Manuscript Em03-D@1 · Em03-D-v1.tex · assumption · 450d878a

Model specification: Local interaction and bounded probe effect

Bridge B: one compact local scalar coupling › Probe solution and future processing test · lines 1008–1037

Em03-D@1#spec:local, Em03-D@1#eq:localaction, Em03-D@1#eq:probeeffect

Let

ρ = - F, λ = ϵ ρ, ϵ > 0.

The interaction is

S_{int} = - ϵ \int_{E} ρ (x) ϕ (x) ψ (x) d vol_{g} .

The coupled equations are

T_{ϵ} (ϕ ψ) = 0, T_{ϵ} = (P ϵ ρ ϵ ρ P) .

The postinteraction probe effect is

O_{ϵ} = \frac{1}{2} (I + Re W_{ψ} (g / ϵ)) .

The complementary outcome is $I - O_{ϵ}$ . Both outcomes are retained.

Displayed formulas in this passage

Em03-D@1#eq:localaction · line 1015
$S_{int} = - ϵ \int_{E} ρ (x) ϕ (x) ψ (x) d vol_{g} .$
Em03-D@1#eq:probeeffect · line 1030
$O_{ϵ} = \frac{1}{2} (I + Re W_{ψ} (g / ϵ)) .$
unlabeled · line 1011
$ρ = - F, λ = ϵ ρ, ϵ > 0.$
unlabeled · line 1022
$T_{ϵ} (ϕ ψ) = 0, T_{ϵ} = (P ϵ ρ ϵ ρ P) .$