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In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion collisions. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in heavy ion collisions at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of heavy ion collisions. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamic calculations and by comparing them with the experimental data.
Event-by-event viscous hydrodynamics is combined with heavy quark energy loss models to compute heavy flavor flow cumulants $v_2{2}$, $v_3{2}$, and $v_2{4}$ as well as the nuclear modification factors of $D^0$ and $B^0$ mesons in PbPb collisions at 2
We employ a 3+1D anomalous hydrodynamics with initial condition generated by HIJING to simulate the chiral vortical effect and the chiral magnetic effect in heavy-ion collisions. This allows us to calculate the charge-dependent two-particle correlati
Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an i
Recently it has been shown that a realistic description of the medium via event-by-event viscous hydrodynamics plays an important role in the long-standing $R_text{AA}$ vs. $v_2$ puzzle at high $p_T$. In this proceedings we begin to extend this appro
We evaluate the viscous damping of anisotropic flow in heavy-ion collisions for arbitrary temperature-dependent shear and bulk viscosities. We show that the damping is solely determined by effective shear and bulk viscosities, which are weighted aver