Public statement.
def
AVenhance.Ingredients.Amnr
{β : ℝ}
(I : Ingredients β)
{Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ}
(hΦ : IsStreamSeq I Φ)
(m : ℕ)
(κm : ℝ)
(n : ℕ)
(Tm1 : ℝ → Homogenization.Vec 2 → ℝ)
:
The 3-tensors 𝐀_{m,n,r}^{ijk} of e.A.mnr.def (4188-4200), Tm1 = T_{m-1}, κm = κ_m:
A_{n,0}^{ijk} = -L_{n}(t) ∑_l ξ̂_{m,l} F_l^{ji} ∑_p F_l^{kp} ∂_pT, where
F_l = (∇X_{m-1,l})∘X⁻¹_{m-1,l} (flowGrad); the left factor F_l^{ji} is the left Jacobian
that replaces the source's δ_{ij} (see doc/errata.pdf),
A_{r+1}^{ijk} = (∂_t + b_{m-1}·∇) A_r^{ijk} - ∂_ℓ b^i_{m-1} A_r^{ℓjk}.
SIGN OF THE LAST TERM: the source prints +; the minus sign is the one for which
(∂_t + b·∇) ∂_i A^{ijk} = ∂_i A_{r+1}^{ijk} (checked symbolically, ∇·b = 0).
Equations
- One or more equations did not get rendered due to their size.