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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
equation.
07/2012;
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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.
06/2012;
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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 $\eta/s$.
03/2012;
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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
Chapman-Enskog expansion.
02/2012;
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ABSTRACT: We investigate the microscopic origin of the relaxation time coefficient in
relativistic fluid dynamics. We show that the extraction of the shear viscosity
relaxation time via the gradient expansion is ambiguous and in general fails to
give the correct result. The correct value for the shear viscosity relaxation
time is extracted from the slowest non-hydrodynamic pole of the corresponding
retarded Green's function, if such a pole is purely imaginary. According to the
AdS/CFT correspondence, in strongly-coupled $\mathcal{N}=4$ SYM the
non-hydrodynamic poles of the shear stress tensor nearest to the origin have a
nonzero real part, which implies that the transient fluid-dynamical equations
for this gauge theory are not equivalent to the well-known Israel-Stewart
equations.
08/2011;
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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.
Physical Review Letters 05/2011; 106(21):212302. · 7.37 Impact Factor
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ABSTRACT: In this paper we show how to compute the shear relaxation time from an
underlying microscopic theory. We prove that the shear relaxation time in
Israel-Stewart-type theories is given by the inverse of the pole of the
corresponding retarded Green's function, which is nearest to the origin in the
complex energy plane. Consequently, the relaxation time in such theories is a
microscopic, and not a macroscopic, i.e., fluid-dynamical time scale.
03/2011;
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ABSTRACT: We show how the linearized equations of motion of any dissipative current are
determined by the analytical structure of the associated retarded Green's
function. If the singularity of the Green's function, which is nearest to the
origin in the complex-frequency plane, is a simple pole on the imaginary
frequency axis, the linearized equations of motion can be reduced to
relaxation-type equations for the dissipative currents. The value of the
relaxation time is given by the inverse of this pole. We prove that, if the
relaxation time is sent to zero, or equivalently, the pole to infinity, the
dissipative currents approach the values given by the standard gradient
expansion.
02/2011;
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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.
12/2010;
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ABSTRACT: We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.
Physical Review Letters 10/2010; 105(16):162501. · 7.37 Impact Factor
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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
06/2010;
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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.
Physical Review Letters 08/2009; 103(3):032301. · 7.37 Impact Factor
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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
07/2009;
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ABSTRACT: We present the results of deriving the Israel–Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad's 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.
Journal of Physics G Nuclear and Particle Physics 05/2009; 36(6):064029. · 4.18 Impact Factor
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[show abstract]
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ABSTRACT: We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad's 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.
01/2009;
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Proceedings: Hadronic Matter in Collision 1988, Tucson. 01/1988;
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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.
Nuclear Physics A.
