Viscous hydrodynamics and Transport Models

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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
• Workshop on Viscous Hydrodynamics and Transport
  Models in heavy Ion Collisions
• May 2, 2008 BNL, Long Island, NY, USA

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Dissipative Relativistic Fluid DynamicsSummary
and Conclusions

• 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.

Refers to A. Muronga (2007) III
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Non-equilibrium fluid dynamics from kinetic theory

• The equations for the first three moments of
  distribution function
• where

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Non-equilibrium fluid dynamics from kinetic theory
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Thermodynamic integrals for relaxation/coupling
coefficients

• See A. Muronga (2007) II

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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

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2nd order relaxation/coupling coefficients
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Entropy production and transport coefficients
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Relaxation equations for dissipative fluxes

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

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Make the equations tractable

• Macroscopic dynamics
• where

See A. Muronga (2007) I
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Make equations attractable

• Microscopic dynamics
• where

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Physical problems Peoples ideas

• Simple scaling solution A. Muronga
  (2001/2002/2004)

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Ideal fluid vs non-ideal fluid

• Energy equation
• EoS and Transport coefficients
• Temperature evolution

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Time evolution of thermodynamic quantities

• A. Muronga (2002/2004)

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Transport coefficients and relaxation times

• A. Muronga (2004)

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Physical problems

• Boost invariance symmetric transverse A.
  Muronga D. H. Rischke (2004)

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Physical problems Peoples realizations

• (21) 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.

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Physical problems Peoples realizations

• (21) 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.

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Viscous hydro vs transport models

• Bin Zhang et. al.

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Viscous hydro vs transport models
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Viscous hydro vs transport models

• P. Huovinen and D. Molnar

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Viscous hydro vs transport models

• Slide from J.Y. Ollitraults talk

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Viscous hydro vs transport models

• Extracting transport coefficients from transport

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Viscous hydro vs transport models

• Extracting transport coefficients from transport
• A. El, A. Muronga (2007)