arXiv subjects

Wojciech Florkowski

Publications and source records attributed to Wojciech Florkowski.

At least 109 records · Page 6Linked to original sources

arXiv2014

Kinetic description of mixtures of anisotropic fluids

A simple system of coupled kinetic equations for quark and gluon anisotropic systems is solved numerically. The solutions are compared with the predictions of the anisotropic hydrodynamics describing a mixture of anisotropic fluids. We find that the solutions of the kinetic equations can be well reproduced by anisotropic hydrodynamics if the initial distribution are oblate for both quarks and gluons. On the other hand, the solutions of the kinetic equations have a different qualitative behavior from those obtained in anisotropic hydrodynamics if the initial configurations are oblate-prolate or prolate-prolate. This suggests that an extension of the anisotropic hydrodynamics scheme for the mixture of anisotropic fluids is needed, where higher moments of the kinetic equations are used and present simplifications are avoided.

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arXiv2013

Projection method and new formulation of leading-order anisotropic hydrodynamics

The introduced earlier projection method for boost-invariant and cylindrically symmetric systems is used to introduce a new formulation of anisotropic hydrodynamics that allows for three substantially different values of pressure acting locally in three different directions. Our considerations are based on the Boltzmann kinetic equation with the collision term treated in the relaxation time approximation and the momentum anisotropy is included explicitly in the leading term of the distribution function. A novel feature of our work is the complete analysis of the second moment of the Boltzmann equation, in addition to the zeroth and first moments that have been analyzed in earlier studies. We define the final equations of anisotropic hydrodynamics in the leading order as a subset of the analyzed moment equations (and their linear combinations) which agree with the Israel-Stewart theory in the case of small pressure anisotropies.

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arXiv2013

Anisotropic Hydrodynamics for Rapidly Expanding Systems

We exactly solve the relaxation-time approximation Boltzmann equation for a system which is transversely homogeneous and undergoing boost-invariant longitudinal expansion. We compare the resulting exact numerical solution with approximate solutions available in the anisotropic hydrodynamics and second order viscous hydrodynamics frameworks. In all cases studied, we find that the anisotropic hydrodynamics framework is a better approximation to the exact solution than traditional viscous hydrodynamical approaches.

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arXiv2013

Mixture of anisotropic fluids

The recently introduced approach describing coupled quark and gluon anisotropic fluids is generalized to include explicitly the transitions between quarks and gluons. We study the effects of such processes on the thermalization rate of anisotropic systems. We find that the quark-gluon transitions may enhance the overall thermalization rate in the cases where the initial momentum anisotropies correspond to mixed oblate-prolate or prolate configurations. On the other hand, no effect on the thermalization rate is found in the case of oblate configurations. The observed regularities are connected with the late-time behavior of the analyzed systems which is described either by the exponential decay or the power law.

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arXiv2013

Testing viscous and anisotropic hydrodynamics in an exactly solvable case

We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying different non-equilibrium cases and comparing the exact kinetic-theory results to the second-order viscous hydrodynamics results we find that recent formulations of second-order viscous hydrodynamics agree better with the exact solution than the standard Israel-Stewart approach. Additionally, we find that, given the appropriate connection between the kinetic and anisotropic hydrodynamics relaxation times, anisotropic hydrodynamics provides a very good approximation to the exact relaxation time approximation solution.

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arXiv2013

Equilibration of anisotropic quark-gluon plasma produced by decays of color flux tubes

A set of kinetic equations is used to study equilibration of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of ultra-relativistic heavy-ion collisions. The decay rates of the initial color fields are given by the Schwinger formula, and the collision terms are treated in the relaxation-time approximation. By connecting the relaxation time with viscosity we are able to study production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density, eta/s. For the lowest (KSS) value of this ratio, 4 pi eta/s = 1, and realistic initial conditions for the fields, the system approaches the viscous-hydrodynamics regime within 1-2 fm/c. On the other hand, for larger values of the viscosity, 4 pi eta/s greater or equal to 3, the collisions in the plasma become inefficient to destroy collective phenomena which manifest themselves as oscillations of different plasma parameters. The presence of such oscillations brings in differences between the kinetic and hydrodynamic descriptions, which suggest that the viscous-hydrodynamics approach after 1-2 fm/c is not complete if 4 pi eta/s is greater or equal to 3 and should be extended to include dissipative phenomena connected with color conductivity.

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arXiv2013

Hydrodynamics of anisotropic quark and gluon fluids

The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy parameters. The dynamical equations describing such mixtures are derived from kinetic theory with the collisional kernel treated in the relaxation- time approximation allowing for different relaxation times for quarks and gluons. Baryon number conservation is enforced in the quark and anti-quark components of the fluid, but overall parton number non-conservation is allowed in the system. The resulting equations are solved numerically in the (0+1)-dimensional boost-invariant case at zero and finite baryon density.

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arXiv2013

Anisotropic hydrodynamics -- basic concepts

Due to the rapid longitudinal expansion of the quark-gluon plasma created in relativistic heavy ion collisions, potentially large local rest frame momentum-space anisotropies are generated. The magnitude of these momentum-space anisotropies can be so large as to violate the central assumption of canonical viscous hydrodynamical treatments which linearize around an isotropic background. In order to better describe the early-time dynamics of the quark gluon plasma, one can consider instead expanding around a locally anisotropic background which results in a dynamical framework called anisotropic hydrodynamics. In this proceedings contribution we review the basic concepts of the anisotropic hydrodynamics framework presenting viewpoints from both the phenomenological and microscopic points of view.

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arXiv2012

Anisotropic hydrodynamics and the early-thermalization puzzle

The framework of anisotropic hydrodynamics is used in 3+1 dimensions to analyze behavior of matter produced in ultra-relativistic heavy-ion collisions. The model predictions for the hadronic transverse-momentum spectra, directed and elliptic flows, and the HBT radii are presented. We show that the effects of the initial anisotropy of pressure may be compensated by appropriate adjustment of the initial energy density. In this way, the final hadronic observables become insensitive to the early stage dynamics and the early thermalization puzzle may be circumvented.

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arXiv2012

Chromoelectric oscillations in a dynamically evolving anisotropic background

We study the oscillations of a uniform longitudinal chromoelectric field in a dynamically-evolving momentum-space anisotropic background in the weak field limit. Evolution equations for the background are derived by taking moments of the Boltzmann equation in two cases: (i) a fixed relaxation time and (ii) a relaxation time that is proportional to the local inverse transverse momentum scale of the plasma. The second case allows us to reproduce 2nd-order viscous hydrodynamical dynamics in the limit of small shear viscosity to entropy ratio. We then linearize the Boltzmann-Vlasov equation in a dynamically-evolving background and obtain an integro-differential evolution equation for the chromoelectric field. We present numerical solutions to this integro-differential equation for a variety of different initial conditions and shear viscosity to entropy density ratios. The dynamical equations obtained are novel in that they include a non-trivial time-dependent momentum-space anisotropic background and the effect of collisional damping for the first time.

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arXiv2012

Locally anisotropic momentum distributions of hadrons at freeze-out in relativistic heavy-ion collisions

A spheroidal anisotropic local momentum distribution is implemented in the statistical model of hadron production. We show that this form leads to exactly the same ratios of hadronic abundances as the equilibrium distributions, if the temperature is identified with a characteristic transverse-momentum scale. Moreover, to a very good approximation the transverse-momentum spectra of hadrons are the same for isotropic and anisotropic systems, provided the size of the system at freeze-out is appropriately adjusted. We further show that this invariance may be used to improve the agreement between the model and experimental HBT results.

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arXiv2012

Highly-anisotropic hydrodynamics in 3+1 space-time dimensions

Recently formulated model of highly-anisotropic and strongly dissipative hydrodynamics is used in 3+1 dimensions to study behavior of matter produced in ultra-relativistic heavy-ion collisions. We search for possible effects of the initial high anisotropy of pressure on the final soft-hadronic observables. We find that by appropriate adjustment of the initial energy density and/or the initial pseudorapidity distributions, the effects of the initial anisotropy of pressure may be easily compensated and the final hadronic observables become insensitive to early dynamics. Our results indicate that the early thermalization assumption is not necessary to describe hadronic data, in particular, to reproduce the measured elliptic flow v_2. The complete thermalization of matter (local equilibration) may take place only at the times of about 1-2 fm/c, in agreement with the results of microscopic models.

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arXiv2012

Single-freeze-out model for ultra relativistic heavy-ion collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV and the LHC proton puzzle

The single-freeze-out model with parametrized hypersurface and flow geometry is employed to analyze the transverse-momentum spectra of hadrons produced in the Pb+Pb collisions at the collision energy of {$\sqrt{s_{\rm NN}}=2.76$ TeV} at the CERN Large Hadron Collider (LHC). With the notable exception for protons and antiprotons, we find a very good agreement between the model results and the data for the measured hadron species. The additional analysis of the HBT radii of pions helps us to select, from several different types of freeze-out studied in this work, the most realistic form of the freeze-out hypersurface. We find that discrepancy ratio between the model and experiment for the proton/antiproton spectra depends on $p_T$, dropping from 2 in the soft region to 1 around $p_T=1.5$ GeV.

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arXiv2011

Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics

Tensors describing boost-invariant and cylindrically symmetric expansion of a relativistic dissipative fluid are decomposed in a suitable chosen basis of projection operators. This leads to a simple set of scalar equations which determine the fluid behavior. As special examples, we discuss the case of the Israel-Stewart theory and the model of highly-anisotropic and strongly-dissipative hydrodynamics ADHYDRO. We also introduce the matching conditions between the ADHYDRO description suitable for the very early stages of heavy-ion collisions and the Israel-Stewart theory applicable for later stages when the system is close to equilibrium.

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arXiv2011

Highly-anisotropic and strongly-dissipative hydrodynamics with transverse expansion

A recently formulated framework of highly-anisotropic and strongly-dissipative hydrodynamics (ADHYDRO) is used to describe the evolution of matter created in ultra-relativistic heavy-ion collisions. New developments of the model contain: the inclusion of asymmetric transverse expansion (combined with the longitudinal boost-invariant flow) and comparisons of the model results with the RHIC data, which have become possible after coupling of ADHYDRO with THERMINATOR. Various soft-hadronic observables (the transverse-momentum spectra, the elliptic flow coefficient v_2, and the HBT radii) are calculated for different initial conditions characterized by the value of the initial pressure asymmetry. We find that as long as the initial energy density profile is unchanged the calculated observables remain practically the same. This result indicates the insensitivity of the analyzed observables to the initial anisotropy of pressure and suggests that the complete thermalization of the system may be delayed to easily acceptable times of about 1 fm/c.

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arXiv2011

THERMINATOR 2: THERMal heavy IoN generATOR 2

We present an extended version of THERMINATOR, a Monte Carlo event generator dedicated to studies of the statistical production of particles in relativistic heavy-ion collisions. The increased functionality of the code contains the following features: The input of any shape of the freeze-out hypersurface and the expansion velocity field, including the 3+1 dimensional profiles, in particular those generated externally with various hydrodynamic codes. The hypersufraces may have variable thermal parameters, which allows for studies departing significantly from the mid-rapidity region, where the baryon chemical potential becomes large. We include a library of standard sets of hypersurfaces and velocity profiles describing the RHIC Au+Au data at sqrt(s_(NN)) = 200 GeV for various centralities, as well as those anticipated for the LHC Pb+Pb collisions at sqrt(s_(NN)) = 5.5 TeV. A separate code, FEMTO-THERMINATOR, is provided to carry out the analysis of femtoscopic correlations which are an important source of information concerning the size and expansion of the system. We also include several useful scripts that carry out auxiliary tasks, such as obtaining an estimate of the number of elastic collisions after the freeze-out, counting of particles flowing back into the fireball and violating causality (typically very few), or visualizing various results: the particle p_T-spectra, the elliptic flow coefficients, and the HBT correlation radii. We also investigate the problem of the back-flow of particles into the hydrodynamic region, as well as estimate the elastic rescattering in terms of trajectory crossings. The package is written in C++ and uses the CERN ROOT environment.

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arXiv2010

ADHYDRO --- hydrodynamics-like model for highly anisotropic systems

A new framework (ADHYDRO) is presented that has been designed for description of highly-anisotropic systems produced at the very early stages of relativistic heavy-ion collisions. The structure of ADHYDRO is very much similar to perfect-fluid hydrodynamics, however, ADHYDRO includes dissipation effects. Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic systems. With a simple ansatz for the entropy source, that obeys general physical requirements, we obtain the system of equations describing isotropization of the anisotropic systems.

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arXiv2010

Non-boost-invariant motion of dissipative and highly anisotropic fluid

The recently formulated framework of anisotropic and dissipative hydrodynamics (ADHYDRO) is used to describe non-boost-invariant motion of the fluid created at the early stages of heavy-ion collisions. Very strong initial asymmetries of pressure are reduced by the entropy production processes. By the appropriate choice of the form of the entropy source we can reproduce realistic scenarios for the isotropization expected in heavy-ion collisions. Our previous results are generalized by including the realistic equation of state as the limit of the isotropization processes.

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