Modified Boltzmann Transport Equation and Freeze Out

We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.Comment: 9 pages, 2 figure

The 3rd Flow Component as a QGP Signal

Earlier fluid dynamical calculations with QGP show a softening of the directed flow while with hadronic matter this effect is absent. On the other hand, we indicated that a third flow component shows up in the reaction plane as an enhanced emission, which is orthogonal to the directed flow. This is not shadowed by the deflected projectile and target, and shows up at measurable rapidities, $y_cm = 1-2$. To study the formation of this effect initial stages of relativistic heavy ion collisions are studied. An effective string rope model is presented for heavy ion collisions at RHIC energies. Our model takes into account baryon recoil for both target and projectile, arising from the acceleration of partons in an effective field. The typical field strength (string tension) for RHIC energies is about 5-12 GeV/fm, what allows us to talk about "string ropes". The results show that QGP forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. The produced initial state can be used as an initial condition for further hydrodynamical calculations. Such initial conditions lead to the creation of third flow component. Recent $v_1$ measurements are promising that this effect can be used as a diagnostic tool of the QGP

Covariant description of kinetic freeze out through a finite time-like layer

The Freeze Out (FO) problem is addressed for a covariant FO probability and a finite FO layer with a time-like normal vector continuing the line of studies introduced in Ref. [1]. The resulting post FO momentum distribution functions are presented and discussed. We show that in general the post FO distributions are non-thermal and asymmetric distributions even for time-like FO situations.Comment: 10 pages, 12 figures, major rewrite with changed content, corrected typos and new references adde

Covariant description of kinetic freeze out through a finite space-like layer

The problem of Freeze Out (FO) in relativistic heavy ion reactions is addressed. We develop and analyze an idealized one-dimensional model of FO in a finite layer, based on the covariant FO probability. The resulting post FO phase-space distributions are discussed for different FO probabilities and layer thicknesses.Comment: 16 pages, 19 figures, changed content, references adde

Particlization in hybrid models

In hybrid models, which combine hydrodynamical and transport approaches to describe different stages of heavy-ion collisions, conversion of fluid to individual particles, particlization, is a non-trivial technical problem. We describe in detail how to find the particlization hypersurface in a 3+1 dimensional model, and how to sample the particle distributions evaluated using the Cooper-Frye procedure to create an ensemble of particles as an initial state for the transport stage. We also discuss the role and magnitude of the negative contributions in the Cooper-Frye procedure.Comment: 18 pages, 28 figures, EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics"; version accepted for publication, typos and error in Eq.(1) corrected, the purpose of sampling and change from UrQMD to fluid clarified, added discussion why attempts to cancel negative contributions of Cooper-Frye are not applicable her

Longitudinal Scaling of Elliptic Flow in Landau Hydrodynamics

This study presents generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy ion collisions. Obtained results shows longitudinal scaling of elliptic flow $v_2$ as a function of rapidity shifted by beam rapidity ($y-y_{beam}$) for different energies ($\sqrt{s_{NN}}=62.4$ GeV and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued, that the elliptic flow and its longitudinal scaling is due to the initial transverse energy density distribution and initial longitudinal thickness effect.Comment: 7 pages 1 figur

Trends in suicide in a Lithuanian urban population over the period 1984–2003

BACKGROUND: Throughout the last decade of the twentieth century, Lithuania had the highest suicide rates in Europe among both men and women aged 25–64 years. The rates increased from 1986 until 1995, but later there was a slight decrease. This paper describes the trends in suicide deaths in urban population in Lithuania by gender, dates and suicide method over the period 1984–2003. METHODS: Data from the regional mortality register were used to analyze suicide deaths among all men and women aged 25–64 years in Kaunas city, Lithuania over the period 1984–2003. Age-standardized death rates per 100,000 persons (using European standard population) were calculated by gender, suicide method and dates. A joinpoint regression method was used to estimate annual percentage changes (EPACs) and to detect points where the trends changed significantly. RESULTS: The frequency of death by suicide among males was 48% higher in 1994–2003 than in 1984–1993. The corresponding increase among females was 28%. The most common methods of suicide among men were hanging, strangulation and suffocation (87.4% among all suicide deaths). The proportions of hanging, strangulation and suffocation in males increased by 6.9% – from 83.9% to 89.7% – compared to a 24.2% increase in deaths from handgun, rifle and shotgun firearm discharges and a 216.7% increase in deaths from poisoning with solvents, gases, pesticides and vapors. Among females, the most common methods of suicide were hanging, strangulation and suffocation (68.3% of all suicide deaths). The proportion of hanging deaths among females increased during the time period examined, whereas the proportion of poisonings with solid or liquid substances decreased. CONCLUSION: Suicide rates increased significantly among urban men aged 25–64 years in Lithuania throughout the period 1984–2003, whereas among women an increasing but statistically insignificant trend was observed. There were changes in the suicide methods used by both men and women. Changes in the choice of method may have contributed to the changes in suicide rates