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Viscous hydrodynamics and Transport Models

Viscous hydrodynamics and Transport Models. Azwinndini Muronga 1,2 1 Centre for Theoretical Physics and Astrophysics Department of Physics, University of Cape Town, South Africa 2 UCT-CERN Research Centre Department of Physics, University of Cape Town, South Africa

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Viscous hydrodynamics and Transport Models

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  1. Viscous hydrodynamics and Transport Models Azwinndini Muronga1,2 1Centre for Theoretical Physics and Astrophysics Department of Physics, University of Cape Town, South Africa 2UCT-CERN Research Centre Department of Physics, University of Cape Town, South Africa Workshop on “Viscous Hydrodynamics and Transport Models in heavy Ion Collisions” May 2, 2008 : BNL, Long Island, NY, USA

  2. It concerns conservation of net charges, energy-momentum and balance of fluxes. The primary state quantities such as number current, energy-momentum-tensor and entropy current differ from the ideal fluid by additional dissipative fluxes It concerns non-linear, coupled partial differential equations Formulation is relativistic and this add another complexity. The system of equations is still closed by the equation of state. In addition the balance of fluxes is controlled by the transport coefficients. Together with the equation of state they determine the relaxation times/lengths Analytic solutions are rare. Numerical solution poses a challenge. Initial conditions are more interesting. DFD open s a window that one can use to connect the macroscopic and microscopic dynamics of a system under consideration: in our case the system is the hot and dense matter produced in relativistic nuclear collisions. The statement: transport coefficients are as important as the equation of state can no longer be overemphasized. Dissipative Relativistic Fluid DynamicsSummary and Conclusions Refers to: A. Muronga (2007) I&II

  3. Non-equilibrium fluid dynamics from kinetic theory The equations for the first three moments of distribution function where

  4. Non-equilibrium fluid dynamics from kinetic theory

  5. Thermodynamic integrals for relaxation/coupling coefficients See A. Muronga (2007) II

  6. 14-Fields theory of non-equilibrium fluid dynamics The conservation of net charge and of energy-momentum and the balance of fluxes 2nd order entropy 4-current

  7. 2nd order relaxation/coupling coefficients

  8. Entropy production and transport coefficients

  9. Relaxation equations for dissipative fluxes Relaxation equations for the dissipative fluxes Transport and relaxation times/lengths

  10. Make the equations tractable See A. Muronga (2007) I Macroscopic dynamics where

  11. Make equations attractable Microscopic dynamics where

  12. Physical problems: People’s ideas Simple scaling solution: A. Muronga (2001/2002/2004)

  13. Ideal fluid vs non-ideal fluid Energy equation EoS and Transport coefficients Temperature evolution

  14. Time evolution of thermodynamic quantities A. Muronga (2002/2004)

  15. Transport coefficients and relaxation times A. Muronga (2004)

  16. Physical problems Boost invariance + symmetric transverse: A. Muronga + D. H. Rischke (2004)

  17. Physical problems: People’s realizations (2+1) viscous hydro: Formulations U. Heinz, H. Song and A.K. Chaudhuri (2006); A. Muronga (2007) Applications A.K. Chaudhuri (2007) P. Romatchke and U. Romatschke (2007); H. Song and U. Heinz (2008); K. Dusling and D. Teaney (2008); P. Huovinen and D. Molnar (2008); See the talks by P. Huovinen, P. Romatschke, H. Song and K. Dusling.

  18. Physical problems: People’s realizations (2+1) viscous hydro: Formulations U. Heinz, H. Song and A.K. Chaudhuri (2006); A. Muronga (2007) Applications A.K. Chaudhuri (2007) P. Romatchke and U. Romatschke (2007); H. Song and U. Heinz (2008); K. Dusling and D. Teaney (2008); P. Huovinen and D. Molnar (2008); See the talks by P. Huovinen, P. Romatschke, H. Song and K. Dusling.

  19. Viscous hydro vs transport models Bin Zhang et. al.

  20. Viscous hydro vs transport models

  21. Viscous hydro vs transport models P. Huovinen and D. Molnar

  22. Viscous hydro vs transport models Slide from J.Y. Ollitrault’s talk

  23. Viscous hydro vs transport models Extracting transport coefficients from transport

  24. Viscous hydro vs transport models Extracting transport coefficients from transport A. El, A. Muronga (2007)

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