The Analytical Accelerating Solutions Of Relativistic Hydrodynamics And Its Applications At RHIC And LHC

Relativistic hydrodynamic is an important field in high energy physics,it provide many useful methods to study the new,hot,dense matter,which named"quark-gluon plasma"(QGP)that generated at heavy ion collisions at RHIC and LHC.Hydrodynamic theory pro-vides a simple spatiotemporal figure of this hot dense medium's evolution in not only nuclear-nuclear collision but also nucleus-nucleus collisions.Relativistic hydrodynamic also allows people to describe the various stages of medium expansion without additional conditions for any microscopic model:from the possible formation of quark-gluon plasma evolution,followed by frozen hadronization,until to the hadron decay.The solutions and models of hy-drodynamic provide a lot of interesting physics to study the physical properties and behavior of the QGP,such as collective flow effects,jet quenching and so on.The work of this thesis focuses on obtain the exact/analytical solutions of the relativis-tic hydrodynamic with longitudinal accelerating flow.By solving the conservation laws of fluid dynamics in the acceleration coordinate system(or Rindler coordinate),several new exact/analytical solutions with longitudinal accelerated flow are obtained.Using these solu-tions containing longitudinal accelerating behaviors,combined with the famous Cooper-Fyre freeze-out formula,then the final state spectrum of charged-particles is derived.Our model presented many different results for the nuclear-nuclear collisions and nucleus-nucleus col-lisions at the RHIC and LHC energy regions,it reveals the deep connection between the non-uniform evolution,QGP viscosity dependence and the final state spectrum.Using the Csorgo-Nagy-Csanad(CNC)exact solutions and the Buda-Lund model,we estimate the initial thermodynamic quantities of this hot medium.Comparing the Bjorken model with our modified energy density estimation model,the volume-element's effect and the longitudinal accelerated flow of the medium is taken into account.It was found that if there is a longitudinal acceleration effect in medium expansion,the initial energy density es-timation by STAR/PHENIX and ALICE using the Bjorken model requires a slight correction and needs to be compared with more accurate numerical fluid dynamics.Since the CNC model required a very special equation of state,in order to solve this problem,we apply a new approximation,and solve the conservation equations in new coor-dinate directly.We obtain a more general CKCJ analytical solution with the so-called"shock wave"model at the finite center rapidity region.Using this CKCJ analytical solution,we present the final state spectrum of the nuclear-nuclear/nucleus-nucleus collision at the RHIC and LHC energy region.It is also proofed that the CNC analytical solution is a special case of the CKCJ analytical solution.Based on the CKCJ perfect fluid solutions,we solved the relativistic viscous fluid dy-namics equation with Navier-Stokes approximation.A new perturbation solution and the so-called CCNU-Budapest model were obtained.Studying the nature of this perturbation solution,we find that when there are both longitudinal acceleration effects and viscous ef-fects in the medium,the thermodynamic evolution of the medium is affected by these two opposite effects(accelerated effect accelerates evolution,viscous effect slows down the evo-lution).The effects of viscous and the effects of longitudinal accelerated flow are ultimately different in the final yield distribution.Using this perturbative solution,we derive the trans-verse momentum spectrum,the rapidity spectrum and the pseudo-rapidity spectrum of the charged particles.Using this CCNU-Budapest model,the Cu+Cu,Au+Au,Pb+Pb,Xe+Xe collision experiment data of RHIC and LHC were successfully described.A simple prophetic model for the longitudinal effect is presented,too.At the same time,since the first-order viscous surrounding solution is only a long-range effective theory,we also give a numerical solution with second-order viscous(Israel-Stewart)as a comparison.Based on the above published works,we also present some new results in Chapter 5,which are the viscous Hubble-type fluid solutions,the Mach cone caused by the propagation of fast parton in the medium,as well as theoretical analysis and solutions of chiral magnetic hydrodynamics.The last part of this article is the brief summary and outlook.