Elliptic flow in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: hybrid model assessment of the first data

We analyze the elliptic flow parameter v_2 in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV and in Au+Au collisions at sqrt{s_{NN}} =200 GeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model. For initial conditions, we employ Monte-Carlo versions of the Glauber and the Kharzeev-Levin-Nardi models and compare results with each other. We demonstrate that the differential elliptic flow v_2(p_T) hardly changes when the collision energy increases, whereas the integrated v_2 increases due to the enhancement of mean transverse momentum. The amount of increase of both v_2 and mean p_T depends significantly on the model of initialization.Comment: 5 pages, 5 figure

Randomly Stopped Nonlinear Fractional Birth Processes

We present and analyse the nonlinear classical pure birth process \mathpzc{N} (t), $t>0$, and the fractional pure birth process \mathpzc{N}^\nu (t), $t>0$, subordinated to various random times, namely the first-passage time $T_t$ of the standard Brownian motion $B(t)$, $t>0$, the $\alpha$-stable subordinator \mathpzc{S}^\alpha(t), $\alpha \in (0,1)$, and others. For all of them we derive the state probability distribution $\hat{p}_k (t)$, $k \geq 1$ and, in some cases, we also present the corresponding governing differential equation. We also highlight interesting interpretations for both the subordinated classical birth process \hat{\mathpzc{N}} (t), $t>0$, and its fractional counterpart \hat{\mathpzc{N}}^\nu (t), $t>0$ in terms of classical birth processes with random rates evaluated on a stretched or squashed time scale. Various types of compositions of the fractional pure birth process \mathpzc{N}^\nu(t) have been examined in the last part of the paper. In particular, the processes \mathpzc{N}^\nu(T_t), \mathpzc{N}^\nu(\mathpzc{S}^\alpha(t)), \mathpzc{N}^\nu(T_{2\nu}(t)), have been analysed, where $T_{2\nu}(t)$, $t>0$, is a process related to fractional diffusion equations. Also the related process \mathpzc{N}(\mathpzc{S}^\alpha({T_{2\nu}(t)})) is investigated and compared with \mathpzc{N}(T_{2\nu}(\mathpzc{S}^\alpha(t))) = \mathpzc{N}^\nu (\mathpzc{S}^\alpha(t)). As a byproduct of our analysis, some formulae relating Mittag--Leffler functions are obtained