# Viscosity at RHIC Scott Pratt & Kerstin Paech

Viscosity at RHIC Scott Pratt & Kerstin Paech Michigan State University QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. Scott Pratt OUTLINE What is viscosity? Sources of viscosity Bulk viscosity near Tc Scott Pratt

Definition of Viscosity After boosting and rotating, T ( + Txx )vx ( + T )v Txx xx x = 0 ( + Tyy)vy 0

( + Tzz )vz ( + Tyy)vy ( + Tzz )vz 0 0 Tyy 0 0 Txx =P Bv2x vx (2 / 3)v 1 tvx = xTxx + Txx

P, B and are functions of Scott Pratt Tzz Definition of Viscosity Txx = P Bv2x vx (2 / 3)v 1 tvx = xTxx + Txx scosity = change in "pressure" to due expansion

lk viscosity = change due to isotropic expansion ear viscosity = change due to anisotropic expansion Scott Pratt Sources of Viscosity 1. If zvz >xvx , 2 pz > 2 px =(4 P / 3)t collision

Vanishes if mean free path -> 0 Scott Pratt Sources of Viscosity 2. If Rinteraction > 0 , P BP 2 Rint coll 2 Rint

coll Important at early times Scott Pratt v2 from Boltzmann Calculation Finiterange effects dampen v2 Scott Pratt S. Cheng, S. P., P. Csizmadia, Y. Nara, D. Molnar, M. Gyulassy, S.E. Vance & B. Zhang, PRC 65, 024901 (2002)

Sources of Viscosity 3. Longitudinal Fields Txx =Tyy = Tzz = Hyper-shear at very early times Increases transverse acceleration Scott Pratt Sources of Viscosity 4. Longitudinal Fields, r =E / 2, E = Ez

Txx = Tyy = 2 Tzz = Hyper-shear for t< 0.5 fm/c Increases transverse acceleration Scott Pratt Sources of Viscosity 5. Chemical non-equilibrium offset from equilibrium dN =(N Nquil) / t cm

dt Nquil N =t cm t (nquil / s) 2 P B= t cm s n s Using some thermodynamics Large when T falls or when m rises Scott Pratt

Sources of Viscosity 6. Mean fields 2 2 + + m ( equil ) = R(t) 2 t t Langevin "force" 2 d x x

m 2 + + k(x xquil) = R (t) t dt k x = x&quil s = 2 &equil m s can blow up at phase transition! Scott Pratt 2 K.Paech & A.Dumitru, PLB 623, 200 (2005) l 2

2 2 2 2 H = (s fp + m p / l ) qs + qurks(T , m = s ) 4 Example: Linear Sigma Model 1st order when g>3.55 Scott Pratt l 4

2 H = s s + s + qurks(T , m = s ) 4 Example: Linear Sigma Model 1st order when g > 3.5549 Scott Pratt Example: Linear Sigma

Model For g=3.4, Txx -> 0 Scott Pratt How might this affect dynamics? P Txx r "traffic jam" flash-like emission Scott Pratt

Rando m Lesso ns Numerous sources of viscosity Finite collision time (shear) Finite interaction range (shear & bulk) Longitudinal fields (shear) Chemical non-equilibrium (bulk) Non-equilibrium fields (bulk) Shear viscosity important at early times Affects elliptic flow Bulk viscosity important near Tc Affects dynamics ?? Alternatively, effects can be included throug

Explicit chemical evolution Explicit evolution of fields K.Paech & A.Dumitru, PLB 623, 200 (2005) Scott Pratt Support your local theorist!! http://www.phy.duke.edu/~muller/RTI_Complete.pdf Scott Pratt

## Recently Viewed Presentations

• Root Meaning Examples . vinc. Convince, evince, invincible, vincible. Conquer, defeat
• Romanticism: The name given to those schools of thought that value feeling and intuition over reason. Rationalism: The belief that human beings can arrive at truth by using reason, rather than by relying on the authority of the past, on...
• Acoustic Telemetry: Adult Spring-Run Chinook Salmon on The Lower Yuba River. ... Vemco V13 transmitters via esophageal/gastric insertion. Random repeat intervals of 30-90 sec. Methods. ... The area between DPD and Hwy 20 was most likely used largely as a...
• Artistas Literatura Menotti de Picchia Mario de Andrade Oswald de Andrade Manuel Bandeira Cassiano Ricardo Pintura Anita Malfatti Tarsila do Amaral Emiliano Di Cavalcanti Musica Guiomar Novais e Heitor Villa-Lobos Escultura Victor Brecheret Ocaso do Modernismo Base Política e Filosófica...
• Yasir and Navdeep used to go to Seven Kings School in Essex and were Young Ambassadors for Send My Friend to School in 2011. During this time, Yasir and Navdeep visited education projects in Guatemala, met leading politicians, and brought...
• Three (3) parts of the ear: Pinna (outer), Tympanic cavity (middle), Cochlea ((inner) From inconvenience to a complete loss of hearing. ... For each employee exposed at or above 8-hr TWA of 85 decibels . Employees shall be notified 14...
• 12.5 - Kingdoms of Southeast Asia & Korea Geography of SE Asia Two Parts: 1) Indochina - borders China & India 2) Islands - Sumatra, Borneo, Java, etc. Warm, Humid = Monsoon Winds = rain Rivers & valleys intersected by...
• Reduce, Reuse, Recycle Reduce the Spread of Colds & Flu Frequently Wash Hands - 20 Seconds Before Eating, After Handling Body Secretions, & Before Rubbing Eyes or Touching the Face Cough or Sneeze into Your Sleeve, at the Bend of...