# Momentum anisotropies

Kevin Dusling, 05/06/2008

The figures below compare results for the total momentum anisotropy epsilon'_p (here denoted simply as epsilon_p without prime) as a function of proper time for three independent groups running a viscous hydrodynamic code in 2+1 dimensions.

KD+DT = Kevin Dusling and Derek Teaney
HS+UH = Huichao Song + Ulrich Heinz (VISH2+1)
R = Paul + Ulrike Romatschke

I-S = Israel-Stewart
O-G = Oettinger-Grmela

Note: the comparison in this post was done for e_0 = 17 GeV/fm**3, not for e_0 = 30 GeV/fm**3 as will be the case for all future code verification plots.

Comparing R (full I-S) vs. HS+UH (simplified I-S & full I-S):

For HS+UH and R data tables to generate these curves can be downloaded from Song-Romatschke-1107.tar

Kevin Dusling, 7/1/2008 Momentum Anisotropy
Momentum anisotropy as a function of proper time. Includes comparison of the codes by Dusling/Teaney, Song/Heinz and Romatschke.

The raw data for Dusling/Teaney is here: Momentum Anisotropy Data

Huichao Song, 05/17/2008

Time evolution of momentum anisotropy in ideal and viscous hydro (HS+UH, using VISH2+1 with full I-S eqns.)
(total momentum anisotropy vs. ideal fluid part only)

The figure above was updated on 08/04/2008 by H.S. to include an comparison between different full I-S eqn:

• full I-S eqn-(R&R): ${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})+{\frac {1}{2}}\pi ^{mn}\left(5D(\ln T)-\partial _{k}u^{k}\right)}$
• full I-S eqn-(S&H):${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})-{\frac {1}{2}}\pi ^{mn}{\frac {\eta T}{\tau _{\pi }}}d_{k}\left({\frac {\tau _{\pi }}{\eta T}}u^{k}\right)}$

Other formats and data tables for the figure can be downloaded here: Au-global-0508.tar