of the relativistic Boltzmann
[Show abstract][Hide abstract] ABSTRACT: We review the traditional derivation of the fluid-dynamical equations from
kinetic theory according to Israel and Stewart. We show that their procedure to
close the fluid-dynamical equations of motion is not unique. Their approach
contains two approximations, the first being the so-called 14-moment
approximation to truncate the single-particle distribution function. The second
consists in the choice of equations of motion for the dissipative currents.
Israel and Stewart used the second moment of the Boltzmann equation, but this
is not the only possible choice. In fact, there are infinitely many moments of
the Boltzmann equation which can serve as equations of motion for the
dissipative currents. All resulting equations of motion have the same form, but
the transport coefficients are different in each case.
European Physical Journal A 06/2012; 48(11). · 2.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Experimental particle spectra can be successfully described by power-law
tailed energy distributions characteristic to canonical equilibrium
distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide
range of energies, colliding system sizes, and produced hadron sorts. In order
to derive its evolution one needs a corresponding dynamical description of the
system which results in such final state observables. The equations of
relativistic fluid dynamics are obtained from a non-extensive Boltzmann
equation consistent with Tsallis' non-extensive $q$-entropy formula. The
transport coefficients like shear viscosity, bulk viscosity, and heat
conductivity are evaluate based on a linearized collision integral.
European Physical Journal A 05/2012; 48(11). · 2.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The freeze out of the expanding systems, created in relativistic heavy ion collisions, will be discussed. We combine kinetic freeze out equations with Bjorken type system expansion into a unified model. Such a model is a more physical generalization of the earlier simplified non-expanding freeze out models. We shall see that the basic freeze out features, pointed out in the earlier works, are not smeared out by the expansion.
International Journal of Modern Physics E 04/2012; 16(07n08). · 0.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the influence of a temperature-dependent shear viscosity over
entropy density ratio $\eta/s$, different shear relaxation times $\tau_\pi$, as
well as different initial conditions on the transverse momentum spectra of
charged hadrons and identified particles. We investigate the azimuthal flow
asymmetries as a function of both collision energy and centrality. The elliptic
flow coefficient turns out to be dominated by the hadronic viscosity at RHIC
energies. Only at higher collision energies the impact of the viscosity in the
QGP phase is visible in the flow asymmetries. Nevertheless, the shear viscosity
near the QCD transition region has the largest impact on the collective flow of
the system. We also find that the centrality dependence of the elliptic flow is
sensitive to the temperature dependence of $\eta/s$.
Physical Review C 03/2012; 86(1). · 3.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this work we present a general derivation of relativistic fluid dynamics
from the Boltzmann equation using the method of moments. The main difference
between our approach and the traditional 14-moment approximation is that we
will not close the fluid-dynamical equations of motion by truncating the
expansion of the distribution function. Instead, we keep all terms in the
moment expansion. The reduction of the degrees of freedom is done by
identifying the microscopic time scales of the Boltzmann equation and
considering only the slowest ones. In addition, the equations of motion for the
dissipative quantities are truncated according to a systematic power-counting
scheme in Knudsen and inverse Reynolds number. We conclude that the equations
of motion can be closed in terms of only 14 dynamical variables, as long as we
only keep terms of second order in Knudsen and/or inverse Reynolds number. We
show that, even though the equations of motion are closed in terms of these 14
fields, the transport coefficients carry information about all the moments of
the distribution function. In this way, we can show that the particle-diffusion
and shear-viscosity coefficients agree with the values given by the
Physical review D: Particles and fields 02/2012; 85(11).
[Show abstract][Hide abstract] ABSTRACT: We derive equations for fluid dynamics from a non-extensive Boltzmann
transport equation consistent with Tsallis' non-extensive entropy formula. We
evaluate transport coefficients employing the relaxation time approximation and
investigate non-extensive effects in leading order dissipative phenomena at
relativistic energies, like heat conductivity, shear and bulk viscosity.
[Show abstract][Hide abstract] ABSTRACT: We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio η/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in √S(NN)=200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.
[Show abstract][Hide abstract] ABSTRACT: We investigate the effects of a temperature-dependent shear viscosity over entropy density ratio η/s, with a minimum near the phase transition, on the elliptic flow of hadrons in ultrarelativistic heavy-ion collisions at the RHIC and the LHC. We find that the suppression of the elliptic flow in Au+Au collisions at the RHIC is dominated by the viscosity in hadronic matter and in the phase transition region, but insensitive to the viscosity of the quark–gluon plasma (QGP). However, at the highest LHC energy, the elliptic flow becomes sensitive to the shear viscosity of the QGP and insensitive to the hadronic viscosity.
Journal of Physics G Nuclear and Particle Physics 01/2011; 38(12). · 5.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We derive the equations of second order dissipative fluid dynamics from the
relativistic Boltzmann equation following the method of W. Israel and J. M.
Stewart. We present a frame independent calculation of all first- and
second-order terms and their coefficients using a linearised collision
integral. Therefore, we restore all terms that were previously neglected in the
original papers of W. Israel and J. M. Stewart.
[Show abstract][Hide abstract] ABSTRACT: Employing a microscopic transport model we investigate the evolution of high
energetic jets moving through a viscous medium. For the scenario of an
unstoppable jet we observe a clearly strong collective behavior for a low
dissipative system $\eta/s \approx 0.005$, leading to the observation of
cone-like structures. Increasing the dissipation of the system to $\eta/s
\approx 0.32$ the Mach Cone structure vanishes. Furthermore, we investigate
jet-associated particle correlations. A double-peak structure, as observed in
experimental data, is even for low-dissipative systems not supported, because
of the large influence of the head shock.
Journal of Physics Conference Series 08/2010; 270(1).
[Show abstract][Hide abstract] ABSTRACT: We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio $\eta/s$. We also find that a good agreement between these two approaches requires a Knudsen number $Kn < 1/2$. Comment: Version as published in PRC 82, 024910 (2010); 16 pages, 16 figures, typos corrected
[Show abstract][Hide abstract] ABSTRACT: We solve the relativistic Riemann problem in viscous gluon matter employing a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio eta/s from zero to infinity. We show that an eta/s ratio larger than 0.2 prevents the development of well-defined shock waves on time scales typical for ultrarelativistic heavy-ion collisions. Comparisons with viscous hydrodynamic calculations confirm our findings.
[Show abstract][Hide abstract] ABSTRACT: We present numerical methods to solve the Israel-Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)-- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)--dimensional modeling of a relativistic dissipative fluid. Comment: 21 pages, 4 figures
European Physical Journal C 07/2009; · 5.25 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio η/s. We show that an η/s ratio larger than 0.2 prevents the development of well-defined shock waves on time scales typical for ultrarelativistic heavy-ion collisions. These findings are confirmed by viscous hydrodynamic calculations.
[Show abstract][Hide abstract] ABSTRACT: A novel higher order theory of relaxation of heat and viscosity is proposed
based on corrections to the traditional treatment of the relativistic energy
density. In the framework of generalized Bjorken scaling solution to
accelerating longitudinal flow we point out that the energy flux can be
consequently set to zero in the stationary case, independently of the choice of
a specific local rest frame, like the Landau-Lifshitz or Eckart one. We
investigate and compare several cooling and re-heating scenarios for the Quark
Gluon Plasma (QGP) within this approach.
Physical Review C 07/2008; 78(1):014909. · 3.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Entropy production due to shear viscosity during the continuous freeze-out of a longitudinally expanding dissipative fluid is addressed. Assuming the validity of the fluid dynamical description during the continuous removal of interacting matter we estimated a small entropy production as function of the freeze-out duration and the ratio of dissipative to non-dissipative quantities in case of a relativistic massless pion fluid.