207 Appendix D: Formation Time and Brick Estimates The full solution to Eq. (D.27) is One might reasonably wonder the consequences of including Bjorken expansion on our estimate of R$_{AA}$ from D.2.1. Defining D.2.3 Bjorken Expanding Medium v$_{f}$ = 1+ v$_{i}$ 1 − $_{v$_{i}$}$e − 2 ∫ µdx − 1 1+ v$_{i}$ 1 − $_{v$_{i}$}$e − 2 ∫ µdx + 1 . (D.29) ν = n π √ λ 2 M , (D.30) R$_{AA}$ ≃ ∫ L 0 dℓ L e − ν ∫ L ℓ + τ 0 dℓ $^{′}$T $^{2}$( ℓ $^{′}$) (D.31) = ∫ L − τ$_{0}$ 0 dℓ L e − ν ∫ L ℓ + τ $_{0}$( κ ℓ ′ − $_{ℓ}$) 2 / 3 + τ$_{0}$ L , (D.32) κ = dN$_{g}$/dy A$_{T}$ π 2 ζ (3)(16 + 9 N$_{f}$ ) . (D.33) Eq. (D.20) becomes for a uniform brick of SYM plasma where Eq. (C.9) gives The integral in the exponential of Eq. (D.31) is ∫ L ℓ + τ$_{0}$ ( κ ℓ ′ − ℓ$^{)}$$^{2}$$^{/}$$^{3}$ = 3 κ 2 / 3 $^{[}$( L − ℓ ) 1 / 3 − τ 1 / 3 0 $^{]}$. (D.34)