Introduction to Relativistic Hydrodynamics

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Heavy ion collisions Elliptic flow b ◮ initial geometric anisotropy gets transformed to anisotropies in particle momenta spectrum ◮ expanding system develops flow pattern ◮ azimuthal distribution of emitted particles with respect to reaction plane dN dpT dφdy = ◮ elliptic flow v2 sensitive to viscous effects November 22nd, 2012 | TUD - IKP | D. Nowakowski | 32 vn(pT ) cos nφ n y x
Heavy ion collisions Bjorken model: Elliptic flow ◮ Euler equation for vx ∂tvx = − 1 ∂P e + P ∂x ∂ ln s = −c2 s ∂x ◮ assume gaussian entropy profile from the collision s(x, y) = s0 exp − 1 2 ◮ solution of Euler equation 2 σy x 2 + σ2 2 x y σ2 xσ 2 y vx(t) = c2 s σ2 tx + vx,0, vy(t) = x c2 s σ2 ty + vy,0 y ◮ non-central collision (σx < σy) implies |vx| > |vy| ◮ anisotropy in particle spectrum → details next week November 22nd, 2012 | TUD - IKP | D. Nowakowski | 33
Page 1 and 2: Introduction to Relativistic Hydrod
Page 3 and 4: Heavy ion collisions A very naive p
Page 5 and 6: Relativistic hydrodynamics Introduc
Page 7 and 8: Relativistic hydrodynamics Basic eq
Page 9 and 10: Relativistic hydrodynamics Basic eq
Page 11 and 12: Relativistic hydrodynamics Overview
Page 13 and 14: Relativistic ideal hydrodynamics Lo
Page 15 and 16: Relativistic viscous hydrodynamics
Page 17 and 18: Relativistic viscous hydrodynamics
Page 19 and 20: Relativistic hydrodynamics Equation
Page 21 and 22: Heavy ion collisions November 22nd,
Page 23 and 24: Heavy ion collisions Schematic time
Page 25 and 26: Heavy ion collisions Initial condit
Page 27 and 28: Heavy ion collisions Bjorken model
Page 33: Heavy ion collisions Bjorken model:
Page 37 and 38: Heavy ion collision and the Bjorken
Page 39 and 40: Outlook “... it is by no means cl

Introduction to Relativistic Hydrodynamics

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