Young–Laplace capillarity (Δp = γ∇·n̂) · Cohesive 3D smooth-SDF liquid metal bodies minimize surface area across high-curvature meniscus bridges while conserving total volume.

Helmholtz vorticity transport (∇·u = 0, ω = ∇×u) · Velocity vectors deflect tangentially around the impermeable sphere (u·n̂ = 0) and shed alternating Kármán vortices in the downstream wake.

d'Alembert wave equation (∂²u/∂t² = c²∇²u) · Coupled 3D phase-space oscillators propagate energy without mass drift, rendered with thin-film Fresnel dielectric interference.