The effects of fluctuating initial conditions are studied in the context of relativistic heavy ion collisions where a rapidly evolving system is formed. Two-particle correlation analysis is applied to events generated with the NEXSPHERIO hydrodynamic code, starting with fluctuating nonsmooth initial conditions (IC). The results show that the nonsmoothness in the IC survives the hydroevolution and can be seen as topological features of the angular correlation function of the particles emerging from the evolving system. A long range correlation is observed in the longitudinal direction and in the azimuthal direction a double peak structure is observed in the opposite direction to the trigger particle. This analysis provides clear evidence that these are signatures of the combined effect of tubular structures present in the IC and the proceeding collective dynamics of the hot and dense medium.

The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.

In this work, we examine the effect of bulk viscosity on elliptic flow, taking into account the critical behavior of the equation of state and transport coefficients near the QCD phase transition. We found that the $p_T$ dependence of $v_2$ is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, $v_2$ decreases by a factor of $15\%$ at small $p_T$ values ($<1$ GeV). However, for larger values of $p_T$ ($>2$ GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances $v_2$. We point out that Grad’s 14-moment approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.

Elliptic flow at BNL RHIC is computed event by event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15%–30% for $\eta =0$, 30% for $p_{\perp }=0.5\mathrm{GeV}$). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows.

A survey is given on the applications of hydrodynamic model of nucleus-nucleus collisons, focusing especially on i) the resolution of hydrodynamic equations for arbitrary configurations, by usig the smoothed-particle hydrodynamic approach; ii) effects of the event-by-event fluctuation of the initial conditions on the observables; iii) decoupling criteria; iv) analytical solutions; and others